Thermodynamic relation on higher-dimensional black hole with arbitrary cosmological constant

We investigated the Goon–Penco (GP) relation on higher-dimensional Reissner–Nordström black holes with an arbitrary cosmological constant. We found that the GP relation retained its form in four- and higher-dimensional spacetimes. Thus, the reactions in the black holes are universal with respect to dimensionality. Furthermore, the GP relation was found to be universal on any state of the black hole, including near-extremal and near-Nariai cases. Thus, it was shown that the GP relation was prevalent for higher-dimensional Reissner–Nordström black holes with an arbitrary cosmological constant regardless of the initial state.