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Journal articles on the topic 'Curvature singularities'

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Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Van-Brunt, B., and K. Grant. "Hyperbolic Weingarten surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 3 (November 1994): 489–504. http://dx.doi.org/10.1017/s0305004100072765.

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AbstractWeingarten surfaces which can be represented locally as solutions to second order hyperbolic partial differential equations are examined in this paper. In particular, the geometry of the families of curves corresponding to characteristics on these surfaces is investigated and the relationships of these curves with other curves on the surface such as asymptotic lines and lines of curvature are explored. It is shown that singularities in the lines of curvature, i.e. umbilic points, correspond to singularities in the families of characteristics, and that lines of curvature are non-characteristic curves. If there is a linear relation between the Gaussian and mean curvatures and real characteristics exist, then the characteristics form a Tchebychef net on the corresponding Weingarten surface.

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2

Sáez, Mariel, and Oliver C. Schnürer. "Mean curvature flow without singularities." Journal of Differential Geometry 97, no. 3 (July 2014): 545–70. http://dx.doi.org/10.4310/jdg/1406033979.

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3

Andrews, Ben. "Singularities in crystalline curvature flows." Asian Journal of Mathematics 6, no. 1 (2002): 101–22. http://dx.doi.org/10.4310/ajm.2002.v6.n1.a6.

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4

Xin, Yuanlong. "Singularities of mean curvature flow." Science China Mathematics 64, no. 7 (April 26, 2021): 1349–56. http://dx.doi.org/10.1007/s11425-020-1840-1.

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5

RUDNICKI, WIESŁAW, ROBERT J. BUDZYŃSKI, and WITOLD KONDRACKI. "GENERALIZED STRONG CURVATURE SINGULARITIES AND COSMIC CENSORSHIP." Modern Physics Letters A 17, no. 07 (March 7, 2002): 387–97. http://dx.doi.org/10.1142/s021773230200659x.

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A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Królak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the causal structure and the curvature strength of the singularities. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.

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6

Królak, Andrzej. "Strong curvature singularities and causal simplicity." Journal of Mathematical Physics 33, no. 2 (February 1992): 701–4. http://dx.doi.org/10.1063/1.529804.

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7

S Martila, Dmitri. "On Naked Singularities of spacetime Curvature." Journal of Contradiciting Results in Science 1, no. 1 (July 4, 2012): 09–13. http://dx.doi.org/10.5530/jcrsci.2012.1.4.

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8

Mantz, Christiaan L. M., and Tomislav Prokopec. "Resolving Curvature Singularities in Holomorphic Gravity." Foundations of Physics 41, no. 10 (June 4, 2011): 1597–633. http://dx.doi.org/10.1007/s10701-011-9570-3.

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9

Li, Chao, and Christos Mantoulidis. "Positive scalar curvature with skeleton singularities." Mathematische Annalen 374, no. 1-2 (September 15, 2018): 99–131. http://dx.doi.org/10.1007/s00208-018-1753-1.

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10

Benedini Riul, P., and R. Oset Sinha. "A relation between the curvature ellipse and the curvature parabola." Advances in Geometry 19, no. 3 (July 26, 2019): 389–99. http://dx.doi.org/10.1515/advgeom-2019-0002.

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Abstract At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geometry of the projection of the surface to ℝ3 at the singular point. In particular we relate the curvature ellipse of the surface to the curvature parabola of its singular projection.

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11

Baker, Gregory R., and Chao Xie. "Singularities in the complex physical plane for deep water waves." Journal of Fluid Mechanics 685 (September 22, 2011): 83–116. http://dx.doi.org/10.1017/jfm.2011.283.

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AbstractDeep water waves in two-dimensional flow can have curvature singularities on the surface profile; for example, the limiting Stokes wave has a corner of $2\lrm{\pi} / 3$ radians and the limiting standing wave momentarily forms a corner of $\lrm{\pi} / 2$ radians. Much less is known about the possible formation of curvature singularities in general. A novel way of exploring this possibility is to consider the curvature as a complex function of the complex arclength variable and to seek the existence and nature of any singularities in the complex arclength plane. Highly accurate boundary integral methods produce a Fourier spectrum of the curvature that allows the identification of the nearest singularity to the real axis of the complex arclength plane. This singularity is in general a pole singularity that moves about the complex arclength plane. It approaches the real axis very closely when waves break and is associated with the high curvature at the tip of the breaking wave. The behaviour of these singularities is more complex for standing waves, where two singularities can be identified that may collide and separate. One of them approaches the real axis very closely when a standing wave forms a very narrow collapsing column of water almost under free fall. In studies so far, no singularity reaches the real axis in finite time. On the other hand, the surface elevation $y(x)$ has square-root singularities in the complex $x$ plane that do reach the real axis in finite time, the moment when a wave first starts to break. These singularities have a profound effect on the wave spectra.

