Nonperturbative gedanken experiments in Einstein-dilaton-Gauss-Bonnet gravity: nonlinear transitions and tests of the cosmic censorship beyond General Relativity

Abstract

As the only gravity theory with quadratic curvature terms and second-order field equations, Einstein-dilaton-Gauss-Bonnet gravity is a natural testbed to probe the high-curvature regime beyond General Relativity in a fully nonperturbative way. Due to nonperturbative effects of the dilatonic coupling, black holes in this theory have a minimum mass which separates a stable branch from an unstable one. The minimum mass solution is a double point in the phase diagram of the theory, wherein the critical black hole and a wormhole solution coexist. We perform extensive nonlinear simulations of the spherical collapse onto black holes with scalar hair in this theory, especially focusing on the region near the minimum mass. We study the nonlinear transition from the unstable to the stable branch and assess the nonlinear stability of the latter. Furthermore, motivated by modeling the mass loss due to Hawking radiation near the minimum mass at the classical level, we study the collapse of a phantom field onto the black hole. When the black-hole mass decreases past the critical value, the apparent horizon shrinks significantly, eventually unveiling a high-curvature elliptic region. We argue that evaporation in this theory is bound to either violate the weak cosmic censorship or to produce horizonless remnants. Addressing the end-state might require a different evolution scheme.

Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms

“…This conundrum is often overlooked, but was recently explored in Refs. [42,43], where non-linear numerical simulations of evaporating EsGB dilatonic black holes were performed, supporting the idea that the end-point of Hawking evaporation is likely a naked singularity, violating weak cosmic censorship. This is rather concerning scenario, raising question about the consistency of EsGB models.…”

“…For the dilatonic coupling, we focus on the γ = 1 case. Note, however, that as discussed in [42,43] the properties of black hole solutions might differ for other values of γ. In fact, for sufficiently negative values (γ −1), the small mass limit and the small size (radius) limit might not coincide, with small mass limit solutions being regular on and outside the horizon.…”

“…If β < β crit , the picture would be not too different to that of the dilatonic and linear couplings explored in the previous sections and Refs. [42,43], where the formation of a naked singularity is expected. However, if β > β crit , the evaporation process is expected to be similar to that of a Schwarzschild black hole, going all the way down to scales where quantum effects are expected to be important on general grounds, and our theory breaks down.…”

Dynamical spontaneous scalarization in Einstein-Maxwell-scalar models in anti-de Sitter spacetime

“…We will show later that for hyperbolic and power couplings, naked singularities also do not form. In eSTGB theory, the the cosmic censorship has been tested very recently [73,74]. They simulated the mass loss due to evaporation at the classical level using an auxiliary phantom field and suggested that either the weak cosmic censorship is violated or horizonless remnants are produced.…”

On Black Hole Thermodynamics, Singularity, and Gravitational Entropy

“…In addition to the Maxwell-dilaton case, recently some authors have investigated black hole evaporation in the presence of higher order curvature terms (with or without a dilaton), such as the Gauss-Bonnet term. It was found that cosmic censorship can be violated due to the formation of either a naked singularity or a high-curvature elliptic region [62][63][64][65].…”