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Register a new userDynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape
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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.
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By treating the black hole event horizon as a stochastic thermal fluctuating variable for small-large black hole phase transition, we investigate the dynamical process of phase transition for the Kerr AdS black holes on free energy landscape. We find that the extremal points of the off-shell Gibbs free energy correspond to physical black holes. For small-large black hole phase transition, the off-shell Gibbs free energy exhibits a double well behavior with the same depth. Contrary to previous research for the dynamics of phase transition for the Kerr-Newman AdS family black holes on free energy landscape, we find that there is a lower bound for the order parameter and the lower bound corresponds to extremal black holes. In particular, the off-shell Gibbs free energy is zero instead of divergent as previous work suggested for vanishing black hole horizon radius, which corresponds to the Gibbs free energy of thermal AdS space. The investigation for the evolution of the probability distribution for the phase transition indicates that the initial stable small (large) black hole tends to switch to stable large (small) black hole. Increasing the temperature along the coexistence curve, the switching process becomes faster and the probability distribution reaches the final stationary Boltzmann distribution at a shorter time. The distribution of the first passage time indicates the time scale of the small-large black hole phase transition, and the peak of the distribution becomes sharper and shifts to the left with the increase of temperature along the coexistence curve. This suggests that a considerable first passage process occurs at a shorter time for higher temperature.
We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $alpha$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.
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.
This work is devoted to the exploration of shadow cast and center of mass energy in the background of a 4-dimensional charged Gauss-Bonnet AdS black hole. On investigating particle dynamics, we have examined BHs metric function. Whereas, with the help of null geodesics, we pursue to calculate the celestial coordinates and the shadow radius of the black hole. We have made use of the hawking temperature to study the energy emission rate. Moreover, we have explored the center of mass energy and discussed its characteristics under the influence of spacetime parameters. For a better understanding, we graphically represent all of our main findings. The acquired result shows that both charge and AdS radius ($l$) decrease the shadow radius, while the Gauss-Bonnet coupling parameter $alpha$ increases the shadow radius in AdS spacetime. On the other hand, both $Q$ and $alpha$ result in diminishing the shadow radius in asymptotically flat spacetime. Finally, we investigate the energy emission rate and center of mass energy under the influence of $Q$ and $alpha$.
We report on a numerical investigation of the stability of scalarized black holes in Einstein dilaton Gauss-Bonnet (EdGB) gravity in the full dynamical theory, though restricted to spherical symmetry. We find evidence that for sufficiently small curvature-couplings the resulting scalarized black hole solutions are nonlinearly stable. For such small couplings, we show that an elliptic region forms inside these EdGB black hole spacetimes (prior to any curvature singularity), and give evidence that this region remains censored from asymptotic view. However, for coupling values superextremal relative to a given black hole mass, an elliptic region forms exterior to the horizon, implying the exterior Cauchy problem is ill-posed in this regime.
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