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12

MacCallum, Malcolm A. H. "Invariants, singularities and horizons." International Journal of Modern Physics D 28, no. 16 (October 11, 2019): 2040002. http://dx.doi.org/10.1142/s0218271820400027.

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Local curvature invariants can be used in locating and characterizing singularities and horizons. After outlining the available invariants and their properties, examples of their use in these contexts, and related general results and conjectures, are presented.

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13

Debin, Clément. "A COMPACTNESS THEOREM FOR SURFACES WITH BOUNDED INTEGRAL CURVATURE." Journal of the Institute of Mathematics of Jussieu 19, no. 2 (April 10, 2018): 597–645. http://dx.doi.org/10.1017/s1474748018000154.

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We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.

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14

Colding, Tobias, and William Minicozzi. "Generic mean curvature flow I; generic singularities." Annals of Mathematics 175, no. 2 (March 1, 2012): 755–833. http://dx.doi.org/10.4007/annals.2012.175.2.7.

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15

Cheeger, Jeff, Tobias H. Colding, and Gang Tian. "Constraints on singularities under Ricci curvature bounds." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 6 (March 1997): 645–49. http://dx.doi.org/10.1016/s0764-4442(97)86982-0.

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16

Mazzeo, Rafe, and Frank Pacard. "Constant scalar curvature metrics with isolated singularities." Duke Mathematical Journal 99, no. 3 (September 1999): 353–418. http://dx.doi.org/10.1215/s0012-7094-99-09913-1.

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17

Zhang, Yong-Liang, Xian-Zi Dong, Mei-Ling Zheng, Zhen-Sheng Zhao, and Xuan-Ming Duan. "Steering electromagnetic beams with conical curvature singularities." Optics Letters 40, no. 20 (October 14, 2015): 4783. http://dx.doi.org/10.1364/ol.40.004783.

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18

Cinti, Eleonora, Carlo Sinestrari, and Enrico Valdinoci. "Neckpinch singularities in fractional mean curvature flows." Proceedings of the American Mathematical Society 146, no. 6 (February 21, 2018): 2637–46. http://dx.doi.org/10.1090/proc/14002.

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19

Krechetnikov, Rouslan. "Marangoni-driven singularities via mean-curvature flow." Journal of Physics A: Mathematical and Theoretical 43, no. 24 (May 25, 2010): 242001. http://dx.doi.org/10.1088/1751-8113/43/24/242001.

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20

Joshi, Pankaj S., and Andrzej Królak. "Naked strong curvature singularities in Szekeres spacetimes." Classical and Quantum Gravity 13, no. 11 (November 1, 1996): 3069–74. http://dx.doi.org/10.1088/0264-9381/13/11/020.

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21

Gálvez, José A., Laurent Hauswirth, and Pablo Mira. "Surfaces of constant curvature inR3with isolated singularities." Advances in Mathematics 241 (July 2013): 103–26. http://dx.doi.org/10.1016/j.aim.2012.11.019.

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22

Brander, David, and Martin Svensson. "Timelike Constant Mean Curvature Surfaces with Singularities." Journal of Geometric Analysis 24, no. 3 (February 2, 2013): 1641–72. http://dx.doi.org/10.1007/s12220-013-9389-6.

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23

BEESHAM, A. "HIGHER DIMENSIONAL INHOMOGENEOUS DUST COLLAPSE AND COSMIC CENSORSHIP." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2747. http://dx.doi.org/10.1142/s0217751x02011746.

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The singularity theorems of general relativity predict that gravitational collapse finally ends up in a spacetime singularity1. The cosmic censorship hypothesis (CCH) states that such a singularity is covered by an event horizon2. Despite much effort, there is no rigorous formulation or proof of the CCH. In view of this, examples that appear to violate the CCH and lead to naked singularities, in which non-spacelike curves can emerge, rather than black holes, are important to shed more light on the issue. We have studied several collapse scenarios which can lead to both situations3. In the case of the Vaidya-de Sitter spacetime4, we have shown that the naked singularities that arise are of the strong curvature type. Both types of singularities can also arise in higher dimensional Vaidya and Tolman-Bondi spacetimes, but black holes are favoured in some sense by the higher dimensions. The charged Vaidya-de Sitter spacetime also exhibits both types of singularities5.

