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On the Existence of Conformally Coupled Scalar Field Hair for Black Holes in (Anti-)de Sitter Space

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Abstract

The Einstein-conformally coupled scalar field system is studied in the presence of a cosmological constant. We consider a massless or massive scalar field with no additional self-interaction, and spherically symmetric black hole geometries. When the cosmological constant is positive, no scalar hair can exist and the only solution is the Schwarzschild–de Sitter black hole. When the cosmological constant is negative, stable scalar field hair exists provided the mass of the scalar field is not too large.

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  1. Department of Applied Mathematics, The University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK

    Elizabeth Winstanley

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  1. Elizabeth Winstanley
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Winstanley, E. On the Existence of Conformally Coupled Scalar Field Hair for Black Holes in (Anti-)de Sitter Space. Foundations of Physics 33, 111–143 (2003). https://doi.org/10.1023/A:1022871809835

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