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Auteur : Grafiati
Publié le 11 mars 2023

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1

Bortoluzzi, D., L. Baglivo, M. Benedetti, F. Biral, P. Bosetti, A. Cavalleri, M. Da Lio et al. « LISA Pathfinder test mass injection in geodesic motion : status of the on-ground testing ». Classical and Quantum Gravity 26, no 9 (20 avril 2009) : 094011. http://dx.doi.org/10.1088/0264-9381/26/9/094011.

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2

Bortoluzzi, D., M. Benedetti, L. Baglivo, M. De Cecco et S. Vitale. « Measurement of momentum transfer due to adhesive forces : On-ground testing of in-space body injection into geodesic motion ». Review of Scientific Instruments 82, no 12 (décembre 2011) : 125107. http://dx.doi.org/10.1063/1.3658479.

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3

Townsend, Paul K., et Mattias N. R. Wohlfarth. « Cosmology as geodesic motion ». Classical and Quantum Gravity 21, no 23 (10 novembre 2004) : 5375–96. http://dx.doi.org/10.1088/0264-9381/21/23/006.

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4

Recio-Mitter, David. « Geodesic complexity of motion planning ». Journal of Applied and Computational Topology 5, no 1 (12 janvier 2021) : 141–78. http://dx.doi.org/10.1007/s41468-020-00064-w.

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5

Mannheim, Philip D. « Dynamical mass and geodesic motion ». General Relativity and Gravitation 25, no 7 (juillet 1993) : 697–715. http://dx.doi.org/10.1007/bf00756938.

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6

Jun, Wang, et Wang Yong-Jiu. « Geodesic Motion in Spinning Spaces ». Communications in Theoretical Physics 46, no 6 (décembre 2006) : 995–1000. http://dx.doi.org/10.1088/0253-6102/46/6/008.

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7

Camci, Ugur. « Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes ». International Journal of Modern Physics : Conference Series 38 (janvier 2015) : 1560072. http://dx.doi.org/10.1142/s2010194515600721.

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In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for [Formula: see text] of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.
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8

Heck, T., et M. Sorg. « Geodesic Motion in Trivializable Gauge Fields ». Zeitschrift für Naturforschung A 46, no 8 (1 août 1991) : 655–68. http://dx.doi.org/10.1515/zna-1991-0802.

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AbstractThe geodesic problem is studied for a Riemannian structure, which is generated by an SO(4) trivializable gauge field. The topological and elliptic geometric defects of such a structure act as attractors for the geodesic curves
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9

Ramos, A., C. Arias, R. Avalos et E. Contreras. « Geodesic motion around hairy black holes ». Annals of Physics 431 (août 2021) : 168557. http://dx.doi.org/10.1016/j.aop.2021.168557.

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10

Gupta, Kumar S., et Siddhartha Sen. « Black hole decay as geodesic motion ». Physics Letters B 574, no 1-2 (novembre 2003) : 93–97. http://dx.doi.org/10.1016/j.physletb.2003.09.024.

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11

Thirukkanesh, S., et S. D. Maharaj. « Radiating relativistic matter in geodesic motion ». Journal of Mathematical Physics 50, no 2 (février 2009) : 022502. http://dx.doi.org/10.1063/1.3076901.

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12

YOUM, DONAM. « NULL GEODESICS IN BRANE WORLD UNIVERSE ». Modern Physics Letters A 16, no 37 (7 décembre 2001) : 2371–80. http://dx.doi.org/10.1142/s0217732301005813.

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We study null bulk geodesic motion in the brane world cosmology in the RS2 scenario and in the static universe in the bulk of the charged topological AdS black hole. We obtain equations describing the null bulk geodesic motion as observed in one lower dimension. We find that the null geodesic motion in the bulk of the brane world cosmology in the RS2 scenario is observed to be under the additional influence of extra non-gravitational force by the observer on the three-brane, if the brane universe does not possess the Z2 symmetry. As for the null geodesic motion in the static universe in the bulk of the charged AdS black hole, the extra force is realized even when the brane universe has the Z2 symmetry.
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13

PONCE DE LEON, J. « THE PRINCIPLE OF LEAST ACTION FOR TEST PARTICLES IN A FOUR-DIMENSIONAL SPACE–TIME EMBEDDED IN 5D ». Modern Physics Letters A 23, no 04 (10 février 2008) : 249–59. http://dx.doi.org/10.1142/s0217732308026376.

