Static spherically symmetric solutions in mimetic gravity: rotation curves & wormholes

TL;DR

This paper explores static spherically symmetric solutions in mimetic gravity with a potential, demonstrating how to model phenomena like galaxy rotation curves and wormholes without dark matter.

Contribution

It extends previous mimetic gravity models by incorporating a potential for the mimetic field, enabling reconstruction of various astrophysical and cosmological scenarios.

Findings

Reconstructed potentials that produce polynomial corrections to Schwarzschild spacetime.

Demonstrated how to explain galaxy rotation curves without dark matter.

Explored solutions leading to traversable wormholes.

Abstract

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering in addition a potential for the mimetic field. An appropriate choice of such potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which traversable wormholes. Finally, we analytically reconstruct potentials which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild spacetime. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.