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The fundamental equation of the thermodynamic system gives the relation between internal energy, entropy and volume of two adjacent equilibrium states. Taking higher dimensional charged Gauss-Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, the effective temperature of spacetime is the same, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contain an extra terms besides the sum of the entropies of the two horizons. The corrected terms of the entropy is a function of horizon radius ratio, and is independent of the charge of the spacetime.
We study the instability of the charged Gauss-Bonnet de Sitter black holes under gravito-electromagnetic perturbations. We adopt two criteria to search for an instability of the scalar type perturbations, including the local instability criterion bas
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for th
The basic equations of the thermodynamic system give the relationship between the internal energy, entropy and volume of two neighboring equilibrium states. By using the functional relationship between the state parameters in the basic equation, we g
We investigate the thermodynamics of Gauss-Bonnet black holes in asymptotically de Sitter spacetimes embedded in an isothermal cavity, via a Euclidean action approach. We consider both charged and uncharged black holes, working in the extended phase
We study the linear instability of the charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet-AdS black holes by exploring the quasinormal modes. We find that the linear instability is triggered by superradiance. The cha