Charged Gauss-Bonnet Black Holes Research Articles

Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives

Exploring the phase transition in charged Gauss–Bonnet black holes: a holographic thermodynamics perspectives

No scalar-haired Cauchy horizon theorem in charged Gauss–Bonnet black holes

Recently, a “no inner (Cauchy) horizon theorem” for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document}) black holes, as in the case without GB term. On the other hand, for the non-planar (k=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 1$$\\end{document}) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a “no-go theorem” for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions.

Thermodynamics and phase transition in central charge criticality of charged Gauss-Bonnet AdS black holes

In this paper, we investigate the thermodynamics of D-dimensional charged Gauss-Bonnet black holes in anti-de Sitter spacetime. By considering the variations of the cosmological constant, the Newton's constant and the Gauss-Bonnet coupling constant in bulk, one can rewrite the first law of thermodynamics in a holographic form, where the contributions of thermodynamical variables in bulk and the boundary field theory are both included. Based on this approach, we study the phase transition in the central charge criticality when D=4, 5, and 6. Besides, a triple point where the small/intermediate/large black holes can coexist is found in D=6.

Charged Gauss–Bonnet black holes supporting non-minimally coupled scalar clouds: analytic treatment in the near-critical regime

Recent numerical studies have revealed the physically intriguing fact that charged black holes whose charge-to-mass ratios are larger than the critical value (Q/M)_{text {crit}}=sqrt{2(9+sqrt{6})}/5 can support hairy matter configurations which are made of scalar fields with a non-minimal negative coupling to the Gauss–Bonnet invariant of the curved spacetime. Using analytical techniques, we explore the physical and mathematical properties of the composed charged-black-hole-nonminimally-coupled-linearized-massless-scalar-field configurations in the near-critical Q/Mgtrsim (Q/M)_{text {crit}} regime. In particular, we derive an analytical resonance formula that describes the charge-dependence of the dimensionless coupling parameter bar{eta }_{text {crit}}=bar{eta }_{text {crit}}(Q/M) of the composed Einstein–Maxwell-nonminimally-coupled-scalar-field system along the existence-line of the theory, a critical border that separates bald Reissner–Nordström black holes from hairy charged-black-hole-scalar-field configurations. In addition, it is explicitly shown that the large-coupling -bar{eta }_{text {crit}}(Q/M)gg 1 analytical results derived in the present paper for the composed Einstein–Maxwell-scalar theory agree remarkably well with direct numerical computations of the corresponding black-hole-field resonance spectrum.

Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.

Instability in charged Gauss–Bonnet–de Sitter black holes

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.

Infinitesimally thin static scalar shells surrounding charged Gauss-Bonnet black holes

We reveal the existence of a new form of spontaneously scalarized black-hole configurations. In particular, it is proved that Reissner-Nordström black holes in the highly charged regime Q/M > (Q/M)crit = sqrt{21}/5 can support thin matter shells that are made of massive scalar fields with a non-minimal coupling to the Gauss-Bonnet invariant of the curved spacetime. These static scalar shells, which become infinitesimally thin in the dimensionless large-mass Mμ » 1 regime, hover a finite proper distance above the black-hole horizon [here {M, Q} are respectively the mass and electric charge of the central supporting black hole, and μ is the proper mass of the supported scalar field]. In addition, we derive a remarkably compact analytical formula for the discrete resonance spectrum {left{eta left(Q/M, Mmu; nright)right}}_{n=0}^{n=infty } of the non-trivial coupling parameter which characterizes the bound-state charged-black-hole-thin-massive-scalar-shell cloudy configurations of the composed Einstein-Maxwell-scalar field theory.

Extended thermodynamics and entropic force of de Sitter space–time with charged Gauss–Bonnet Black Hole

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss–Bonnet gravity in low dimensions. In this paper, we investigate extended thermodynamics and entropic force of de Sitter space–time with charged Gauss–Bonnet black hole. Think of four-dimensional charged Gauss–Bonnet Black Hole in de Sitter space–time as a thermodynamic system, the state parameters of Space–time must satisfy the basic equations of thermodynamics. By using the functional relation between the state parameters in the basic equation, the equivalent temperature and the space–time entropy of the state parameters satisfying the first law of thermodynamics are obtained. The interaction force between the horizon of the black hole and the cosmic horizon is composed of two parts, one of which is proportional to the Gauss–Bonnet factor. The other part is only related to the ratio of the two horizons. The entropic forces between the two event horizons promote the separation of the cosmic horizon from the black hole event horizon, but the entropic forces of the two parts vary with the position ratio of the two event horizons. This paper explores the characteristics of four-dimensional Gauss–Bonnet gravity and seeks for the intrinsic factors of the expansion of the universe by analyzing the variation law of entropy force between two horizons with the position ratio.

