A Lifshitz Black Hole in Four Dimensional R^2 Gravity

Understand

We consider a higher derivative gravity theory in four dimensions with a negative cosmological constant and show that vacuum solutions of both Lifshitz type and Schr\"{o}dinger type with arbitrary dynamical exponent z exist in this system.

• Then we find an analytic black hole solution which asymptotes to the vacuum Lifshitz solution with z=3/2 at a specific value of the coupling constant.
• We analyze the thermodynamic behavior of this black hole and find that the black hole has zero entropy while non-zero temperature, which is very similar to the case of BTZ black holes in new massive gravity at a specific coupling.
• In addition, we find that the three dimensional Lifshitz black hole recently found by E.