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It is well known that, in the five-dimensional scenario of braneworld and space–time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional reduction of the geodesic equation in 5D, without any reference to the test particle whatsoever. In this work we obtain the equation of motion in 4D directly from the principle of least action. So our main thrust is not the geometry but the particle observed in 4D. A clear physical picture emerges from our work. Specifically, that the deviation from the geodesic motion in 4D is due to the variation of the rest mass of a particle, which is induced by the scalar field in the 5D metric and the explicit dependence of the space–time metric on the extra coordinate. Thus, the principle of least action not only leads to the correct equations of motion, but also provides a concrete physical meaning for a number of algebraic quantities appearing in the geometrical reduction of the geodesic equation.
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14

Berman, Sigal, Dario G. Liebermann et Joseph McIntyre. « Constrained motion control on a hemispherical surface : path planning ». Journal of Neurophysiology 111, no 5 (1 mars 2014) : 954–68. http://dx.doi.org/10.1152/jn.00132.2013.

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Surface-constrained motion, i.e., motion constraint by a rigid surface, is commonly found in daily activities. The current work investigates the choice of hand paths constrained to a concave hemispherical surface. To gain insight regarding paths and their relationship with task dynamics, we simulated various control policies. The simulations demonstrated that following a geodesic path (the shortest path between 2 points on a sphere) is advantageous not only in terms of path length but also in terms of motor planning and sensitivity to motor command errors. These stem from the fact that the applied forces lie in a single plane (that of the geodesic path). To test whether human subjects indeed follow the geodesic, and to see how such motion compares to other paths, we recorded movements in a virtual haptic-visual environment from 11 healthy subjects. The task comprised point-to-point motion between targets at two elevations (30° and 60°). Three typical choices of paths were observed from a frontal plane projection of the paths: circular arcs, straight lines, and arcs close to the geodesic path for each elevation. Based on the measured hand paths, we applied k-means blind separation to divide the subjects into three groups and compared performance indicators. The analysis confirmed that subjects who followed paths closest to the geodesic produced faster and smoother movements compared with the others. The “better” performance reflects the dynamical advantages of following the geodesic path and may also reflect invariant features of control policies used to produce such a surface-constrained motion.
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15

Chemissany, Wissam, André Ploegh et Thomas Van Riet. « Scaling cosmologies, geodesic motion and pseudo-SUSY ». Classical and Quantum Gravity 24, no 18 (3 septembre 2007) : 4679–89. http://dx.doi.org/10.1088/0264-9381/24/18/009.

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16

Courty, Jean-Michel, et Serge Reynaud. « Quantum fluctuations for drag-free geodesic motion ». Journal of Optics B : Quantum and Semiclassical Optics 2, no 2 (1 avril 2000) : 90–93. http://dx.doi.org/10.1088/1464-4266/2/2/304.

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17

Visinescu, Mihai. « Geodesic motion in Taub--NUT spinning space ». Classical and Quantum Gravity 11, no 7 (1 juillet 1994) : 1867–79. http://dx.doi.org/10.1088/0264-9381/11/7/021.

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18

Pereira, P. R. C. T., N. O. Santos et A. Z. Wang. « Geodesic motion and confinement in Lanczos spacetime ». Classical and Quantum Gravity 13, no 6 (1 juin 1996) : 1641–54. http://dx.doi.org/10.1088/0264-9381/13/6/026.

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19

Hojman, Sergio, Luis Nuñez, Alberto Patiño et Hector Rago. « Symmetries and conserved quantities in geodesic motion ». Journal of Mathematical Physics 27, no 1 (janvier 1986) : 281–86. http://dx.doi.org/10.1063/1.527375.

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20

Al Majid, A., et R. Dufour. « Damping in High Transient Motion ». Journal of Vibration and Acoustics 125, no 2 (1 avril 2003) : 223–27. http://dx.doi.org/10.1115/1.1547702.

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An original method for evaluating the dissipative effect in SDOF systems due to the transient phenomenon was presented in a previous article. This method based on the use of an additional dimension, and the general relativity concept was validated experimentally. However, the function of the forcing frequency required to establish the metric of the space was identified using an experimental transfer function. In the present paper the main objective is to solve the geodesic equations in order to avoid the experimental identification of the function contained in the metric. The variational problem of the metric of Riemannian space gives three geodesic equations for the SDOF system studied. Solving these equations gives in particular the transient forced response which, when compared with experimental results, permits validating the proposed method and therefore proving that the transient motion bends the space-time.
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21

TURAKULOV, Z. YA, et A. T. MUMINOV. « MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME III : DEVELOPMENT OF TECHNIQUES OF CALCULATIONS ». Modern Physics Letters A 21, no 26 (30 août 2006) : 1981–90. http://dx.doi.org/10.1142/s0217732306021293.

