Black holes and wormholes in the Einstein-scalar-Gauss-Bonnet generalized theories of gravity

TL;DR

This dissertation explores black hole and wormhole solutions within Einstein-scalar-Gauss-Bonnet theories, demonstrating how arbitrary coupling functions can evade classical no-hair theorems and produce novel, physically characterized solutions including traversable wormholes without exotic matter.

Contribution

It introduces a broad class of Einstein-scalar-Gauss-Bonnet theories with arbitrary coupling functions, deriving new black hole and wormhole solutions that challenge existing no-hair theorems and include cosmological constant effects.

Findings

New black hole solutions with various coupling functions

Traversable wormholes without exotic matter

Black holes with de Sitter and anti-de Sitter asymptotics

Abstract

In this Ph.D. dissertation we study the emergence of black-hole and wormhole solutions in the framework of the Einstein-scalar-Gauss-Bonnet (EsGB) theory. Particularly we study a family of theories where the coupling function $f(\phi)$ between the scalar field of the theory and the quadratic Gauss-Bonnet gravitational term has an arbitrary form. At first, we analytically derive that the aforementioned family of theories may evade the constraints imposed by Bekenstein's No-Scalar Hair theorems and new solutions for black holes may be found. Then, using numerical integration methods we find solutions for black holes for many different forms of the coupling function. Also we derive their physical characteristics namely their mass, scalar charge, horizon area and entropy as well. Subsequently, by introducing a cosmological constant in the theory we investigate the existence of novel black-hole solutions. Specifically, assuming that the cosmological constant may be positive or negative we find numerical solutions which are asymptotically de Sitter or anti-de Sitter. In addition, as in the case of the asymptotically flat black holes, for each case we derive their physical characteristics. Finally, in the framework of the EsGB theory we derive novel wormhole solutions. The Gauss-Bonnet wormholes are traversable, may have a single or a double throat and do not demand the existence of exotic matter.