The phase diagram of Einstein-Weyl gravity

TL;DR

This paper presents a phase diagram for Einstein-Weyl gravity, classifying solutions based on mass and Yukawa-like corrections, with implications for compact stars and their equations of state.

Contribution

It provides the first classification of Einstein-Weyl solutions in terms of asymptotic gravitational fields and introduces a phase diagram illustrating different solution types.

Findings

Different equations of state lead to distinct Yukawa corrections.

The phase diagram maps solution types by mass and correction strength.

Implications for phenomenology of compact stars.

Abstract

Thanks to their interpretation as first order correction of General Relativity at high energies, quadratic theories of gravity gained much attention in recent times. Particular attention has been drawn to the Einstein-Weyl theory, where the addition of the squared Weyl tensor to the action opens the possibility of having non-Schwarzschild black holes in the classical spectrum of the theory. Static and spherically symmetric solutions of this theory have been studied and classified in terms of their small scales behaviour; however, a classification of these solutions in terms of the asymptotic gravitational field is still lacking. In this paper we address this point and present a phase diagram of the theory, where the different types of solutions are shown in terms of their mass and the strength of a Yukawa-like correction to the gravitational field. In particular we will show that, in the case of compact stars, different equations of state imply different Yukawa corrections to the gravitational potential, with possible phenomenological implications.