Exact Bachian singularity in quadratic gravity

TL;DR

This paper presents an explicit static spherically symmetric solution in quadratic gravity for specific parameter values, revealing a global geometric structure that aids understanding and benchmarking in the field.

Contribution

It provides the first explicit solution for a particular quadratic gravity model, enhancing understanding of spherical spacetimes and serving as a benchmark for solution methods.

Findings

Explicit solution with a central singularity and horizons for specific parameters

Reveals global geometric structure in quadratic gravity

Serves as a benchmark for solution accuracy

Abstract

For specifically coupled values of the quadratic gravity parameters, we present a fully explicit static spherically symmetric solution. It contains the central singularity surrounded by the black-hole or the cosmological horizon for the negative or positive cosmological parameter, respectively. This spacetime, thus, belongs to the already analyzed classes of solutions expressed in terms of the Frobenius expansions, continuous fractions, or numerical simulations; however, it has not been explicitly identified before. The purpose of the presented highly-constrained somehow unphysical model is to reveal a global geometric picture that may occur in spherical spacetimes within quadratic gravity, which is typically hidden in more general approximative solutions. At the same time, it can serve as a solid benchmark for evaluating the accuracy of the methods employed to obtain such solutions.