Entropic force between two horizons of a charged Gauss-Bonnet black hole in de Sitter spacetime

The basic equations of the thermodynamic system give the relationship between the internal energy, entropy and volume of two neighboring equilibrium states. By using the functional relationship between the state parameters in the basic equation, we give the differential equation satisfied by the entropy of spacetime. We can obtain the expression of the entropy by solving the differential equationy. This expression is the sum of entropy corresponding to the two event horizons and the interaction term. The interaction term is a function of the ratio of the locations of the black hole horizon and the cosmological horizon. The entropic force, which is strikingly similar to the Lennard-Jones force between particles, varies with the ratio of the two event horizons. The discovery of this phenomenon makes us realize that the entropic force between the two horizons may be one of the candidates to promote the expansion of the universe.

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a 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, 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 contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.

Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity.

Static charged Gauss-Bonnet black holes cannot be overcharged by the new version of gedanken experiments

Based on the new version of the gedanken experiments proposed by Sorce and Wald, we examine the weak cosmic censorship conjecture (WCCC) under the spherically charged infalling matter collision process in the static charged Gauss-Bonnet black holes. After considering the null energy condition and assuming the stability condition, we derive the perturbation inequality of the matter source. As a result, we find that the static charged Gauss-Bonnet black holes cannot be overcharged under the second-order approximation of the perturbation when the null energy condition is taken into account, although they can be destroyed in the old version of gedanken experiments. Our result shows that the WCCC holds for the above collision process in the Einstein-Maxwell-Gauss-Bonnet gravity and indicates that WCCC may also be valid in the higher curvature gravitational theories.

Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes

In this paper, we study the thermodynamic geometry of charged Gauss-Bonnet black holes (and Reissner-Nordstr\"om black holes, for the sake of comparison) in anti--de Sitter spacetimes in both ($T$, $V$) and ($S$, $P$) planes. The thermodynamic phase space is known to have an underlying contact and metric structure; Ruppeiner geometry then naturally arises in this framework. Sign of Ruppeiner curvature can be used to probe the nature of interactions between the black hole microstructures. It is found that there are both attraction and repulsion dominated regions which are in general determined by the electric charge, Gauss-Bonnet coupling, and horizon radius of the black hole. The results are physically explained by considering that these black hole systems consist of charged as well as neutral microstructures much like a binary mixture of fluids.

Geometrothermodynamic analysis and P–V criticality of higher dimensional charged Gauss–Bonnet black holes with first order entropy correction

We consider a charged Gauss-Bonnet black hole in $d$-dimensional spacetime and examine the effect of thermal fluctuations on the thermodynamics of the concerned black hole. At first we take the first order logarithmic correction term in entropy and compute the thermodynamic potentials like Helmholtz free energy $F$, enthalpy $H$ and Gibbs free energy $G$ in the spherical, Ricci flat and hyperbolic topology of the black hole horizon, respectively. We also investigate the $P$-$V$ criticality and calculate the critical volume $V_c$, critical pressure $P_c$ and critical temperature $T_c$ using different equations when $P$-$V$ criticality appears. We show that there is no critical point without thermal fluctuations for this type of black hole. We find that the presence of logarithmic correction in it is necessary to have critical points and stable phases. Moreover, we study the stability of the black holes by employing the specific heat. Finally, we study the geometrothermodynamics and analyse the Ricci scalar of the Ruppeiner metric graphically for the same.

Charged Gauss-Bonnet black holes with curvature induced scalarization in the extended scalar-tensor theories

Recently new scalarized black hole solutions were constructed in the extended scalar-tensor-Gauss-Bonnet gravity, where the scalar field is sourced by the curvature of the spacetime via the Gauss-Bonnet invariant. A natural extension of these results is to consider the case of nonzero black hole charge. In addition we have explored a large set of coupling functions between the Gauss-Bonnet invariant and the scalar field, that was not done until now even in the uncharged case, in order to understand better the behavior of the solutions and the deviations from pure general relativity. The results show that in the case of nonzero black hole charge two bifurcation points can exist - one at larger masses where the scalarized solutions bifurcated from the Reissner-Nordstrom one, and one at smaller masses where the scalar charge of the solutions decreases again to zero and the branch merges again with the GR one. All of the constructed scalarized branches do not reach an extremal limit. We have examined the entropy of the black holes with nontrivial scalar field and it turns out, that similar to the uncharged case, the fundamental branch which possesses scalar field with no nodes is thermodynamically favorable over the Reissner-Nordstrom one for the considered coupling functions, while the rest of the branches possessing scalar field with one or more zeros have lower entropy compared to the GR case and they are supposed to be unstable.