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24

Barve, Sukratu, and T. P. Singh. "Are Naked Singularities Forbidden by the Second Law of Thermodynamics?" Modern Physics Letters A 12, no. 32 (October 20, 1997): 2415–19. http://dx.doi.org/10.1142/s021773239700251x.

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By now, many examples of naked singularities in classical general relativity are known. It may, however, be that a physical principle over and above the general theory prevents the occurrence of such singularities in nature. Assuming the validity of the Weyl curvature hypothesis, we propose that naked singularities are forbidden by the second law of thermodynamics.

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25

VICKERS, J. A. "WEAK SINGULARITIES IN GENERAL RELATIVITY." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2779. http://dx.doi.org/10.1142/s0217751x02012065.

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According to the Cosmic Censorship hypothesis realistic singularities should be hidden by an event horizon. However there are many examples of physically realistic space–times which are geodesically incomplete, and hence possess singularities according to the usual definition, which are not inside an event horizon. Many of these counterexamples to the cosmic censorship conjecture have a curvature tensor which is reasonably behaved (for example bounded or integrable) as one approaches the singularity. We give a class of weak singularities which may be described as having distributional curvature1. Because of the non–linear nature of Einstein's equations such distributional geometries are described using a diffeomorphism invariant theory of non–linear generalised functions2. We also investigate the propagation of test fields on space–times with weak singularities. We give a class of singularities3,4 which do not disrupt the Cauchy development of test fields and result in space–times which satisfy Clarke's criterion of 'generalised hyperbolicity'. We consider that points which are well behaved in this way, and where Einstein's equations make sense distributionally, should be regarded as interior points of the space–time rather than counterexamples to cosmic censorship.

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26

BROOKS, ROGER. "PLANE WAVE GRAVITONS, CURVATURE SINGULARITIES AND STRING PHYSICS." Modern Physics Letters A 06, no. 09 (March 21, 1991): 841–49. http://dx.doi.org/10.1142/s0217732391000877.

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Bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates are discussed. So are string propagation and supersymmetry in space-times with curvature singularities.

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27

Izumiya, Shyuichi, and Farid Tari. "Projections of surfaces in the hyperbolic space along horocycles." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 2 (March 30, 2010): 399–418. http://dx.doi.org/10.1017/s0308210509000213.

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We study orthogonal projections of embedded surfaces M in H3+ (−1) along horocycles to planes. The singularities of the projections capture the extrinsic geometry of M related to the lightcone Gauss map. We give geometric characterizations of these singularities and prove a Koenderink-type theorem that relates the hyperbolic curvature of the surface to the curvature of the profile and of the normal section of the surface. We also prove duality results concerning the bifurcation set of the family of projections.

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28

COWLEY, STEPHEN J., GREG R. BAKER, and SALEH TANVEER. "On the formation of Moore curvature singularities in vortex sheets." Journal of Fluid Mechanics 378 (January 10, 1999): 233–67. http://dx.doi.org/10.1017/s0022112098003334.

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Moore (1979) demonstrated that the cumulative influence of small nonlinear effects on the evolution of a slightly perturbed vortex sheet is such that a curvature singularity can develop at a large, but finite, time. By means of an analytical continuation of the problem into the complex spatial plane, we find a consistent asymptotic solution to the problem posed by Moore. Our solution includes the shape of the vortex sheet as the curvature singularity forms. Analytic results are confirmed by comparison with numerical solutions. Further, for a wide class of initial conditions (including perturbations of finite amplitude), we demonstrate that 3/2-power singularities can spontaneously form at t=0+ in the complex plane. We show that these singularities propagate around the complex plane. If two singularities collide on the real axis, then a point of infinite curvature develops on the vortex sheet. For such an occurrence we give an asymptotic description of the vortex-sheet shape at times close to singularity formation.

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29

IZUMIYA, SHYUICHI, DONGHE PEI, and TAKASI SANO. "SINGULARITIES OF HYPERBOLIC GAUSS MAPS." Proceedings of the London Mathematical Society 86, no. 2 (March 2003): 485–512. http://dx.doi.org/10.1112/s0024611502013850.

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In this paper we adopt the hyperboloid in Minkowski space as the model of hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in hyperbolic space. The hyperbolic Gauss map has been introduced by Ch. Epstein [J. Reine Angew. Math. 372 (1986) 96–135] in the Poincaré ball model, which is very useful for the study of constant mean curvature surfaces. However, it is very hard to perform the calculation because it has an intrinsic form. Here, we give an extrinsic definition and we study the singularities. In the study of the singularities of the hyperbolic Gauss map (indicatrix), we find that the hyperbolic Gauss indicatrix is much easier to calculate. We introduce the notion of hyperbolic Gauss–Kronecker curvature whose zero sets correspond to the singular set of the hyperbolic Gauss map (indicatrix). We also develop a local differential geometry of hypersurfaces concerning their contact with hyperhorospheres.2000 Mathematical Subject Classification: 53A25, 53A05, 58C27.