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The studies of influence of spin on a photon's motion in a Schwarzschild spacetime is continued. In the previous paper13the first-order correction to the geodesic motion is found for the first half of the photon world line. The system of equations for the first-order correction to the geodesic motion is reduced to a non-uniform linear ordinary differential equation. The equation obtained is solved by the standard method of integration of the Green function.
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22

Szydłowski, Marek. « On Invariant Qualitative Chaos in Multi-Black-Hole Spacetimes ». International Journal of Modern Physics D 06, no 06 (décembre 1997) : 741–70. http://dx.doi.org/10.1142/s0218271897000443.

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It is analytically shown when chaos exists in the behavior of null and timelike geodesics in the general case of geodesic motion in static and diagonal fields of general relativity. We demonstrate the effectiveness of our method of investigating chaos in the behavior of geodesic motion in the multi-black-hole spacetimes. An optical model of chaotic behavior of geodesics in spacetimes with cylindrical symmetry is presented. The Lyapunov characteristic time is defined and estimated for geodesic motion of a test particle in the external fields of general relativity. We find that its value is positive in some compact regions of the configuration space. This means that the trajectories have the property of local instability which implies the sensitive dependence on initial conditions.
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23

Bormotova, Irina, Elena Kopteva et Zdeněk Stuchlík. « Geodesic Structure of the Accelerated Stephani Universe ». Symmetry 13, no 6 (3 juin 2021) : 1001. http://dx.doi.org/10.3390/sym13061001.

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For the spherically symmetric Stephani cosmological model with an accelerated expansion, we investigate the main scenarios of the test particle and photon motion. We show that a comoving observer sees an appropriate picture. In the case of purely radial motion, the radial velocity decreases slightly with time due to the universe expansion. Both particles and photons spiral out of the center when the radial coordinate is constant. In the case of the motion with arbitrary initial velocity, the observable radial distance to the test particle can increase under negative observable radial velocity.
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24

Grunau, Saskia, et Jutta Kunz. « Hyperelliptic Functions and Motion in General Relativity ». Mathematics 10, no 12 (7 juin 2022) : 1958. http://dx.doi.org/10.3390/math10121958.

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Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g=2: higher dimensional Schwarzschild black holes, rotating dyonic U(1)2 black holes, and black rings.
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25

Sahu, Pradip Kumar, et Bibhuti Bhusan Biswal. « Geodesic Approach for an Efficient Trajectory Planning of Mobile Robot Manipulators ». International Journal of Mathematical, Engineering and Management Sciences 4, no 5 (1 octobre 2019) : 1196–207. http://dx.doi.org/10.33889/ijmems.2019.4.5-094.

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In this paper, the geodesic approach has been employed for an effective, optimal, accurate and smooth trajectory planning of a mobile robot manipulator mechanism. Generally, geodesic can be described as the shortest curvature between two loci on a Riemannian manifold. In order to attain the planned end-effector motion, Riemannian metrics has been consigned to the forward kinematics of mobile robot wheel as well as the mobile robot manipulator workspace. The rotational angles of wheel and joint kinematic parameters are chosen as local coordinates of spaces to represent Cartesian trajectories for mobile wheel rotation trajectories and joint trajectories respectively. The geodesic equalities for a given set of boundary conditions are evaluated for the chosen Riemannian metrics and the computational results of the geodesic equations have been shown. So as to verify and validate the efficiency of the chosen geodesic scheme, the method has been implemented for the motion planning and optimization of a mobile robot with a simple 3R manipulator installed upon its platform.
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26

ROBERTS, MARK D. « THE STRING DEVIATION EQUATION ». Modern Physics Letters A 14, no 25 (20 août 1999) : 1739–51. http://dx.doi.org/10.1142/s021773239900184x.

