Branches Of Black Holes Research Articles

Topological natures of the Gauss-Bonnet black hole in AdS space

In the recent proposal [S. W. Wei et al., Black Hole Solutions as Topological Thermodynamic Defects, Phys. Rev. Lett. 129, 191101 (2022).], the black holes were viewed as topological thermodynamic defects by using the generalized off shell free energy. In this paper, we follow such proposal to study the local and global topological natures of the Gauss-Bonnet black holes in anti--de Sitter (AdS) space. The local topological natures are reflected by the winding numbers, where the positive and negative winding numbers correspond to the stable and unstable black hole branches. The global topological natures are reflected by the topological numbers, which are defined as the sum of the winding numbers for all black hole branches and can be used to classify the black holes into different classes. When the charge is present, we find that the topological number is independent on the values of the parameters, and the charged Gauss-Bonnet AdS black holes can be divided into the same class of the Reissner-Nordstr\"om anti-de Sitter black hole black holes with the same topological number 1. However, when the charge is absent, we find that the topological number has certain dimensional dependence. This is different from the previous studies, where the topological number is found to be a universal number independent of the black hole parameters. Furthermore, the asymptotic behaviors of curve $\ensuremath{\tau}({r}_{h})$ in small and large radii limit can be a simple criterion to distinguish the different topological number. We find a new asymptotic behavior as $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}0)=0$ and $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}\ensuremath{\infty})=0$ in the black hole system, which shows topological equivalency with the asymptotic behaviors $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}0)=\ensuremath{\infty}$ and $\ensuremath{\tau}({r}_{h}\ensuremath{\rightarrow}\ensuremath{\infty})=\ensuremath{\infty}$. We also give an intuitional proof of why there are only three topological classes in the black hole system under the condition $({\ensuremath{\partial}}_{{r}_{h}}S{)}_{P}>0$.

Black Hole Solutions as Topological Thermodynamic Defects.

In this Letter, employing the generalized off-shell free energy, we treat black hole solutions as defects in the thermodynamic parameter space. The results show that the positive and negative winding numbers corresponding to the defects indicate the local thermodynamical stable and unstable black hole solutions, respectively. The topological number defined as the sum of the winding numbers for all the black hole branches at an arbitrary given temperature is found to be a universal number independent of the black hole parameters. Moreover, this topological number only depends on the thermodynamic asymptotic behaviors of the black hole temperature at small and large black hole limits. Different black hole systems are characterized by three classes via this topological number. This number could help us in better understanding the black hole thermodynamics and, further, shed new light on the fundamental nature of quantum gravity.

Absence of isolated critical points with nonstandard critical exponents in the four-dimensional regularization of Lovelock gravity

Hyperbolic vacuum black holes in Lovelock gravity theories of odd order $N$, in which $N$ denotes the order of higher-curvature corrections, are known to have the so-called isolated critical points with nonstandard critical exponents (as $\alpha = 0$, $\beta = 1$, $\gamma = N-1$, and $\delta = N$), different from those of mean-field critical exponents (with $\alpha = 0$, $\beta = 1/2$, $\gamma = 1$, and $\delta = 3$). Motivated by this important observation, here, we explore the consequences of taking the $D \to 4$ limit of Lovelock gravity and the possibility of finding nonstandard critical exponents associated with isolated critical points in four-dimensions by use of the four-dimensional regularization technique, proposed recently by Glavan and Lin \cite{Glavan2020}. To do so, we first present $\text{AdS}_4$ Einstein-Lovelock black holes with fine-tuned Lovelock couplings in the regularized theory, which is needed for our purpose. Next, it is shown that the regularized $4D$ Einstein-Lovelock gravity theories of odd order $N > 3$ do not possess any physical isolated critical point, unlike the conventional Lovelock gravity. In fact, the critical (inflection) points of the equation of state always occur for the branch of black holes with negative entropy. The situation is quite different for the case of the regularized $4D$ Einstein-Lovelock gravity with cubic curvature corrections ($N=3$). In this case ($N=3$), although the entropy is non-negative and the equation of state of hyperbolic vacuum black holes has a nonstandard Taylor expansion about its inflection point, but there is no criticality associated with this special point. At the inflection point, the physical properties of the black hole system change drastically ...

Scalar perturbations around rotating regular black holes and wormholes: Quasinormal modes, ergoregion instability, and superradiance

We study scalar test-field perturbations on top of a Kerr--black-bounce background, i.e. a family of rotating regular black holes and/or rotating traversable wormholes that can mimic Kerr black holes. We compute the quasi-normal modes for a massless field in both the regular black holes and wormhole branches, confirming the stability of the former and identifying a set of growing modes that renders the latter unstable. We further compute the superradiance amplification factors, for massless and massive fields, in the regular black hole branch, confirming that these objects superradiate, though to a lesser degree than the corresponding Kerr black holes.

The imaginary potential and entropic force of heavy quarkonia in strongly coupled {mathcal {N}}=4 supersymmetric Yang\u2013Mills plasma on the Coulomb branch

There are two important different mechanisms, the imaginary potential and entropic force, to investigate the dissociation of heavy quarkonia. In this paper, we calculate these two quantities for static and moving quarkonia in the rotating black 3-brane Type IIB supergravity solution dual to {mathcal {N}}=4 super Yang–Mills theory on the Coulomb branch (cSYM) at strong coupling. At Tne 0 , there are two black hole branches: the large and small black hole branches. We investigate the effects of rotating parameter and rapidity for the static and moving quakonium at the large and small black hole branches. We find both mechanisms have the same results. In the large black hole branch: as T/Lambda and beta increase the thermal width decreases and so the suppression becomes stronger. In the small black hole branch: increasing T/Lambda leads to increasing the thermal width and the quarkonium dissociates harder but beta has an opposite effect.

