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Register a new userLinear Instability of the Charged Massless Scalar Perturbation in Regularized 4D Charged Einstein-Gauss-Bonnet Anti de-Sitter Black Hole
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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 charged massless scalar perturbation becomes more unstable when increasing the Gauss-Bonnet coupling constant or the black hole charge. Meanwhile, decreasing} the AdS radius will make the charged massless scalar perturbation} more stable. The stable region in parameter space $(alpha,Q,Lambda)$ is given. Moreover, we find that the charged massless scalar perturbation is more unstable for larger scalar charge. The modes of multipoles are more stable than that of the monopole.
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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.
We study the charge of the 4D-Einstein-Gauss-Bonnet black hole by a negative charge and a positive charge of a particle-antiparticle pair on the horizons r- and r+, respectively. We show that there are two types of the Schwarzschild black hole. We show also that the Einstein-Gauss-Bonnet black hole charge has quantified values. We obtain the Hawking-Bekenstein formula with two logarithmic corrections, the second correction depends on the cosmological constant and the black hole charge. Finally, we study the thermodynamics of the EGB-AdS black hole.
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.
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.
We investigated the superradiance and stability of the novel 4D charged Einstein-Gauss-Bonnet black hole which is recently inspired by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. We found that the positive Gauss-Bonnet coupling consant $alpha$ enhances the superradiance, while the negative $alpha$ suppresses it. The condition for superradiant instability is proved. We also worked out the quasinormal modes (QNMs) of the charged Einstein-Gauss-Bonnet black hole and found that the real part of all the QNMs live beyond the superradiance condition and the imaginary parts are all negative. Therefore this black hole is superradiant stable. When $alpha$ makes the black hole extremal, there are normal modes.
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