Black holes and wormholes in Deser-Woodard gravity

Abstract

The Deser-Woodard gravity is a modified theory of gravity in which nonlocality plays a central role. In this context, nonlocality is a consequence of the inverse of the d'Alembertian operator $\square^{-1}$ in the effective action. Here, exact black hole and wormhole solutions are built in the revised Deser-Woodard gravity following a recent approach, where a special tetrad frame simplifies the complicated field equations of the theory. Using the Schwarzschild metric and the Reissner-Nordstr\"om metric as initial seed solutions, the developed algorithm generates new traversable wormholes, singular black holes and a regular black hole as solutions of the vacuum field equations of the modified theory. Also, the auxiliary fields, which are responsible for the nonlocality, are computed. However, even for a regular black hole solution, in which spacetime does not contain a curvature singularity, the corresponding auxiliary fields diverge at the event horizon. Regarding observational results, the shadow angular radius is computed for the new solutions. In particular, the deviation of the Schwarzschild black hole in the Deser-Woodard gravity casts a larger shadow than the corresponding black hole in general relativity.