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On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space

Elizabeth Winstanley
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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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Elizabeth Winstanley. 2002-08-06. On the existence of conformally coupled scalar field hair for black holes in (anti-)de Sitter space. https://doi.org/10.1023/a%3A1022871809835

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