Shrouded black holes in Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates black holes in Einstein-Gauss-Bonnet gravity with a scalar field, revealing scalar wall formation near horizons, analytical and numerical solutions, and cosmological consistency including gravitational wave speed predictions.

Contribution

It introduces a novel scalar-Gauss-Bonnet coupling model with spontaneous symmetry restoration near black holes, providing analytical and numerical solutions and discussing cosmological implications.

Findings

Scalar walls form near black hole horizons under certain conditions.

Analytical solutions are derived in the test field regime.

Model predicts gravitational wave speed close to light speed.

Abstract

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like potential. For a proper choice of sign, the non-minimal coupling to gravity leads to symmetry restoration near the black hole horizon, prompting the development of the scalar wall in its vicinity. The wall thickness depends on the bare mass of the scalar and can be much smaller than the Schwarzschild radius. In a weakly coupled regime, the quadratic coupling to the Gauss-Bonnet invariant effectively becomes linear, and no walls are formed. We find approximate analytical solutions for the scalar field in the test field regime, and obtain numerically static black hole solutions within this setup. We discuss cosmological implications of the model and show that it is fully consistent with the existence of an inflationary stage, unlike the spontaneous scalarization scenario assuming the opposite sign of the non-minimal coupling to gravity. Our model predicts the speed of gravitational waves to be extremely close to unity, - in a comfortable agreement with the observation of the GW170817 event and its electromagnetic counterpart.