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5D Schwarzschild-Like Spacetimes with Arbitrary Magnetic Field

Tonatiuh Matos
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Abstract

We find a new class of exact solutions of the five-dimensional Einstein equations whose corresponding four-dimensional spacetime possesses a Schwarzschild-like behavior. The electromagnetic potential depends on a harmonic function and can be choosen to be of a monopole, dipole, etc. field. The solutions are asymptotically flat and for vanishing magnetic field the four metrics are of the Schwarzschild solution. The spacetime is singular in $r=2m$ for higher multipole moments, but regular for monopoles or vanishing magnetic fields in this point. The scalar field posseses a singular behavior. #(Preprint CINVESTAV 15/93)#

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Tonatiuh Matos. 1994-02-02. 5D Schwarzschild-Like Spacetimes with Arbitrary Magnetic Field. https://doi.org/10.1103/physrevd.49.4296

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