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Register a new userThermodynamics of Gauss-Bonnet-de Sitter Black Holes
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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 space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. In the uncharged case, we find both Hawking-Page and small-to-large black hole phase transitions, whose character depends on the sign of the Gauss-Bonnet coupling. In the charged case, we demonstrate the presence of a swallowtube, signaling a compact region in phase space where a small-to-large black hole transition occurs.
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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 based on the $AdS_2$ Breitenl{o}hner-Freedman (BF) bound at extremality and the dynamical instability via quasinormal modes by full numerical analysis. We uncover the gravitational instability in five spacetime dimensions and above, and construct the complete parameter space in terms of the ratio of event and cosmological horizons and the Gauss-Bonnet coupling. We show that the BF bound violation is a sufficient but not necessary condition for the presence of dynamical instability. While the physical origin of the instability without the Gauss-Bonnet term has been argued to be from the $AdS_2$ BF bound violation, our analysis suggests that the BF bound violation can not account for all physical origin of the instability for the charged Gauss-Bonnet black holes.
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 the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the black hole horizon can act as the order parameter to characterize the black hole phase transition. We also disclose that different from the five-dimensional neutral black holes, the charged ones allow the repulsive interaction among its microstructure for small black hole of higher temperature. Another significant difference between them is that the microscopic interaction changes during the small-large black hole phase transition for the charged case, where the black hole microstructure undergoes a sudden change. These results are helpful for peeking into the microstructure of charged black holes in the Gauss-Bonnet gravity.
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.
In this paper, we investigate a class of $5$-dimensional black holes in the presence of Gauss-Bonnet gravity with dyonic charges. At first step, thermodynamical quantities of the black holes and their behaviors are explored for different limits. Thermal stability and the possibility of the van der Waals like phase transition are addressed and the effects of different parameters on them are investigated. The second part is devoted to simulation of the trajectory of particles around these black holes and investigation of the angular frequency of particles motion. The main goal is understanding the effects of higher curvature gravity (Gauss-Bonnet gravity) and magnetic charge on the structure of black holes and the geodesic paths of particles moving around these black holes.
We obtain rotating black hole solutions to the novel 3D Gauss-Bonnet theory of gravity recently proposed. These solutions generalize the BTZ metric and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts, whose properties we also discuss. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss-Bonnet rotating black strings.
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