The gravitational energy problem for cosmological models in teleparallel gravity. (English) Zbl 1204.83077

Summary: We present a method to calculate the gravitational energy when asymptotic boundary conditions for the space-time are not given. This is the situation for most of the cosmological models. The expression for the gravitational energy is obtained in the context of the teleparallel equivalent of general relativity. We apply our method first to the Schwarzschild-de Sitter solution of Einstein’s equation, and then to the Robertson-Walker universe. We show that in the first case our method leads to an average energy density of the vacuum space-time, and in the latter case the energy vanishes in the case of null curvature.


83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
83C40 Gravitational energy and conservation laws; groups of motions
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
Full Text: DOI arXiv


[1] DOI: 10.1007/BF02108013
[2] DOI: 10.1007/BF02848334
[3] DOI: 10.1023/B:GERG.0000022386.29438.be · Zbl 1055.83013
[4] DOI: 10.1007/BF02059009
[5] DOI: 10.1007/BF02108014
[6] DOI: 10.1023/A:1003670928681 · Zbl 0968.83051
[7] Szabados L. B., Living Rev. Rel. 12
[8] DOI: 10.1086/368258
[9] DOI: 10.1070/PU1982v025n03ABEH004517 · Zbl 0541.53023
[10] DOI: 10.1007/s10714-006-0339-5 · Zbl 1137.83365
[11] DOI: 10.1088/0264-9381/23/22/011 · Zbl 1133.83379
[12] DOI: 10.1002/andp.200510161 · Zbl 1082.83502
[13] DOI: 10.1023/A:1018836025605 · Zbl 0941.83043
[14] DOI: 10.1103/PhysRevD.47.1407
[15] d’Inverno R., Introducing Einstein’s Relativity (1996)
[16] Landau L. D., Course of Theoretical Physics 2, in: The Classical Theory of Fields (2004)
[17] DOI: 10.1142/S0217732307025285 · Zbl 1143.83320
[18] DOI: 10.1103/PhysRevD.78.044035
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