Spontaneously vectorized Einstein-Gauss-Bonnet black holes

TL;DR

This paper constructs and analyzes spontaneously vectorized black holes coupled to the Gauss-Bonnet invariant, exploring their existence, stability, and properties with various coupling functions and mass effects.

Contribution

It introduces new vectorized black hole solutions with different coupling functions and examines their domains of existence and physical characteristics.

Findings

Vectorized black holes exist within bounded domains between Schwarzschild and critical solutions.

The horizon radius of vectorized black holes is smaller than that of Schwarzschild black holes for the same mass.

The vector field does not contribute to entropy since it vanishes at the horizon.

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.