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It is well known that the relative motion of many particles can be described by the geodesic deviation equation. Less well known is that the geodesic deviation equation can be derived from the second covariant variation of the point particle's action. Here it is shown that the second covariant variation of the string action leads to a string deviation equation. This equation is a candidate for describing the relative motion of many strings, and can be reduced to the geodesic deviation equation. Like the geodesic deviation equation, the string deviation equation can also be expressed in terms of momenta and projecta. It is also shown that a combined action exists, the first variation of which gives the deviation equations. The combined actions allow the deviation equations to be expressed solely in terms of the Riemann tensor, the coordinates and momenta. In particular geodesic deviation can be expressed as: [Formula: see text] and string deviation can be expressed as: [Formula: see text]
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27

Potashov, Ivan M., Julia V. Tchemarina et Alexander N. Tsirulev. « Geodesic motion near self-gravitating scalar field configurations ». Discrete and Continuous Models and Applied Computational Science 27, no 3 (15 décembre 2019) : 231–41. http://dx.doi.org/10.22363/2658-4670-2019-27-3-231-241.

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We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.
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28

Potashov, Ivan M., Julia V. Tchemarina et Alexander N. Tsirulev. « Geodesic motion near self-gravitating scalar field configurations ». Russian Family Doctor 27, no 3 (15 décembre 2019) : 231–41. http://dx.doi.org/10.17816/rfd10660.

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We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.
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29

Potashov, Ivan M., Julia V. Tchemarina et Alexander N. Tsirulev. « Geodesic motion near self-gravitating scalar field configurations ». Russian Family Doctor 27, no 3 (15 décembre 2019) : 231–41. http://dx.doi.org/10.17816/rfd10667.

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We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.
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30

CHEN, JUHUA, et YONGJIU WANG. « TIMELIKE GEODESIC MOTION IN HORAVA–LIFSHITZ SPACE–TIME ». International Journal of Modern Physics A 25, no 07 (20 mars 2010) : 1439–48. http://dx.doi.org/10.1142/s0217751x10048962.

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Recently a nonrelativistic renormalizable theory of gravitation has been proposed by P. Horava. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory is expected to flow to the relativistic value λ = 1, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. In this paper under allowing the lapse function to depend on the spatial coordinates xi as well as t, we obtain the spherically symmetric solutions. And then by analyzing the behavior of the effective potential for the particle, we investigate the timelike geodesic motion of particle in the Horava–Lifshitz space–time. We find that the nonradial particle falls from a finite distance to the center along the timelike geodesics when its energy is in an appropriate range. However, we find that it is complexity for radial particle along the timelike geodesics. There are three different cases due to the energy of radial particle: (i) when the energy of radial particle is higher than a critical value EC, the particle will fall directly from infinity to the singularity; (ii) when the energy of radial particle equals to the critical value EC, the particle orbit at r = rC is unstable, i.e. the particle will escape from r = rC to the infinity or to the singularity, depending on the initial conditions of the particle; (iii) when the energy of radial particle is in a proper range, the particle will rebound to the infinity or plunge to the singularity from a infinite distance, depending on the initial conditions of the particle.
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31

Baleanu, Dumitru. « Geodesic Motion on Extended Taub-NUT Spinning Space ». General Relativity and Gravitation 30, no 2 (février 1998) : 195–207. http://dx.doi.org/10.1023/a:1018840626704.

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32

Sonego, Sebastiano, et Hans Westman. « Particle detectors, geodesic motion and the equivalence principle ». Classical and Quantum Gravity 21, no 2 (5 décembre 2003) : 433–44. http://dx.doi.org/10.1088/0264-9381/21/2/008.

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33

Müller, Daniel. « Geodesic motion on closed spaces : Two numerical examples ». Physics Letters A 376, no 4 (janvier 2012) : 221–26. http://dx.doi.org/10.1016/j.physleta.2011.11.041.

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34

Holm, Christian. « Christoffel formula and geodesic motion in hyperspin manifolds ». International Journal of Theoretical Physics 25, no 11 (novembre 1986) : 1209–13. http://dx.doi.org/10.1007/bf00668691.

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35

Saaidi, K. « (Non-)geodesic motion in chameleon Brans Dicke model ». Astrophysics and Space Science 345, no 2 (27 mars 2013) : 431–37. http://dx.doi.org/10.1007/s10509-013-1407-4.

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36

Baleanu, D. « The geodesic motion in Kaluza-Klein spinning space ». Il Nuovo Cimento B Series 11 109, no 12 (décembre 1994) : 1303–15. http://dx.doi.org/10.1007/bf02722841.

