The first law and Ruppeiner geometry for Grumiller black hole. (9th May 2018) - Yang, Si-Jiang; He, You-Biao; Du, Juan-Juan
Abstract: This paper presents a geometric derivation of the integral formula of the first law for Grumiller black hole, which is an exact example that the mass of the whole space-time is infinite, but the mass of the black hole is finite. The results show that the Rindler acceleration should be considered as a new thermodynamic variable. Having the first law, we investigate Ruppeiner geometry for Rindler acceleration fixed ensemble and pressure fixed ensemble. Both of the geometries are curved. To uncover possible microscopic interactions, we plot the graphs for curvature scalar and study its behavior. For pressure fixed ensemble, we find, by comparing with heat capacity, the vanishing point of curvature scalar indicating the change of stability.