A Static Spherically Symmetric Solution of the Einstein-aether Theory

Understand

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.