Black Holes and Wormholes Beyond Classical General Relativity

TL;DR

This paper explores static spherically symmetric solutions in modified gravity models, analyzing black holes and wormholes with quantum corrections, and finds that quantum effects do not resolve singularities or convert black holes into traversable wormholes.

Contribution

It investigates non-singular static metrics and quantum corrections in higher-order $F(R)$ gravity, providing new insights into black hole and wormhole solutions beyond classical general relativity.

Findings

Quantum corrections do not resolve singularities at r=0.

Effective metrics remain related to black holes, not traversable wormholes.

Quantum effects do not convert black holes into traversable wormholes.

Abstract

In the paper, only Static Spherically Symmetric space-times in four dimensions are considered within modified gravity models. The non-singular static metrics, including black holes not admitting a de Sitter core in the center and traversable wormholes, are reconsidered within a class of higher-order $F(R)$, satisfying the constraints $F(0)=\frac{dF}{dR}(0)=0$. Furthermore, by making use of the so-called effective field theory formulation of gravity, the quantum corrections to Einstein-Hilbert's action due to higher-derivative terms related to curvature invariants are investigated. In particular, in the case of Einstein-Hilbert action plus cubic curvature Goroff-Sagnotti contribution, the second-order correction in the Goroff-Sagnotti coupling constant is computed. In general, it is shown that the effective metrics, namely Schwarzschild expression plus small quantum corrections, are related to black holes and not to traversable wormholes. In this framework, within the approximation considered, the resolution of singularity for $r=0$ is not accomplished. The related properties of these solutions are investigated.