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37

Alqahtani, L. S., et J. M. Speight. « Ricci magnetic geodesic motion of vortices and lumps ». Journal of Geometry and Physics 98 (décembre 2015) : 556–74. http://dx.doi.org/10.1016/j.geomphys.2015.07.008.

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38

Arutyunov, Gleb, Martin Heinze et Daniel Medina-Rincon. « Superintegrability of geodesic motion on the sausage model ». Journal of Physics A : Mathematical and Theoretical 50, no 24 (17 mai 2017) : 244002. http://dx.doi.org/10.1088/1751-8121/aa6e0c.

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39

Patino, Alberto. « Symmetries and constants of motion of geodesic equations ». Canadian Journal of Physics 67, no 5 (1 mai 1989) : 485–88. http://dx.doi.org/10.1139/p89-087.

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Results for the symmetries of equations and equivalent Lagrangians are applied to the problem of geodesic motion in Riemannian space–times. These results are compared with those calculated previously, and the construction of conserved quantities is achieved.
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40

Camci, U. « Symmetries of geodesic motion in Gödel-type spacetimes ». Journal of Cosmology and Astroparticle Physics 2014, no 07 (1 juillet 2014) : 002. http://dx.doi.org/10.1088/1475-7516/2014/07/002.

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41

Brill, D. R., et M. D. Matlin. « Geodesic motion in a Kaluza-Klein bubble spacetime ». Physical Review D 39, no 10 (15 mai 1989) : 3151–54. http://dx.doi.org/10.1103/physrevd.39.3151.

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42

Bezares, Miguel, Gonzalo Palomera, Daniel J. Pons et Enrique G. Reyes. « The Ehlers–Geroch theorem on geodesic motion in general relativity ». International Journal of Geometric Methods in Modern Physics 12, no 03 (27 février 2015) : 1550034. http://dx.doi.org/10.1142/s0219887815500346.

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We provide a detailed and rigorous proof of (a generalized version of) the Ehlers–Geroch theorem on geodesic motion in metric theories of gravity: we assume that (M, g) is a spacetime satisfying an averaged form of the dominant energy condition and some further technical assumptions indicated in the bulk of this paper. Then, a small body which is allowed to deform the original spacetime metric g moves, nonetheless, along a geodesic of (M, g).
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43

Sahu, Pradip Kumar. « Optimal Trajectory Planning of Industrial Robots using Geodesic ». IAES International Journal of Robotics and Automation (IJRA) 5, no 3 (1 septembre 2016) : 190. http://dx.doi.org/10.11591/ijra.v5i3.pp190-198.

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<p>This paper intends to propose an optimal trajectory planning technique using geodesic to achieve smooth and accurate trajectory for industrial robots. Geodesic is a distance minimizing curve between any two points on a Riemannian manifold. A Riemannian metric has been assigned to the workspace by combining its position and orientation space together in order to attain geodesic conditions for desired motion of the end-effector. Previously, trajectory has been planned by considering position and orientation separately. However, practically we cannot plan separately because the manipulator joints are interlinked. Here, trajectory is planned by combining position and orientation together. Cartesian trajectories are shown by joint trajectories in which joint variables are treated as local coordinates of position space and orientation space. Then, the obtained geodesic equations for the workspace are evaluated for initial conditions of trajectory and results are plotted. The effectiveness of the geodesic method validated through numerical computations considering a Kawasaki RS06L robot model. The simulation results confirm the accuracy, smoothness and the optimality of the end-effector motion. </p>
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44

SLANÝ, PETR, JIŘÍ KOVÁŘ et ZDENĚK STUCHLÍK. « RELATIVISTIC DYNAMICS WITH COSMOLOGICAL CONSTANT : CIRCULAR GEODESIC MOTION OF TEST PARTICLES ». International Journal of Modern Physics A 24, no 08n09 (10 avril 2009) : 1598–601. http://dx.doi.org/10.1142/s0217751x09045078.

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We present results of our recent studies concerning effects of Λ > 0 in astrophysically motivated problems. Here we summarize properties of circular geodesic motion of test particles in the equatorial plane of Kerr-de Sitter black-hole and naked-singularity spacetimes. Along with the standard analysis of geodesic equations of the ordinary geometry, we introduce alternative inertial forces formalism defined within the General Theory of Relativity in the framework of optical reference geometry.
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45

Holm, Darryl D., et Cesare Tronci. « Geodesic flows on semidirect-product Lie groups : geometry of singular measure-valued solutions ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 465, no 2102 (27 octobre 2008) : 457–76. http://dx.doi.org/10.1098/rspa.2008.0263.

