Explore nonlinear black hole and cosmological solutions in nonlocal gravity (NLG)

Develop and analyze black hole solutions and cosmological models within the full nonlinear regime of nonlocal gravity (NLG), whose field equations are highly nonlinear partial integro-differential equations involving the causal kernel K(x, x'). Establish methods to solve these equations and explicitly obtain such nonlinear solutions.

Background

The paper outlines the nonlocal gravity (NLG) framework as a nonlocal extension of the teleparallel equivalent of general relativity, leading to modified Einstein equations with additional terms dependent on a nonlocal constitutive relation characterized by a causal kernel K(x, x'). The authors emphasize that the full nonlinear NLG field equations are highly complex partial integro-differential equations and explicitly state that the nonlinear regime, including black hole and cosmological solutions, has not been explored due to these difficulties.

To make progress, the paper adopts the local limit of NLG—introducing a scalar susceptibility S(x)—and demonstrates that Gödel’s universe is a solution in this limit when S is constant. This approach sidesteps the open challenge posed by the full nonlocal equations but does not resolve the need for genuine nonlinear NLG solutions for astrophysically relevant spacetimes.