Gravitational collapse of charged scalar fields
In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the \(3+1\) formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with \(|Q|<M\). By increasing the fundamental charge of the scalar field \(q\) we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.
KeywordsGravitational collapse Eintein–Maxwell–Klein–Gordon system Cosmic censorship Charged scalar fields
The authors wish to thank Dario Núñez and Marcelo Salgado for many useful discussions and comments. This work was supported in part by Dirección General de Estudios de Posgrado (DGEP-UNAM), by CONACyT through Grant 82787, and by DGAPA-UNAM through Grants IN113907 and IN115310. J.M.T. also acknowledges a CONACyT postgraduate scholarship.
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