Hawking--Page phase transitions in four-dimensional Einstein--Gauss--Bonnet gravity

Wang, Yuan‐Yuan; Su, Bing‐Yu; Li, Nan

doi:10.48550/arxiv.2008.01985

Cited by 15 publications

(18 citation statements)

References 68 publications

(74 reference statements)

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“…As discussed, the canonical ensemble consists of a series of black hole spacetimes with arbitrary radius. The probability distribution of these black hole states ρ(r, t), which is a function of the black hole radius r and time t, satisfies the Fokker-Planck equation on the free energy landscape [23,[28][29][30][31] ∂ρ(r, t) ∂t = D ∂ ∂r e −βG(r) ∂ ∂r e βG(r) ρ(r, t) , (18) where β = 1/kT is the inverse temperature and D = kT /ζ is the diffusion coefficient with k being the Boltzman constant and ζ being dissipation coefficient. We take k = ζ = 1 without loss of generality.…”

Section: B Probabilistic Evolution On the Free Energy Landscapementioning

confidence: 99%

“…In [10], the vacuum solution found by Glavan and Lin in [1] was generalized to be charged in AdS space. Then, the thermodynamics and phase transitions in extended phase space, where the cosmological constant is taken as the thermodynamic pressure, was studied in [11][12][13][14][15][16][17][18][19]. Especially, it is shown in [14] that there exists the small-large black hole phase transition both in the canonical ensemble and in the grand canonical ensemble, which has an analogy of the van der Walls liquid-gas phase transition.…”

Section: Introductionmentioning

confidence: 99%

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Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

Li¹,

Wang²

2020

Preprint

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By treating black hole as a state in canonical ensemble or in grand canonical ensemble, we study the phase transition and the kinetics of the four dimensional charged Anti-de Sitter (AdS) black hole in Gauss-Bonnet (GB) gravity based on the free energy landscape. Below the critical temperature, the free energy landscape topography has the shape of double basins with each representing one stable/unstable black hole phase (the small or the large black hole). The thermodynamic small/large black hole phase transition is determined by the equal depths of the basins. We also demonstrate the underlying kinetics of the phase transition by studying the time evolution of the probability distribution of the state in the ensemble as well as the mean first passage time (MFPT) and the kinetic fluctuations of the state switching process caused by the thermal fluctuations. The results show that the final distribution is determined by the Boltzmann law and the MFPT and its fluctuation are closely related to the free energy landscape topography through the barrier heights between the small and the large black hole states and the ensemble temperature. Furthermore, we provide a complete description of the kinetics of phase transition by investigating the temperature dependence of the MFPT and the kinetic fluctuations with different physical parameters. It is shown that the free energy is the result of the delicate balance and competition between the two relatively large numbers, the energy and entropy multiplied by temperature compared to kT . Low energy (mass) and low entropy can give rise to a stable thermodynamic state in terms of free energy minimum (energy/mass preferred) while the high energy (mass) and high entropy (entropy preferred) can also give rise to a stable state in terms of free energy minimum. The comparable free energy barrier with respect to kT makes it possible for the switching from small size black hole state to the large size black hole state under thermal fluctuations and vice versa. When the GB coupling coupling constant increases, or the electric charge (potential) increases, or the pressure (absolute value of cosmological constant) decreases, it is easier for the small black hole state to escape to the large black hole state. Meanwhile, the inverse process becomes harder, i.e. the small (large) black hole state becomes less (more) stable.

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Section: B Probabilistic Evolution On the Free Energy Landscapementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

Li¹,

Wang²

2020

Preprint

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“…The Hawking-Page phase transition has been widely studied in the literature from holography to modified gravity theories [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In general, these studies are based on the assumption that black holes can be treated as the thermodynamic entities.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of Hawking-Page phase transition with the non-Markovian effects

Li,

Wang

2022

Preprint

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Based on the free energy landscape description of Hawking-Page phase transition, the transition process from the Schwarzschild-anti-de Sitter black hole to the thermal anti-de Sitter space are considered to be stochastic under the thermal fluctuations. If the correlation time of the effective thermal bath is comparable or even longer than the oscillating time of the spacetime state in the potential well on the free energy landscape, the non-Markovian model of the black hole phase transition is required to study the kinetics of the transition processes. The non-Markovian or memory effect is represented by the time dependent friction kernel and the kinetics is then governed by the generalized Langevin equation complemented by the free energy potential. As the concrete examples, we study the effects of the exponentially decay friction kernel and the oscillatory friction kernel on the kinetics of Hawking-Page phase transition. For the exponentially decayed friction, the non-Markovian effects promote the transition process, and for the oscillatory friction, increasing the oscillating frequency also speeds up the transition process.

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“…The consequences of the theory is widely investigated in the literature, exploring its effects in black-holes [10], wormholes [11], compact stars [12] and also in cosmology [13]. Also, many works has been done to generalize the idea to higher/lower dimensions, relations to other theories and also its quantum aspects of the theory [14]. For example, in [15], the authors showed that in order to have a well-defined linearized theory the metric should be locally conformally flat.…”

Section: Introductionmentioning

confidence: 99%

Anisotropy in constraint 4D Gauss-Bonnet gravity

Shahidi,

Khosravi

2021

Preprint

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Recently a new 4D Einstein-Gauss-Bonnet theory has been introduced [Phys. Rev. Lett. 124 (2020) 081301] with a serious debate that it does not possess a covariant equation of motion in 4D. In this note, we will present a new proposal to make this happen, by introducing a Lagrange multiplier to the action which eliminates the higher dimensional term from the equation of motion. The theory has then a covariant 4D equation of motion which is useful to study the less symmetric metrics. On top of FRW universe, the constraint theory is equivalent to the original 4D Einstein-Gauss-Bonnet gravity. We will also consider the anisotropy of the model and compare the theory with observational data. We will see that the theory becomes non-conservative and the matter density abundance falls more rapidly at larger redshifts compared to the conservative matter sources.

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Hawking--Page phase transitions in four-dimensional Einstein--Gauss--Bonnet gravity

Cited by 15 publications

References 68 publications

Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape

Kinetics of Hawking-Page phase transition with the non-Markovian effects

Anisotropy in constraint 4D Gauss-Bonnet gravity

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