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30

Benedini Riul, P., M. A. S. Ruas, and R. Oset Sinha. "The geometry of corank 1 surfaces in ℝ4." Quarterly Journal of Mathematics 70, no. 3 (December 21, 2018): 767–95. http://dx.doi.org/10.1093/qmath/hay064.

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Abstract We study the geometry of surfaces in ℝ4 with corank 1 singularities. For such surfaces, the singularities are isolated and, at each point, we define the curvature parabola in the normal space. This curve codifies all the second-order information of the surface. Also, using this curve, we define asymptotic and binormal directions, the umbilic curvature and study the flat geometry of the surface. It is shown that we can associate to this singular surface a regular one in ℝ4 and relate their geometry.

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31

Ura, Tatsumasa. "Constant negative Gaussian curvature tori and their singularities." Tsukuba Journal of Mathematics 42, no. 1 (July 2018): 65–95. http://dx.doi.org/10.21099/tkbjm/1541559651.

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32

Neves, André. "Finite time singularities for Lagrangian mean curvature flow." Annals of Mathematics 177, no. 3 (May 1, 2013): 1029–76. http://dx.doi.org/10.4007/annals.2013.177.3.5.

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33

Petters, Arlie O. "Curvature of caustics and singularities of gravitational lenses." Nonlinear Analysis: Theory, Methods & Applications 30, no. 1 (December 1997): 627–34. http://dx.doi.org/10.1016/s0362-546x(97)00068-0.

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34

Miyamoto, U., H. Maeda, and a. T. Harada. "Quantum Effect and Curvature Strength of Naked Singularities." Progress of Theoretical Physics 113, no. 3 (March 1, 2005): 513–33. http://dx.doi.org/10.1143/ptp.113.513.

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35

Oliveira-Neto, G., E. V. Corrêa Silva, N. A. Lemos, and G. A. Monerat. "Probing singularities in quantum cosmology with curvature scalars." Physics Letters A 373, no. 23-24 (May 2009): 2012–16. http://dx.doi.org/10.1016/j.physleta.2009.04.002.

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36

Troyanov, Marc. "Prescribing curvature on compact surfaces with conical singularities." Transactions of the American Mathematical Society 324, no. 2 (February 1, 1991): 793–821. http://dx.doi.org/10.1090/s0002-9947-1991-1005085-9.

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37

Neves, André. "Singularities of Lagrangian Mean Curvature Flow: Monotone case." Mathematical Research Letters 17, no. 1 (2010): 109–26. http://dx.doi.org/10.4310/mrl.2010.v17.n1.a9.

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38

Reverberi, L. "Gravitational contraction and curvature singularities inf(R) gravity." Journal of Physics: Conference Series 442 (June 10, 2013): 012036. http://dx.doi.org/10.1088/1742-6596/442/1/012036.

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39

Krȯlak, Andrzej. "Strong cosmic censorship and the strong curvature singularities." Journal of Mathematical Physics 28, no. 11 (November 1987): 2685–87. http://dx.doi.org/10.1063/1.527829.

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40

Grillo, G. "On a class of naked strong-curvature singularities." Classical and Quantum Gravity 8, no. 4 (April 1, 1991): 739–49. http://dx.doi.org/10.1088/0264-9381/8/4/017.

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41

White, Brian. "Subsequent singularities in mean-convex mean curvature flow." Calculus of Variations and Partial Differential Equations 54, no. 2 (February 6, 2015): 1457–68. http://dx.doi.org/10.1007/s00526-015-0831-4.

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42

Colding, Tobias Holck, Tom Ilmanen, and William P. Minicozzi. "Rigidity of generic singularities of mean curvature flow." Publications mathématiques de l'IHÉS 121, no. 1 (February 21, 2015): 363–82. http://dx.doi.org/10.1007/s10240-015-0071-3.

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43

Han, Xiaoli, and Jiayu Li. "Singularities of symplectic and Lagrangian mean curvature flows." Frontiers of Mathematics in China 4, no. 2 (March 11, 2009): 283–96. http://dx.doi.org/10.1007/s11464-009-0018-4.

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44

Huisken, Gerhard, and Carlo Sinestrari. "Mean curvature flow singularities for mean convex surfaces." Calculus of Variations and Partial Differential Equations 8, no. 1 (January 1, 1999): 1–14. http://dx.doi.org/10.1007/s005260050113.

