Abstract
We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.
This is a preview of subscription content, log in via an institution to check access.
References
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Pergamon, New York (1975)
Harrison, B.K., Thorne, K.S., Wakano, M., Wheeler, J.A.: Gravitation Theory and Gravitational Collapse. Univ. Chicago Press, Chicago (1965)
Zel'dovich, Ya.B., Novikov, I.D.: The Structure and Evolution of the Universe. University of Chicago Press (1983)
Zel'dovich, Ya.B., Novikov, I.D.: Stars and Relativity. University of Chicago Press (1971)
Frolov, V.P., Novikov, I.D.: Physics of Black Holes. Kluwer Academic (1998)
Novikov, I.D.: Commun. of the Shternberg State Astronom. Inst. 132, 43 (1964)
Ruban, V.A.: Sov. Phys. JETP (Letters) 8, 414 (1968); Reprinted: Gen. Rel. Grav. 33, 369 (2001)
Ruban, V.A.: Sov. Phys. JETP 29, 1027 (1969); Reprinted: Gen. Rel. Grav. 33, 375 (2001)
Ruban, V.A.: Zh.Eksp. Teor. Fiziki 85, 801 (1983) Sov. Phys. JETP 58, 463 (1983)
Kantowski, R., Sachs, R.K.: J. Math. Phys. 7, 443 (1966)
Novikov, I.D.: Commun. of the Shternberg State Astronom. Inst. 132, 3 (1964); Reprinted: Gen. Rel. Grav. 33, 2259 (2001)
Tolman, R.C.: Proc. Nat. Acad. USA 20, 169 (1934)
Datt, B.: Z. Physik 108, 314 (1938); Reprinted: Gen. Rel. Grav. 31, 1619 (1999)
Lemaître, G.: Ann. Soc. Sci. Bruxelles 53, 51 (1933); Reprinted: Gen. Rel. Grav. 29, 641 (1997)
Misner, C.W., Sharp, D.H.: Phys. Rev. B 136, 571 (1964)
Podurets, M.A.: Astron. 41, 28; Sov. Astr. A. J. 8, 19 (1964)
Berezin, V.A., Kuzmin, V.A., Tkachev, I.I.: Phys. Rev. D 36, 2919 (1987)
Poisson, E., Israel, W.: Phys. Rev. D 41, 1796 (1990)
Gair, J.R.: Class. Quant. Grav. 19, 6345 (2002)
Hellaby, C., Lake, K.: Astrophys. Journal 290, 381 (1985); Errata ibid. 300, 461 (1986)
Hellaby, C.: Some properties of singularities in the Tolman model. Ph. D. Theses (1985)
Bizon, P., Malec, E., Murchadha, ÂO.N.: Class. Quant. Grav. 7, 1953 (1990)
Humphreys, N.P., Maartens, R., Matravers, D.R.: Regular Spherical Dust Spacetimes [gr-qc/9804023]
Israel, W.: Nuovo Cimento B 44, 1 (1966); ibid. 48, 463 (1967); Misner, C.W., Thorne, K.S., Wheeler, J.W.: Gravitation. p. 552 Freeman, San Francisco (1973)
Hellaby, C.: Class. Quantum Grav. 4, 635 (1987)
Tryon, E.P.: Nature 246, 396 (1973)
Fomin, P.I.: Doklady Akad. Nauk Ukr. SSR. 9A, 831 (1975)
Vilenkin, A.V.: Phys. Lett. B 117, 25 (1982)