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Energy and Momentum of Robinson-Trautman Space-Times

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Abstract

Robinson and Trautman space-times are studied in the context of teleparallel equivalent of general relativity (TEGR). These space-times are the simplest class of asymptotically flat geometries admitting gravitational waves. We calculate the total energy for such space-times using two methods, the gravitational energy-momentum and the translational momentum 2-form. The two methods give equal results of these calculations. We show that the value of energy depends on the gravitational mass M, the Gaussian curvature of the surfaces λ(u,θ) and on the function K(u,θ). The total energy reduces to the energies of Schwarzschild’s and Bondi’s space-times under specific forms of the function K(u,θ).

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Notes

  1. Space-time indices μ,ν,… and SO(3,1) indices a,b,… run from 0 to 3. Time and space indices are indicated to μ=0,i, and a=(0),(i).

  2. Latin indices are rasing and lowering with the aid of O ab and O ab.

  3. Throughout this paper we use the relativistic units, c=G=1 and κ=8π.

  4. These calculations have been checked using Maple “15” software.

  5. ⋯ means terms which are multiplied by dθ∧dr, dθ∧dt, dr∧dϕ etc.

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Authors and Affiliations

  1. Center for Theoretical Physics, British University in Egypt, Sherouk City, 11837, P.O. Box 43, Egypt

    Gamal G. L. Nashed

  2. Mathematics Department, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt

    Gamal G. L. Nashed

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  1. Gamal G. L. Nashed
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Correspondence to Gamal G. L. Nashed.

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Nashed, G.G.L. Energy and Momentum of Robinson-Trautman Space-Times. Int J Theor Phys 53, 1654–1665 (2014). https://doi.org/10.1007/s10773-013-1964-x

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