Spherically Symmetric Solutions in Higher-Derivative Gravity

TL;DR

This paper investigates static, spherically symmetric solutions in higher-derivative gravity theories, revealing three distinct families of solutions including black holes, nonsingular vacua, and wormholes, with implications for quantum gravity models.

Contribution

It provides a detailed classification of solutions in quadratic curvature gravity, including new families beyond Schwarzschild, and analyzes their properties and physical relevance.

Findings

Identified three asymptotic solution families: Schwarzschild, non-Schwarzschild black holes, and nonsingular vacua.

Discovered solutions resembling wormholes that connect different spacetime sheets.

Analyzed the parameter space and physical conditions for each solution family.

Abstract

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type `no-hair' theorem. From a Frobenius analysis of the asymptotic small-radius behaviour, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analysed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match on to an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to `vacuum' solutions. In addition to the three families identified from near-origin behaviour, there are solutions that may be identified as `wormholes', which can match symmetrically on to another sheet of spacetime at finite radius.