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Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole

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 Publication date 2020
  fields Physics
and research's language is English




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In this paper, the new formalism of thermodynamic geometry proposed in [1] is employed in investigating phase transition points and the critical behavior of a Gauss Bonnet-AdS black hole in four dimensional spacetime. In this regard, extrinsic and intrinsic curvatures of a certain kind of hypersurface immersed in the thermodynamic manifold contain information about stability/instability of heat capacities. We, therefore, calculate the intrinsic curvature of the $Q$-zero hypersurface for a four-dimensional neutral Gauss Bonnet black hole case in the extended phase space. Interestingly, intrinsic curvature can be positive for small black holes at low temperature, which indicates a repulsive interaction among black hole microstructures. This finding is in contrast with the five-dimensional neutral Gauss Bonnet black hole with only dominant attractive interaction between its microstructures.



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In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes $R_Nt^2$ and $K_Nt$ are calculated with the temperature parameter $t=T/T_c-1$ where $T_c$ the critical value of the temperature. Near the critical point, we find that the critical amplitude of $R_Nt^2$ and $K_Nt$ is $-frac{1}{2}$ when $trightarrow0^+$, whereas $R_Nt^2approx -frac{1}{8}$ and $K_Ntapprox-frac{1}{4}$ in the limit $trightarrow0^-$. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.
Understanding the dynamic process of the thermodynamic phase transition can provide the deep insight into the black hole microscopic properties and structures. We in this paper study the dynamic properties of the stable small-large black hole phase transition for the five-dimensional neutral Gauss-Bonnet AdS black hole. Firstly, by using the first law of black holes, we prove that the extremal points of the free energy on the landscape denote the real black hole solutions satisfying the field equations. The local maximal and minimal points correspond to local unstable and stable black hole states, respectively. Especially, on the free energy landscape, the wells of the coexistence small and large black holes have the same depth. Then we investigate the probability evolution governed by the Fokker-Planck equation. Due to the thermal fluctuation, we find that the small (large) black hole state can transit to the large (small) black hole state. Furthermore, the first passage time is calculated. For each temperature, a single peak is presented, which suggests that there is a considerable fraction of the first passage events taking place at short time. And the higher the temperature is, the faster decrease of the probability is. These results will uncover some intriguing dynamic properties of the stable small-large black hole phase transition in modified 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.
107 - M. Bousder , M. Bennai 2021
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.
119 - Anurag Sahay , Rishabh Jha 2017
We obtain the Ruppeiner geometry associated with the non-extended state space ($Lambda$ constant) of the charged Gauss-Bonnet AdS (GB-AdS) black holes and confirm that the state space Riemannian manifold becomes strongly curved in regions where the black hole system develops strong statistical correlations in the grand canonical ensemble ($M$ and $Q$ fluctuating). We establish the exact proportionality between the state space scalar curvature $R$ and the inverse of the singular free energy near the isolated critical point for the grand canonical ensemble in spacetime dimension $d=5$, thus hopefully moving a step closer to the agenda of a concrete physical interpretation of $R$ for black holes. On the other hand, we show that while $R$ signals the Davies transition points (which exist in GB-AdS black holes for $d ge 6$) through its divergence, it does not scale as the inverse of the singular free energy there. Furthermore, adapting to the black hole case the ideas developed in cite{rupp2} in the context of pure fluids, we find that the state space geometry encodes phase coexistence and first order transitions, identifies the asymptotically critical region and even suggests a Widom line like crossover regime in the supercritical region for $5-d$ case. The sign of $R$ appears to imply a significant difference between the microscopic structure of the small and the large black hole branches in $d=5$. We show that thermodynamic geometry informs the microscopic nature of coexisting thermal GB-AdS and black hole phases near the Hawking-Page phase transition.
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