Horizon Thermodynamics and Gravitational Field Equations in Horava-Lifshitz Gravity

Understand

We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Ho\v{r}ava-Lifshtiz theory with/without detailed balance.

• It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon.
• This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches.
• We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Ho\v{r}ava-Lifshtiz theory.