Non-Spinning Black Holes in Alternative Theories of Gravity

TL;DR

This paper investigates non-spinning black holes within alternative gravity theories, analyzing their solutions, metric deformations, and observable effects like horizon shifts and gravitational wave corrections.

Contribution

It identifies classes of theories with solutions matching Einstein's equations and provides explicit metric deformations and observable predictions in the small coupling regime.

Findings

Existence of solutions matching Einstein's vacuum equations

Deformation of Schwarzschild metric in alternative theories

Quantified shifts in horizon and orbital parameters, and gravitational wave corrections

Abstract

We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and another that does not. In the latter, we find a deformation to the Schwarzschild metric that solves the modified field equations in the small coupling approximation. We calculate the event horizon shift, the innermost stable circular orbit shift, and corrections to gravitational waves, mapping them to the parametrized post-Einsteinian framework.