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Published: 9 March 2023

Last updated: 10 March 2023

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1

De Laurentis, Mariafelicia, and Antonio Jesus Lopez-Revelles. "Newtonian, Post-Newtonian and Parametrized Post-Newtonian limits of f(R, 𝒢) gravity." International Journal of Geometric Methods in Modern Physics 11, no. 10 (November 2014): 1450082. http://dx.doi.org/10.1142/s0219887814500820.

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We discuss in detail the weak field limit of f(R, 𝒢) gravity taking into account analytic functions of the Ricci scalar R and the Gauss–Bonnet invariant 𝒢. Specifically, we develop, in metric formalism, the Newtonian, Post-Newtonian (PN) and Parametrized Post-Newtonian (PPN) limits starting from general f(R, 𝒢) Lagrangian. The special cases of f(R) and f(𝒢) gravities are considered. In the case of the Newtonian limit of f(R, 𝒢) gravity, a general solution in terms of Green's functions is achieved.

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2

Nazari, Elham, and Mahmood Roshan. "Post-Newtonian Magnetohydrodynamics." Astrophysical Journal 868, no. 2 (November 27, 2018): 98. http://dx.doi.org/10.3847/1538-4357/aaeb25.

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3

Szekeres, Peter, and Tamath Rainsford. "Post-Newtonian Cosmology." General Relativity and Gravitation 32, no. 3 (March 2000): 479–90. http://dx.doi.org/10.1023/a:1001976317159.

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4

Pascual-Sánchez, J. F., A. San Miguel, and F. Vicente. "Relativistic versus Newtonian Frames." Positioning 04, no. 01 (2013): 109–14. http://dx.doi.org/10.4236/pos.2013.41011.

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5

Kremer, Gilberto M. "Post-Newtonian kinetic theory." Annals of Physics 426 (March 2021): 168400. http://dx.doi.org/10.1016/j.aop.2021.168400.

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6

Sanghai, Viraj A. A., and Timothy Clifton. "Parameterized post-Newtonian cosmology." Classical and Quantum Gravity 34, no. 6 (February 22, 2017): 065003. http://dx.doi.org/10.1088/1361-6382/aa5d75.

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7

Asfour, Amal. "Hogarth's Post-Newtonian Universe." Journal of the History of Ideas 60, no. 4 (1999): 693–716. http://dx.doi.org/10.1353/jhi.1999.0032.

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8

Nazari, Elham, Ali Kazemi, Mahmood Roshan, and Shahram Abbassi. "Post-Newtonian Jeans Analysis." Astrophysical Journal 839, no. 2 (April 17, 2017): 75. http://dx.doi.org/10.3847/1538-4357/aa68e0.

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9

Blanchet, L., T. Damour, and G. Schaefer. "Post-Newtonian hydrodynamics and post-Newtonian gravitational wave generation for numerical relativity." Monthly Notices of the Royal Astronomical Society 242, no. 3 (June 1, 1990): 289–305. http://dx.doi.org/10.1093/mnras/242.3.289.

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10

Szekeres, Peter. "Newtonian and Post-Newtonian Limits of Relativistic Cosmology." General Relativity and Gravitation 32, no. 6 (June 2000): 1025–39. http://dx.doi.org/10.1023/a:1001965526092.

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11

Hwang, Jai-chan, and Hyerim Noh. "Newtonian, Post-Newtonian and Relativistic Cosmological Perturbation Theory." Nuclear Physics B - Proceedings Supplements 246-247 (January 2014): 191–95. http://dx.doi.org/10.1016/j.nuclphysbps.2013.10.085.

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12

Gambi, J. M., M. C. Rodríguez-Teijeiro, and M. L. García del Pino. "Newtonian and post-Newtonian passive Geolocation by TDOA." Aerospace Science and Technology 51 (April 2016): 18–25. http://dx.doi.org/10.1016/j.ast.2016.01.016.

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13

Hwang, Jai-chan, and Hyerim Noh. "Magnetohydrodynamics with Post-Newtonian Corrections." Astrophysical Journal 899, no. 1 (August 12, 2020): 59. http://dx.doi.org/10.3847/1538-4357/ab9ff9.

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14

Asada, Hideki, and Toshifumi Futamase. "Chapter 2. Post-Newtonian Approximation." Progress of Theoretical Physics Supplement 128 (1997): 123–81. http://dx.doi.org/10.1143/ptps.128.123.

