Regular sources of the Kerr-Schild class for rotating and nonrotating black hole solutions

Alexander Burinskii, Emilio Elizalde, Sergi R. Hildebrandt, and Giulio Magli
Phys. Rev. D 65, 064039 – Published 5 March 2002
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Abstract

A unified approach to regular interiors of black holes with smooth matter distributions in the core region is given. The approach is based on a class of Kerr-Schild metrics representing minimal deformations of the Kerr-Newman solution, and allows us to give a common treatment for (charged and uncharged) rotating and nonrotating black holes. It is shown that the requirement of smoothness of the source constrains the structure of the core region in many respects: in particular, for Schwarzschild holes a de Sitter core can be selected, which is surrounded by a smooth shell giving a leading contribution to the total mass of the source. In the rotating, noncharged case the source has a similar structure, taking the form of a (anisotropic and rotating) de Sitter–like core surrounded by a rotating elliptic shell. The Kerr singular ring is regularized by anisotropic matter rotating in the equatorial plane, so that the negative sheet of the Kerr geometry is absent. In the charged case the sources take the form of “bags,” which can have de Sitter or anti–de Sitter interiors and a smooth domain wall boundary, with a tangential stress providing charge confinement. The Arnowitt-Deser-Misner and Tolman relations are used to calculate the total mass of the sources.

  • Received 26 September 2001

DOI:https://doi.org/10.1103/PhysRevD.65.064039

©2002 American Physical Society

Authors & Affiliations

Alexander Burinskii*

  • Gravity Research Group, NSI, Russian Academy of Sciences, B. Tulskaya 52, Moscow 113191, Russia

Emilio Elizalde

  • Instituto de Ciencias del Espacio (CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC/CSIC), Edifici Nexus, Gran Capità 2-4, 08034 Barcelona, Spain

Sergi R. Hildebrandt

  • Institut d’Estudis Espacials de Catalunya (IEEC/CSIC), Edifici Nexus, Gran Capità 2-4, 08034 Barcelona, Spain

Giulio Magli§

  • Dipartimento di Matematica del Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy

  • *Email address: bur@ibrae.ac.ru
  • Presently on leave at the Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307. Email address: elizalde@ieec.fcr.es
  • Email address: hildebrandt@ieec.fcr.es
  • §Email address: magli@mate.polimi.it

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Issue

Vol. 65, Iss. 6 — 15 March 2002

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