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Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity. (English) Zbl 1191.83016
Summary: An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function \(G(\xi )=1-\xi ^{2}-2mA\xi ^{3}-q^{2}A^{2}\xi ^{4}\). The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form \((1-\xi ^{2})(1+r_{+}\)A\(\xi )(1+r_{-}\)A\(\xi )\) with \(r_{\pm }\) as the horizons of Reissner-Nordström space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner-Nordström black hole. In calculating the energy content of this tetrad field using the gravitational energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the gravitational energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the energy.

MSC:
83C15 Exact solutions to problems in general relativity and gravitational theory
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