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The EPDiff equation (or the dispersionless Camassa–Holm equation in one dimension) is a well-known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect product DiffⓈ , where denotes the space of scalar functions. This paper generalizes the second construction to consider geodesic motion on DiffⓈ , where denotes the space of scalar functions that take values on a certain Lie algebra (e.g. = ⊗ (3)). Measure-valued delta-like solutions are shown to be momentum maps possessing a dual pair structure, thereby extending previous results for the EPDiff equation. The collective Hamiltonians are shown to fit into the Kaluza–Klein theory of particles in a Yang–Mills field and these formulations are shown to apply also at the continuum partial differential equation level. In the continuum description, the Kaluza–Klein approach produces the Kelvin circulation theorem.
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Uniyal, Rashmi, Hemwati Nandan et K. D. Purohit. « Geodesic motion in a charged 2D stringy black hole spacetime ». Modern Physics Letters A 29, no 29 (21 septembre 2014) : 1450157. http://dx.doi.org/10.1142/s0217732314501570.

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We study the time-like geodesics and geodesic deviation for a two-dimensional (2D) stringy black hole (BH) spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of BH parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector. The results are also compared with an another 2D stringy BH spacetime.
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LACQUANITI, VALENTINO, et GIOVANNI MONTANI. « DYNAMICS OF MATTER IN A COMPACTIFIED KALUZA–KLEIN MODEL ». International Journal of Modern Physics D 18, no 06 (juin 2009) : 929–46. http://dx.doi.org/10.1142/s0218271809014844.

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A long-standing problem in Kaluza–Klein models is the description of matter dynamics. Within the 5D model, the dimensional reduction of the geodesic motion for a 5D free test particle formally restores electrodynamics, but the reduced 4D particle shows a charge–mass ratio that is upper-bounded, such that it cannot fit in with any kind of elementary particle. At the same time, from the quantum dynamics viewpoint, there is the problem of the generation of huge massive modes. We present a criticism against the 5D geodesic approach and face the hypothesis that in Kaluza–Klein space the geodesic motion does not deal with the real dynamics of the test particle. We propose a new approach: starting from the conservation equation for the 5D matter tensor, within the Papapetrou multipole expansion, we prove that the 5D dynamical equation differs from the 5D geodesic one. Our new equation provides right coupling terms without bounding and in such a scheme the tower of massive modes is removed.
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CAMCI, UGUR. « DIRAC ANALYSIS AND INTEGRABILITY OF GEODESIC EQUATIONS FOR CYLINDRICALLY SYMMETRIC SPACETIMES ». International Journal of Modern Physics D 12, no 08 (septembre 2003) : 1431–44. http://dx.doi.org/10.1142/s0218271803003621.

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Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.
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Blaga, Cristina, Paul Blaga et Tiberiu Harko. « Jacobi and Lyapunov Stability Analysis of Circular Geodesics around a Spherically Symmetric Dilaton Black Hole ». Symmetry 15, no 2 (24 janvier 2023) : 329. http://dx.doi.org/10.3390/sym15020329.

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We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potential of the geodesic motion. The Lyapunov stability analysis leads to the same results. Hence, we can conclude that, in the particular case of the geodesic motion on circular orbits in the Gibbons–Maeda–Garfinkle–Horowitz–Strominger, the Lyapunov and the Jacobi stability analysis gives equivalent results.
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HANAN, WILLIAM, et EUGEN RADU. « CHAOTIC MOTION IN MULTI-BLACK HOLE SPACETIMES AND HOLOGRAPHIC SCREENS ». Modern Physics Letters A 22, no 06 (28 février 2007) : 399–406. http://dx.doi.org/10.1142/s0217732307022815.

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We investigate the geodesic motion in D-dimensional Majumdar–Papapetrou multi-black hole spacetimes and find that the qualitative features of the D = 4 case are shared by the higher dimensional configurations. The motion of timelike and null particles is chaotic, the phase space being divided into basins of attraction which are separated by a fractal boundary, with a fractal dimension dB. The mapping of the geodesic trajectories on a screen placed in the asymptotic region is also investigated. We find that the fractal properties of the phase space induces a fractal structure on the holographic screen, with a fractal dimension dB - 1.
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