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45

Teixeira, Ralph Costa. "Medial Axes and Mean Curvature Motion II: Singularities." Journal of Mathematical Imaging and Vision 23, no. 1 (July 2005): 87–105. http://dx.doi.org/10.1007/s10851-005-4969-0.

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46

Takimoto, K. "Isolated singularities for some types of curvature equations." Journal of Differential Equations 197, no. 2 (March 2004): 275–92. http://dx.doi.org/10.1016/j.jde.2003.10.010.

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47

Clarke, C. J. S., and A. Królak. "Conditions for the occurence of strong curvature singularities." Journal of Geometry and Physics 2, no. 2 (1985): 127–43. http://dx.doi.org/10.1016/0393-0440(85)90012-9.

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48

Martínez-Niconoff, Gabriel, P. Martinez-Vara, G. Diaz-Gonzalez, J. Silva-Barranco, and A. Carbajal-Domínguez. "Surface Plasmon Singularities." International Journal of Optics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/152937.

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With the purpose to compare the physical features of the electromagnetic field, we describe the synthesis of optical singularities propagating in the free space and on a metal surface. In both cases the electromagnetic field has a slit-shaped curve as a boundary condition, and the singularities correspond to a shock wave that is a consequence of the curvature of the slit curve. As prototypes, we generate singularities that correspond to fold and cusped regions. We show that singularities in free space may generate bifurcation effects while plasmon fields do not generate these kinds of effects. Experimental results for free-space propagation are presented and for surface plasmon fields, computer simulations are shown.

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49

Nashed, Gamal G. L. "Rotating black holes in the teleparallel equivalent of general relativity." International Journal of Modern Physics D 25, no. 07 (June 2016): 1650079. http://dx.doi.org/10.1142/s0218271816500796.

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We derive set of solutions with flat transverse sections in the framework of a teleparallel equivalent of general relativity which describes rotating black holes. The singularities supported from the invariants of torsion and curvature are explained. We investigate that there appear more singularities in the torsion scalars than in the curvature ones. The conserved quantities are discussed using Einstein–Cartan geometry. The physics of the constants of integration is explained through the calculations of conserved quantities. These calculations show that there is a unique solution that may describe true physical black hole.

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50

Yudi Handayana, I. Gusti Ngurah, and Lily Maysari Angraini. "SINGULARITAS SEMU PADA RUANG-WAKTU REISSNER-NORDSTRÖM." ORBITA: Jurnal Kajian, Inovasi dan Aplikasi Pendidikan Fisika 5, no. 2 (November 28, 2019): 82. http://dx.doi.org/10.31764/orbita.v5i2.1203.

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ABSTRAKPenelitian ini mengkaji singularitas semu pada metrik Reissner-Nordström, yang merupakan solusi persamaan medan Einstein untuk model partikel bermuatan. Kajian dilakukan dengan menganalisis titik-titik singular pada metrik, menghitung tensor kelengkungan Riemann, serta menghitung scalar Kretschmann pada titik-titik tersebut. Perhitungan dilakukan dengan bantuan program Maxima. Hasilnya, singularitas nyata hanya terjadi pada r = 0, sedangkan singularitas semu terjadi pada . Singularitas semu tersebut merupakan representasi dari horizon peristiwa. Terdapat tiga kemungkinan situasi pada horizon peristiwa. Hal menarik terdapat pada situasi r = M, dimana terjadi keseimbangan antara massa dan muatan yang memungkinkan tarikan gravitasi dan tolakan elektromagnetik saling meniadakan. Penelitian ini juga menghasilkan persamaan geodesik pada titik-titik yang tidak menghasilkan nilai infinite pada skalar Kretschmaan. Kata Kunci : Kelengkungan Riemann, Metrik Reisner-Nordström, Singularitas, Persamaan Geodesik ABSTRACTThis study examines pseudo singularities on the Reissner-Nordström metric which is a solution to Einstein's field equations for charged particle models. The study was carried out by analyzing the singular points on the metric calculating the Riemann curvature tensor, and calculating Kretschmann's scalar at these points. The results show that real singularities only occur at r = 0, whereas pseudo singularity occurs at . There is a point of pseudo singularity that representing the event horizon. There are two possible situations on the event horizon. Interesting things are in the case r = M, where here is a balance between mass and charge which allows gravitational pull and electromagnetic repulsion to cancel each other. This study also yields the geodesic equation point that not yields infinite value of Kretschmaan scalar. Keywords: Riemann tensor, Reissner-Nordström Metrik, Singularities, Geodesik equation

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