Abstract
We consider the Denisov-Solov'ov example which shows that the inertial mass is not well defined in General Relativity. It is shown that the mathematical reason why this is true is a wrong application of the Stokes theorem. Then we discuss the role of the order of asymptotically flatness in the definition of the mass. In conclusion some comments on conservation laws in General Relativity are presented.
Similar content being viewed by others
References
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman, San Francisco).
Wald, R. (1984).General Relativity (University of Chicago Press), Chicago.
Sachs, R. K., Wu, H. (1977).General Relativity for Mathematicians (Springer-Verlag, New York).
Logunov, A., Mestvirishvili, M. (1989).The Relativistic Theory of Gravitation (Mir, Moscow).
Thirring, W., Wallner, R. (1978).Brazilian J. Phys. 8, 686.
Denisov, V. I., Solov'ov, V. O. (1983).Theor. Math. Phys. 56, 832.
Schoen, R., Yau, S.-T. (1979).Commun. Math. Phys. 65, 45.
Schoen, R., Yau, S.-T. (1979).Commun. Math. Phys. 79, 231.
Bando, S., Kasue, A., Nakajima, H. (1989).Invent. Math. 97, 313.
Bartnik, R. (1986).Commun. Pure App. Math. XXXIX, 661.
Ashtekar, A. (1980). InGeneral Relativity and Gravitation, A. Held, ed. (Plenum Press, New York), vol. 2.
LeBrun, C. (1988).Commun. Math. Phys. 118, 591.
Dalton, K. (1989).Gen. Rel. Grav. 21, 533.
Vargas, J. G., Torr, D. G. (1991).Gen. Rel. Grav. 23, 713.
Benn, I. M. (1982).Ann. Inst. H. Poincaré XXXVIIA, 67.
Ferraris, M., Francaviglia, M. (1992).Class. Quant. Grav. 9, S79.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bozhkov, Y., Rodrigues, W.A. Mass and energy in General Relativity. Gen Relat Gravit 27, 813–819 (1995). https://doi.org/10.1007/BF02113065
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02113065