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15

Calura, Mirco, Pierluigi Fortini, and Enrico Montanari. "Post-Newtonian Lagrangian planetary equations." Physical Review D 56, no. 8 (October 15, 1997): 4782–88. http://dx.doi.org/10.1103/physrevd.56.4782.

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16

Lisbôa, A. F. Steklain, and P. S. Letelier. "The Post-Newtonian Hill Problem." Journal of Physics: Conference Series 490 (March 11, 2014): 012156. http://dx.doi.org/10.1088/1742-6596/490/1/012156.

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17

Krisher, Timothy P. "Parametrized post-Newtonian gravitational redshift." Physical Review D 48, no. 10 (November 15, 1993): 4639–44. http://dx.doi.org/10.1103/physrevd.48.4639.

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18

Aarseth, S. J. "Post-Newtonian N-body simulations." Monthly Notices of the Royal Astronomical Society 378, no. 1 (June 11, 2007): 285–92. http://dx.doi.org/10.1111/j.1365-2966.2007.11774.x.

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19

Roshan, Mahmood. "Parametrized post-Newtonian virial theorem." Classical and Quantum Gravity 29, no. 21 (September 13, 2012): 215001. http://dx.doi.org/10.1088/0264-9381/29/21/215001.

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20

Ayal, S., T. Piran, R. Oechslin, M. B. Davies, and S. Rosswog. "Post‐Newtonian Smoothed Particle Hydrodynamics." Astrophysical Journal 550, no. 2 (April 2001): 846–59. http://dx.doi.org/10.1086/319769.

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21

Jones, Christopher B. "Post-Newtonian paradigm or bust!" Futures 25, no. 10 (December 1993): 1085–88. http://dx.doi.org/10.1016/0016-3287(93)90079-9.

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22

Kremer, Gilberto Medeiros. "Post-Newtonian Jeans Equation for Stationary and Spherically Symmetrical Self-Gravitating Systems." Universe 8, no. 3 (March 13, 2022): 179. http://dx.doi.org/10.3390/universe8030179.

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The post-Newtonian Jeans equation for stationary self-gravitating systems is derived from the post-Newtonian Boltzmann equation in spherical coordinates. The Jeans equation is coupled with the three Poisson equations from the post-Newtonian theory. The Poisson equations are functions of the energy-momentum tensor components which are determined from the post-Newtonian Maxwell–Jüttner distribution function. As an application, the effect of a central massive black hole on the velocity dispersion profile of the host galaxy is investigated and the influence of the post-Newtonian corrections are determined.

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23

Dionysiou, D. D., E. N. Sarris, P. G. Tsikouras, and G. A. Papadopoulos. "Newtonian and post-newtonian tidal theory: Variable G and earthquakes." Earth, Moon, and Planets 60, no. 2 (February 1993): 127–40. http://dx.doi.org/10.1007/bf00614379.

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24

Nordtvedt, Ken. "Second post-Newtonian order renormalization of first post-Newtonian order gravity in the solar system." Astrophysical Journal 407 (April 1993): 758. http://dx.doi.org/10.1086/172558.

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25

Gonzalez-Espinoza, Manuel, Giovanni Otalora, Lucila Kraiselburd, and Susana Landau. "Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity." Journal of Cosmology and Astroparticle Physics 2022, no. 05 (May 1, 2022): 010. http://dx.doi.org/10.1088/1475-7516/2022/05/010.

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Abstract We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for F(T) gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.

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26

Kremer, Gilberto M. "Post-Newtonian non-equilibrium kinetic theory." Annals of Physics 441 (June 2022): 168865. http://dx.doi.org/10.1016/j.aop.2022.168865.

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27

Avilez-Lopez, A., A. Padilla, Paul M. Saffin, and C. Skordis. "The Parametrized Post-Newtonian-Vainshteinian formalism." Journal of Cosmology and Astroparticle Physics 2015, no. 06 (June 25, 2015): 044. http://dx.doi.org/10.1088/1475-7516/2015/06/044.

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28

Kazemi, Ali, Mahmood Roshan, and Elham Nazari. "Post-Newtonian Corrections to Toomre's Criterion." Astrophysical Journal 865, no. 1 (September 24, 2018): 71. http://dx.doi.org/10.3847/1538-4357/aadbaf.

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29

Santoro, F., L. Neira, D. Ibaceta, and R. Aquilano. "Post-newtonian approximation and collapsed stars." Astronomical & Astrophysical Transactions 17, no. 1 (September 1998): 77–81. http://dx.doi.org/10.1080/10556799808235427.

