Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-04-30
Int.J.Mod.Phys.D16:65,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages, Latex
Scientific paper
10.1142/S0218271807009310
We give two classes of spherically symmetric exact solutions of the couple gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function $H({R},t)$. The second solution depends on a constant parameter $\eta$. These solutions reproduce the same metric, i.e., the Reissner--Nordstr$\ddot{o}$m metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition which M{\o}ller required for a consistent energy-momentum complex: Namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than $1/\sqrt{R}$ for $R\to \infty$. It is also shown that the second exact solution meets the M{\o}ller's condition.
Nashed Gamal G. L.
Shirafuji Takeshi
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