Joule-Thomson expansion of charged Gauss-Bonnet black holes in AdS space

The Joule-Thomson expansion process is studied for charged Gauss-Bonnet black holes in AdS space. First, in five-dimensional space-time, the isenthalpic curve in $T\ensuremath{-}P$ graph is obtained and the cooling-heating region is determined. Second, the explicit expression of Joule-Thomson coefficient is obtained from the basic formulas of enthalpy and temperature. Our methods can also be applied to van der Waals system as well as other black hole systems. And the inversion curve $\stackrel{\texttildelow{}}{T}(\stackrel{\texttildelow{}}{P})$ which separates the cooling region and heating region is obtained and investigated. Third, interesting dependence of the inversion curves on the charge ($Q$) and the Gauss-Bonnet parameter ($\ensuremath{\alpha}$) is revealed. In $\stackrel{\texttildelow{}}{T}\ensuremath{-}\stackrel{\texttildelow{}}{P}$ graph, the cooling region decreases with charge, but increases with the Gauss-Bonnet parameter. Fourth, by applying our methods, the Joule-Thomson expansion process for $\ensuremath{\alpha}=0$ case in four dimension is studied, where the Gauss-Bonnet AdS black hole degenerates into RN-AdS black hole. The inversion curves for van der Waals systems consist of two parts. One has positive slope, while the other has negative slope. However, for black hole systems, the slopes of the inversion curves are always positive, which seems to be a universal feature.

Phase Transition of the Higher Dimensional Charged Gauss-Bonnet Black Hole in de Sitter Spacetime

We study the phase transition of charged Gauss-Bonnet-de Sitter (GB-dS) black hole. For black holes in de Sitter spacetime, there is not only black hole horizon, but also cosmological horizon. The thermodynamic quantities on both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are additional connections between them. Using the effective temperature approach, we obtained the effective thermodynamic quantities of charged GB-dS black hole. According to Ehrenfest classification, we calculate some response functions and plot their figures, from which one can see that the spacetime undergoes a second-order phase transition at the critical point. It is shown that the critical values of effective temperature and pressure decrease with the increase of the value of GB parameterα.

Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state $T=T(v, P)$, we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the $T-v$ ($T-r_{h}$) line with fixed pressure $P$. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge $Q$ and dimension $d$. The result shows that the small/large black hole phase transitions appear for any $d$, which is reminiscent of the liquid/gas transition of a van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for $d=6$ and $Q\in(0.1705, 0.1946)$.

P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space

We study the P − V criticality and phase transition in the extended phase space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. The black holes can have a Ricci flat (k = 0), spherical (k = 1), or hyperbolic (k = −1) horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black holes, no P − V criticality and phase transition appear, while for the black holes with a spherical horizon, even when the charge of the black hole is absent, the P − V criticality and the small black hole/large black hole phase transition will appear, but it happens only in d = 5 dimensions; when the charge does not vanish, the P − V criticality and the small black hole/large phase transition always appear in d = 5 dimensions; in the case of d ≥ 6, to have the P − V criticality and the small black hole/large black hole phase transition, there exists an upper bound for the parameter $ b=\widetilde{\alpha }{{\left| Q \right|}^{{{-2 \left/ {{\left( {d-3} \right)}} \right.}}}} $ , where $ \widetilde{\alpha } $ is the Gauss-Bonnet coefficient and Q is the charge of the black hole. We calculate the critical exponents at the critical point and find that for all cases, they are the same as those in the van der Waals liquid-gas system.

Hairy charged Gauss-Bonnet solitons and black holes

We study the stability of ($4+1$)-dimensional charged Gauss-Bonnet black holes and solitons. We observe an instability related to the condensation of a scalar field and construct explicit ``hairy'' black hole and soliton solutions of the full system of coupled field equations. We investigate the cases of a massless scalar field as well as that of a tachyonic scalar field. The solitons with scalar hair exist for a particular range of the charge and the gauge coupling. This range is such that for intermediate values of the gauge coupling a ``forbidden band'' of charges for the hairy solitons exists. We also discuss the behavior of the black holes with scalar hair when changing the horizon radius and/or the gauge coupling and find that various scenarios at the approach of a limiting solution appear. One observation is that hairy Gauss-Bonnet black holes never tend to a regular soliton solution in the limit of vanishing horizon radius. We also prove that extremal Gauss-Bonnet black holes can not carry massless or tachyonic scalar hair and show that our solutions tend to their planar counterparts for large charges.