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30

Blanchet, Luc. "Post-Newtonian Expansion of Gravitational Radiation." Progress of Theoretical Physics Supplement 136 (1999): 146–57. http://dx.doi.org/10.1143/ptps.136.146.

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31

Frisch, David H. "Simple aspects of post‐Newtonian gravitation." American Journal of Physics 58, no. 4 (April 1990): 332–37. http://dx.doi.org/10.1119/1.16165.

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32

Denisov, V. L., and M. I. Denisov. "Generalization of the post-Newtonian formalism." Theoretical and Mathematical Physics 91, no. 3 (June 1992): 677–82. http://dx.doi.org/10.1007/bf01017345.

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33

Zet, G., and V. Manta. "Post-Newtonian estimation in relativistic optics." International Journal of Theoretical Physics 32, no. 6 (June 1993): 1013–20. http://dx.doi.org/10.1007/bf01215307.

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34

Oliynyk, Todd A. "Post-Newtonian Expansions for Perfect Fluids." Communications in Mathematical Physics 288, no. 3 (February 18, 2009): 847–86. http://dx.doi.org/10.1007/s00220-009-0738-z.

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35

Bini, Donato, Paolo Carini, Robert T. Jantzen, and Daniel Wilkins. "Thomas precession in post-Newtonian gravitoelectromagnetism." Physical Review D 49, no. 6 (March 15, 1994): 2820–27. http://dx.doi.org/10.1103/physrevd.49.2820.

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36

Benacquista, Matthew J. "Second-order parametrized-post-Newtonian Lagrangian." Physical Review D 45, no. 4 (February 15, 1992): 1163–73. http://dx.doi.org/10.1103/physrevd.45.1163.

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37

Cho, H. T. "Post-Newtonian approximation for spinning particles." Classical and Quantum Gravity 15, no. 8 (August 1, 1998): 2465–78. http://dx.doi.org/10.1088/0264-9381/15/8/022.

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38

Keck, John W. "The Natural Motion of Matter in Newtonian and Post-Newtonian Physics." Thomist: A Speculative Quarterly Review 71, no. 4 (2007): 529–54. http://dx.doi.org/10.1353/tho.2007.0001.

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39

Sharif, M., and H. Rizwana Kausar. "Newtonian and post Newtonian expansionfree fluid evolution in f(R) gravity." Astrophysics and Space Science 337, no. 2 (October 5, 2011): 805–13. http://dx.doi.org/10.1007/s10509-011-0863-y.

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40

Brans, Carl H. "Gravity: Newtonian, Post-Newtonian, RelativisticGravity: Newtonian, Post-Newtonian, Relativistic. EricPoisson Clifford M.Will794 pp. Cambridge U. P., Cambridge, 2014. Price: $85.00 (hardcover). ISBN 978-1-107-03286." American Journal of Physics 83, no. 9 (September 2015): 823. http://dx.doi.org/10.1119/1.4917313.

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41

Schastok, J., M. Soffel, H. Ruder, and M. Schneider. "The post - Newtonian rotation of Earth: a first approach." Symposium - International Astronomical Union 128 (1988): 341–47. http://dx.doi.org/10.1017/s0074180900119709.

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The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

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42

Wanex, Lucas F. "Chaotic Amplification in the Relativistic Restricted Three-body Problem." Zeitschrift für Naturforschung A 58, no. 1 (January 1, 2003): 13–22. http://dx.doi.org/10.1515/zna-2003-0102.

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The relativistic equations of motion for the restricted three-body problem are derived in the first post-Newtonian approximation. These equations are integrated numerically for seven different trajectories in the earth-moon orbital system. Four of the trajectories are determined to be chaotic and three are not chaotic. Each post-Newtonian trajectory is compared to its Newtonian counterpart. It is found that the difference between Newtonian and post-Newtonian trajectories for the restricted three-body problem is greater for chaotic trajectories than it is for trajectories that are not chaotic. Finally, the possibility of using this Chaotic Amplification Effect as a novel test of general relativity is discussed.

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43

Cheng, Xu-Hui, and Guo-Qing Huang. "A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries." Symmetry 13, no. 4 (April 1, 2021): 584. http://dx.doi.org/10.3390/sym13040584.

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In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.

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44

Marquina, José E. "Euler y la Mecánica." Revista Mexicana de Física E 65, no. 1 (January 21, 2019): 77. http://dx.doi.org/10.31349/revmexfise.65.77.

