Abstract
We construct spontaneously vectorized black holes where a real vector field is coupled to the Gauss-Bonnet invariant. We employ three coupling functions for the vector field, and determine the respective domains of existence of the vectorized black holes. These domains of existence are bounded by the marginally stable Schwarzschild black holes and the critical vectorized black holes. We also address the effects of a mass term. For a given black hole mass the horizon radius is smaller for the vectorized black holes than for the Schwarzschild black holes. Since the vector field vanishes at the horizon, there is no contribution from the Gauss-Bonnet term to the entropy of the vectorized black holes.
Highlights
Black holes in General Relativity (GR) satisfy uniqueness theorems [1]
The black holes of GR remain solutions of the generalized set of field equations, but succumb to a tachyonic instability induced by the contribution from the invariant in the vector field equation acting as an effective mass
Such spontaneously vectorized black hole solutions have been obtained in GR, where an additional vector field has been non-minimally coupled to the Maxwell invariant with an appropriate coupling function [72]
Summary
Black holes in General Relativity (GR) satisfy uniqueness theorems [1]. The Schwarzschild and Kerr black holes represent the static, respectively stationary rotating, black hole solutions of the Einstein equations in vacuum. Schwarzschild and Kerr black holes remain solutions of the EsGB equations independent of the value of the GB coupling constant They lose their stability when scalarization sets in. The black holes of GR remain solutions of the generalized set of field equations, but succumb to a tachyonic instability induced by the contribution from the invariant in the vector field equation acting as an effective mass. Such spontaneously vectorized black hole solutions have been obtained in GR, where an additional vector field has been non-minimally coupled to the Maxwell invariant with an appropriate coupling function [72].
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