Geodesic
Some properties of the dynamics of collapse in massive and massless
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 114-126 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We investigate the dynamics of collapse in massive and massless relativistic theories of gravity for different equations of state for matter numerically and analytically. This allows clarifying the character of the collapse dynamics in the massive relativistic theory of gravity; in particular, we establish the graviton-mass dependence of the time of reaching the turning point (i.e., the point of transition from contraction to expansion). For the massless relativistic theory of gravity, we clarify the relation between the known general relativity solution for cold dust and the corresponding solution in the relativistic theory of gravity. We show that the harmonic time is singular, including the case of a smooth distribution of matter corresponding to a compact object with a strongly diffused boundary, which means that the Oppenheimer–Snyder solution cannot be fully embedded into the Minkowski space. We in addition investigate the effect of a nonzero pressure on the collapse dynamics.
Keywords: gravity theory, general relativity, relativistic theory of gravity, collapse
Mots-clés : graviton mass. 
@article{TMF_2016_187_1_a8,
     author = {K. V. Antipin and A. Dubikovsky and P. K. Silaev},
     title = {Some properties of the~dynamics of collapse in massive and massless},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {114--126},
     year = {2016},
     volume = {187},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a8/}
}
TY  - JOUR
AU  - K. V. Antipin
AU  - A. Dubikovsky
AU  - P. K. Silaev
TI  - Some properties of the dynamics of collapse in massive and massless
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 114
EP  - 126
VL  - 187
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a8/
LA  - ru
ID  - TMF_2016_187_1_a8
ER  - 
%0 Journal Article
%A K. V. Antipin
%A A. Dubikovsky
%A P. K. Silaev
%T Some properties of the dynamics of collapse in massive and massless
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 114-126
%V 187
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a8/
%G ru
%F TMF_2016_187_1_a8
K. V. Antipin; A. Dubikovsky; P. K. Silaev. Some properties of the dynamics of collapse in massive and massless. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 1, pp. 114-126. http://geodesic.mathdoc.fr/item/TMF_2016_187_1_a8/

[1] R. C. Tolman, Proc. Natl. Acad. Sci. USA, 20:3 (1934), 169–176 | DOI | Zbl | Zbl

[2] J. R. Oppenheimer, H. Snyder, Phys. Rev., 56:5 (1939), 455–459 | DOI | Zbl

[3] A. A. Logunov, M. A. Mestvirishvili, Relyativistskaya teoriya gravitatsii, Nauka, M., 1989 | MR

[4] A. A. Logunov, Relyativistskaya teoriya gravitatsii, Nauka, M., 2012 | MR

[5] A. A. Logunov, M. A. Mestvirishvili, TMF, 121:1 (1999), 4–24 | DOI | DOI | Zbl

[6] S. S. Gershtein, A. A. Logunov, M. A. Mestvirishvili, TMF, 161:2 (2009), 295–304 | DOI | DOI | MR | Zbl

[7] A. A. Logunov, M. A. Mestvirishvili, TMF, 174:2 (2013), 292–302 | DOI | DOI | MR | Zbl

[8] Yu. V. Chugreev, EChAYa, 21:3 (1990), 697–725 | MR

[9] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 2, Teoriya polya, Nauka, M., 2001 | MR | Zbl

[10] T. W. Marshall, The gravitational collapse of a dust ball, arXiv: 0907.2339

[11] T. W. Marshall, Fields tell matter how to move, arXiv: 1103.6168

[12] R. M. Avakyan, Tochnye resheniya uravnenii Einshteina i ikh interpretatsiya, Izd-vo Tartusskogo un-ta, Tartu, 1988

[13] A. V. Genk, TMF, 87:1 (1991), 130–140 | DOI | MR

[14] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, GITTL, M., 1955 | MR | Zbl

[15] A. A. Logunov, M. A. Mestvirishvili, EChAYa, 40:1 (2009), 136–143

[16] A. A. Logunov, M. A. Mestvirishvili, TMF, 181:2 (2014), 401–416 | DOI | DOI | MR | Zbl

[17] S. S. Gershtein, A. A. Logunov, M. A. Mestvirishvili, YaF, 61:8 (1998), 1526–1536

[18] M. A. Mestvirishvili, Yu. V. Chugreev, TMF, 80:2 (1989), 305–312 | DOI | MR | Zbl

[19] C. Gundlach, J. M. Martín-García, Living Rev. Relativity, 10 (2007), 5, 57 pp. | DOI | Zbl