Abstract
Within a fourth-order theory of gravity we give,for a static asymptotically flat spacetime, anexpression of the active mass (gravitational mass), infirst order in the coupling constant, α, of the curvature squared term in the Lagrangiandensity, a generalization of the Tolman expression forthe energy, which establishes a relationship between theactive mass and the source structure in a static spacetime. Within this approximation, we canprove that the fourth-order theory shares with Generalrelativity (GR) the property that, for sources ofcompact support, the active mass is independent of any two-dimensional surface which encloses thesupport of the matter distribution. Finally, we provethat only for conformally invariant sources thefourth-order theory and GR share the same static andasymptotically flat solutions.
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REFERENCES
Eddington, A. (1924). The Mathematical Theory of Relativity (2nd ed., Cambridge University Press, Cambridge).
Pauli, W. (1921). Theory of Relativity (Pergamon Press, New York).
Buchdahl, H. A. (1948). Proc. Edinburgh Math. Soc. 8, 89.
Havas, P. (1977). Gen. Rel. Grav. 8, 631.
Weinberg, S. (1979). In General Relativity, S. W. Hawking and W Israel, eds. (Cambrigde University Press, Cambridge).
Stelle, K. S. (1978). Gen. Rel. Grav. 9, 353; (1977). Phys. Rev. D 16, 953. Utiyama, R., and DeWitt, B. S. (1962). J. Math. Phys. 3, 608.
Starobinsky, A. A. (1980). Phys. Lett. B 91, 99.
Mijic, M., Morris, M. M. and Suen, W. M. (1986). Phys. Rev. D 34, 2934.
Mijic, M., Morris, M. S., and Wai-Mo Suen (1989). Phys. Rev. D 39, 1496.
Schmidt, H.-J.(1994). Phys. Rev. D 49, 6354; Erratum (1996) D 54, 7906.
Schmidt, H.-J. (1997). Gravit. Cosmol. 3, 266, gr-qc/ 9712097.
Barraco, D. E., and Hamity, V.H. (1993). Gen. Rel. Grav. 25, 461.
Barraco, D. E., et al. (1996) Gen. Rel. Grav. 28, 339.
Witten, E. (1981). Commun. Math. Phys. 80, 381.
Strominger, A. (1984). Phys. Rev. D 30, 2257.
Barraco, D. E., and Hamity, V. H (1990). Int. J. Theor. Phys. 29, 547.
Wald, R. M. (1984). General Relativity (University of Chicago Press, Chicago).
Tolman, R. C. (1930). Phys. Rev. 35, 875.
Barraco, D. E., and Hamity, V. H. (1994). Class. Quantum Grav. 11, 2113.
Will, C. M. (1992). Int. J. Mod. Phys. D 1, 92.
Zumberge, M. A., et al. (1991). Phys. Rev. Lett. 67, 3051.
Moody, M. V., and Paik, H. J. (1993). Phys. Rev. Lett. 70, 1195.
Moore, M. W., et al. (1994). Class. Quant. Grav. 11, A97.
Kung, J. H. (1995). Phys. Rev. D 52, 6922.
Landau, L., and Lifshitz, E. (1951). The Classical Theory of Fields (Addison-Wesley, Mass.).
Kung, J. H. (1996). Phys. Rev. D 53, 3017.
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Barraco, D., Hamity, V.H. A Theorem Relating Solutions of a Fourth-Order Theory of Gravity to General Relativity. General Relativity and Gravitation 31, 213–218 (1999). https://doi.org/10.1023/A:1018892110584
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DOI: https://doi.org/10.1023/A:1018892110584