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En este trabajo se presentan las principales aportaciones de Leonhard Euler a la mecánica, que van desde la invaluable transcripción de la mecánica newtoniana al lenguaje del cálculo diferencial e integral, hasta su peculiar interpretación, en términos de la impenetrabilidad, de la Tercera Ley de Newton, pasando por su profunda valoración del concepto de inercia y su aportación relativa a plantear la Segunda Ley de Newton en coordenadas cartesianas. In this work it is presented the Leonhard Euler more important contributions to mechanics, from the invaluable transcriptions of the newtonian mechanics to integral and diferential calculus, up to his peculiar interpretation of the Newton’s Third Law in terms of the impenetrability, going through his profound evaluation about the inertia concept and his great idea to pose the Newton’s Second Law in cartesians coordinates.

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45

Lemos, A. S., G. C. Luna, E. Maciel, and F. Dahia. "Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials." Classical and Quantum Gravity 36, no. 24 (November 22, 2019): 245021. http://dx.doi.org/10.1088/1361-6382/ab561f.

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46

Klioner, S. A. "Angular velocity of rotation of extended bodies in general relativity." Symposium - International Astronomical Union 172 (1996): 309–20. http://dx.doi.org/10.1017/s0074180900127585.

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We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of N arbitrarily composed and shaped, deformable weakly self-gravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the post-Newtonian generalizations of the Tisserand axes and the principal axes of inertia.

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47

Fukushima, T. "Post-Newtonian treatise on the rotational motion of a finite body." Symposium - International Astronomical Union 114 (1986): 35–40. http://dx.doi.org/10.1017/s0074180900147953.

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The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.

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48

Feldbacher-Escamilla, Christian J. "Newtons Methodologie: Eine Kritik an Duhem, Feyerabend und Lakatos." Archiv für Geschichte der Philosophie 101, no. 4 (December 1, 2019): 584–615. http://dx.doi.org/10.1515/agph-2019-4004.

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Abstract The Newtonian research program consists of the core axioms of the Principia Mathematica, a sequence of force laws and auxiliary hypotheses, and a set of methodological rules. The latter underwent several changes and so it is sometimes claimed that, historically seen, Newton and the Newtonians added methodological rules post constructione in order to further support their research agenda. An argument of Duhem, Feyerabend, and Lakatos aims to provide a theoretical reason why Newton could not have come up with his theory of the Principia in accordance with his own methodology: Since Newton’s starting point, Kepler’s laws, contradict the law of universal gravitation, he could not have applied the so-called method of analysis and synthesis. In this paper, this argument is examined with reference to the Principia’s several editions. Newton’s method is characterized, and necessary general background assumptions of the argument are made explicit. Finally, the argument is criticized based on a contemporary philosophy of science point of view.

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49

CIUFOLINI, IGNAZIO. "NEW CLASS OF METRIC THEORIES OF GRAVITY NOT DESCRIBED BY THE PARAMETRIZED POST-NEWTONIAN (PPN) FORMALISM." International Journal of Modern Physics A 06, no. 30 (December 20, 1991): 5511–32. http://dx.doi.org/10.1142/s0217751x91002604.

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After an introduction to theories of gravity alternative to general relativity, metric theories (Sec. 1) and the parametrized post-Newtonian (PPN) formalism (Sec. 2), we define a new class of metric theories of gravity (Sec. 3). It turns out that the post-Newtonian approximation of these new theories is not described by the PPN formalism (Sec. 4); in fact, in the limit of weak field and slow motions, the post-Newtonian expression of the metric tensor contains an, a priori, infinite set of new terms and correspondingly an, a priori, infinite set of new PPN parameters. As a consequence, the parametrized post-Newtonian formulas describing the classical relativistic tests should include these new parameters, and therefore the experimental values of the classical relativistic effects should not be used to put limits only on the standard ten PPN parameters. Finally, we note that a subset of this new class of theories has the same post-Newtonian limit and value of the PPN parameters as general relativity, and therefore is automatically in agreement with the classical general-relativistic tests (Sec. 4, theory III).

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50

Klioner, Sergei A. "On the Problem of post-Newtonian Rotational Motion." International Astronomical Union Colloquium 165 (1997): 383–90. http://dx.doi.org/10.1017/s0252921100046844.

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AbstractThe problems of modeling of the rotational motion of the Earth are considered in the framework of general relativity. Both, rigid and deformable bodies are discussed. Rigorous definitions of the tensor of inertia, Tisserand-like axes and the angular velocity of rotation of an extended deformable body moving and rotating in external gravitational fields are proposed in the first post-Newtonian approximation. The implications of these post-Newtonian definitions on modeling of Earth rotation are analyzed.

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