Structural stability of spherical horizons

TL;DR

This paper investigates the stability of spherical horizons under quadratic curvature corrections, revealing the existence of horizonless solutions in the second order approach but not in the restricted first order formulation.

Contribution

It demonstrates the structural stability of spherical horizons with quadratic curvature terms and compares second and first order formalisms, highlighting the emergence of horizonless solutions.

Findings

Generic solutions can match horizon solutions and horizonless families in second order formalism.

Horizonless solutions are absent in the restricted first order approach.

The stability analysis extends understanding of horizon structures in modified gravity theories.

Abstract

This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the contribution of operators quadratic in curvature. This we do both in the usual second order approach (in which the independent variable is the spacetime metric) and in the first order one (where the independent variables are the spacetime metric and the connection field). In second order, it is claimed that the generic solution in the asymptotic regime (large radius) can be matched not only with the usual solutions with horizons (like Schwarzschild-de Sitter) but also with a more generic (in the sense that it depends on more arbitrary parameters) horizonless family of solutions. It is however remarkable that these horizonless solutions are absent in the {\em restricted} (that is, when the background connection is the metric one) first order approach.