Black hole solutions in the revised Deser-Woodard nonlocal theory of gravity

TL;DR

This paper explores black hole solutions in a revised nonlocal gravity model, reformulating the equations for simplicity, and finds new solutions with deviations from Schwarzschild, enhancing understanding of nonlocal gravity in strong fields.

Contribution

It introduces a simplified tetrad-based formulation of the revised Deser-Woodard nonlocal gravity model and analytically derives new black hole solutions with specific metric corrections.

Findings

Black hole solutions with inverse power-law corrections to Schwarzschild metric.

Analytical reconstruction of the nonlocal distortion function.

Quantification of deviations from classical Schwarzschild black holes.

Abstract

We consider the revised Deser-Woodard model of nonlocal gravity by reformulating the related field equations within a suitable tetrad frame. This transformation significantly simplifies the treatment of the ensuing differential problem while preserving the characteristics of the original gravitational theory. We then focus on static and spherically symmetric spacetimes in vacuum. Hence, we demonstrate that the gravitational theory under study admits a class of black hole solutions characterized by an inverse power-law correction to the Schwarzschild $g_{tt}$ metric function and a first-order perturbation of the $g_{rr}$ Schwarzschild component. Then, through a stepwise methodology, we analytically solve the full dynamics of the theory, finally leading to the reconstruction of the nonlocal distortion function, within which the new black hole solutions arise. Furthermore, we analyze the geometric properties of the obtained solutions and quantify the deviations from the Schwarzschild prediction. This work provides new insights into compact object configurations and advances our understanding of nonlocal gravity theories in the strong-field regime at astrophysical scales.