Hybrid metric-Palatini gravity: black holes, wormholes, singularities and instabilities

TL;DR

This paper explores static vacuum solutions in hybrid metric-Palatini gravity, revealing diverse structures like naked singularities, wormholes, and black holes, and assesses their stability, contributing to understanding alternative gravity theories.

Contribution

It provides a detailed analysis of static spherically symmetric solutions in HMPG, including black holes, wormholes, and their stability, using scalar-tensor representation and exploring effects of scalar potentials.

Findings

Asymptotically flat solutions often contain naked singularities or wormholes.

Black hole solutions with extremal horizons are rare and special.

Some solutions with nonzero potentials describe stable black holes.

Abstract

The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor representation. This scalar-tensor theory coincides with general relativity with a conformally coupled scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $V (\phi)$, such that both Riemannian and Palatini Ricci scalars are zero, generic asymptotically flat solutions either contain naked singularities or describe traversable wormholes, and there are only special cases of black hole solutions with extremal horizons. There is also a one-parameter family of solutions with an infinite number of extremal horizons between static regions. Examples of analytical solutions with nonzero potentials $V (\phi)$ are also described, among them black hole solutions with simple horizons which are generic but, for canonical scalars, they require (at least partly) negative potentials. With phantom scalars there are ``black universe'' solutions that lead beyond the horizon to an expanding universe instead of a singularity. Most of the solutions under consideration turn out to be unstable under scalar monopole perturbations, but some special black hole solutions are stable.