Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4

Details Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4 Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4

2012-02-28

arxiv.org/abs/1202.6214v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1007/s10773-012-1126-6

We present a systematical study of static D >= 4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure S_{{\beta}}{\times} R^{D-2-{\beta}}, {\beta} {\in} {0,...,D-2} is dimension of a sphere S_{{\beta}}. In case of {\beta} = 0, we assume that there are two parallel hyper-plane shells instead of only one. The space-time has Majumdar-Papapetrou form and it inherits the symmetries of the shell manifold - it is invariant under both rotations of the S_{{\beta}} and translations along R^{D-2-{\beta}}. We find a general solution to the Einstein-Maxwell equations with a given shell. Then, we examine some flat interior solutions with special attention paid to D = 4. A connection to D = 4 non-relativistic theory is pointed out. We also comment on a straightforward generalisation to the case of Kastor-Traschen space-time, i.e. adding a non-negative cosmological constant to the charged dust matter source.

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