A Static Spherically Symmetric Solution of the Einstein-aether Theory

TL;DR

This paper derives a static spherically symmetric solution in Einstein-aether theory, revealing a black hole-like structure with unique asymptotic behavior and horizon properties, differing from classical solutions like Reissner-Nordstrom.

Contribution

It presents a new exact solution in Einstein-aether theory with specific coupling constants, highlighting differences from known solutions in asymptotic behavior and horizon structure.

Findings

Solution has an inner Cauchy horizon and an outer event horizon.

The spacetime approaches a two-dimensional sphere asymptotically.

Electric potential is regular except at the singularity.

Abstract

By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an inner Cauchy horizon and an outer black hole event horizon. But a remarkable difference from the Reissner-Nordstrom solution is that it is not asymptotically flat but approaches a two dimensional sphere. The resulting electric potential is regular in the whole spacetime except for the curvature singularity. On the other hand, the magnetic potential is divergent on both Cauchy horizon and the outer event horizon.