Thermodynamic phase transition of Euler-Heisenberg-AdS black hole on free energy landscape

Abstract

We study the first order phase transition of Euler-Heisenberg-AdS black hole based on free energy landscape. By imposing the reflecting boundary conditions and the initial conditions, we discuss the probabilistic evolution for the black hole states using the Fokker-Planck equation. With the Euler-Heisenberg parameter (quantum electrodynamics parameter) a < 0, we observe that the large (small) Euler-Heisenberg-AdS black hole can have the probability to switch to the small (large) black hole. The coexistent small and large black hole states can be acquired for a certain condition.With 0 ≤ a ≤ 32 7 Q 2 , the system may be in no black hole state for some conditions. For the case of the initial wave packet is located at the small (large) black hole state, we observe that it can have the chance to transition to large (small) black hole state. Furthermore, we can obtain the thermodynamic stable state from the final stationary distribution which is determined by the Euler-Heisenberg parameter and the temperature.

Generalized free energy landscape of black hole phase transition

“…Note that the Euclidean time has the period β determined by the ensemble temperature T . Therefore, the metric (21) with the general time period also describes the Euclidean gravitational instanton with the conical singularity, the geometry of which is depicted in The finite part of the Einstein-Hilbert action includes the contributions from the conical singularity and the AdS bulk. The singularity contribution is proportional to the horizon area of the RNAdS black hole times the deficit angle 1 − β β H , where β H is the inverse Hawking temperature of the RNAdS black hole:…”

“…In this way, one can study the kinetics of black hole phase transition by using the Langevin equation for the dynamical trajectory evolution or the Fokker-Planck equation for the probabilistic evolution. The formalism has been applied to investigate the Markovian dynamics [8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the non-Markovian dynamics [22,23] of the black hole phase transitions.…”

Thermodynamics and Microstructures of Euler-Heisenberg Black Hole in a Cavity

“…Recently, the Euler-Heisenberg black holes in AdS space with QED effects was considered to investigate the influence on black hole phase transition and Ruppeiner geometry in the extended phase space [46]. Some other relevant works has been considered in the literature [47][48][49][50][51][52][53][54][55][56]. Inspired by these researches, we investigate the phase structures of Euler-Heisenberg black holes in a cavity and find some interesting phenomenons, especially the reentrant phase transition.…”

Motion of particles in a magnetically charged Euler-Heisenberg black hole with scalar hair

“…Also in [14] motions of charged particles around the Euler-Heisenberg AdS black hole were studied. A study of the thermodynamics of these black holes was performed in [15,16], while the stability of these black holes, calculating the quasinormal modes, was studied in [17]. Rotating black holes were found in [18,19], while the Euler-Heisenberg theory in modified gravity theories in [20][21][22] was studied and black hole solutions were analyzed.…”