Quasinormal modes of hot, cold and bald Einstein\u2013Maxwell-scalar black holes

Einstein–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function f(phi ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, f(phi )=1+alpha phi ^4 (Blázquez-Salcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

Thermodynamic curvature of the Schwarzschild-AdS black hole and Bose condensation

In the AdS/CFT correspondence, a dynamical cosmological constant Λ in the bulk corresponds to varying the number of colors N in the boundary gauge theory with a chemical potential μ as its thermodynamic conjugate. In this work, within the context of Schwarzschild black holes in AdS5×S5 and its dual finite temperature N=4 superconformal Yang-Mills theory at large N, we investigate thermodynamic geometry through the behavior of the Ruppeiner scalar R. The sign of R is an empirical indicator of the nature of microscopic interactions and is found to be negative for the large black hole branch implying that its thermodynamic characteristics bear qualitative similarities with that of an attraction dominated system, such as an ideal gas of bosons. We find that as the system's fugacity approaches unity, R takes increasingly negative values signifying long range correlations and strong quantum fluctuations signaling the onset of Bose condensation. On the other hand, R for the small black hole branch is negative at low temperatures and positive at high temperatures with a second order critical point which roughly separates the two regions.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and $<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$ cSYM at finite $T$, as well as the heavy quark-antiquark potential and the quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy quark-antiquark potential $V(L)$ to be the Cornell potential, which is confining for large separation $L$. At $T\neq 0$, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with $T$. We also find a second-order phase transition between the large and small black hole branches with critical temperature $T_c=T_{min}$.

Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. II. Transport coefficients and hard probe parameters

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) by using its Type IIB supergravity dual. We compute the transport coefficients, and hard probe parameters of $\mathcal{N} = 4$ cSYM at finite temperature $T$. We use the rotating black 3-brane solution of Type IIB supergravity with a single non-zero rotation parameter $r_{0}$ after analytically continuing $r_{0}\rightarrow -ir_{0}$, and in an ensemble where the Hawking temperature $T$ and a scalar condensate $<\mathcal{O}>\sim r_{0}^4$ are held fixed. We find that the bulk viscosity to entropy density ratio of the large black hole branch decreases with temperature and has a maxima around the critical temperature $T_{c}$ while, for the small black hole branch, it increases with temperature. The other transport coefficients and parameters of hard probes, such as the conductivity, jet quenching parameter, drag force, and momentum diffusion coefficients of the large black hole branch increase with temperature and asymptote to their conformal value while, for the small black hole branch, they decrease with temperature.

Exotic holographic RG flows at finite temperature

Black hole solutions and their thermodynamics are studied in Einstein-scalar theories. The associated zero-temperature solutions are non-trivial holographic RG flows. These include solutions which skip intermediate extrema of the bulk scalar potential or feature an inversion of the direction of the flow of the coupling (bounces). At finite temperature, a complex set of branches of black hole solutions is found. In some cases, first order phase transitions are found between the black-hole branches. In other cases, black hole solutions are found to exist even for boundary conditions which did not allow a zero-temperature vacuum flow. Finite-temperature solutions driven solely by the vacuum expectation value of a perturbing operator (zero source) are found and studied. Such solutions exist generically (i.e. with no special tuning of the potential) in theories in which the vacuum flows feature bounces. It is found that they exhibit conformal thermodynamics.

Geometry of criticality, supercriticality, and Hawking-Page transitions in Gauss-Bonnet-AdS black holes

We obtain the Ruppeiner geometry associated with the nonextended state space ($\mathrm{\ensuremath{\Lambda}}$ 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 $d\ensuremath{\ge}6$) 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 [1] 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 $5\ensuremath{-}d$ 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.

Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes

We study quasinormal modes of static Einstein-Gauss-Bonnet-dilaton black holes. Both axial and polar perturbations are considered and studied from $l=0$ to $l=3$. We emphasize the difference in the spectrum between the Schwarzschild solutions and dilatonic black holes. At large Gauss-Bonnet coupling constant a small secondary branch of black holes is present, when the dilaton coupling is sufficiently strong. The modes of the primary branch can differ from the Schwarzschild modes up to $10\%$. The secondary branch is unstable and possesses long-lived modes. We address the possible effects of these modes on future observations of gravitational waves emitted during the ringdown phase of astrophysical black holes.

The Mixed Phase of Charged AdS Black Holes

We study the mixed phase of charged AdS black hole and radiation when the total energy is fixed below the threshold to produce a stable charged black hole branch. The coexistence conditions for the charged AdS black hole and radiation are derived for the generic case when radiation particles carry charge. The phase diagram of the mixed phase is demonstrated for both fixed potential and charge ensemble. In the dual gauge picture, they correspond to the mixed phase of quark-gluon plasma (QGP) and hadron gas in the fixed chemical potential and density ensemble, respectively. In the nuclei and heavy-ion collisions at intermediate energies, the mixed phase of exotic QGP and hadron gas could be produced. The mixed phase will condense and evaporate into the hadron gas as the fireball expands.

Thermodynamics of higher spin black holes in 3D

We examine the thermodynamic properties of recently constructed black hole solutions in SL(3,R) x SL(3,R) Chern-Simons theory in the presence of a chemical potential for spin-3 charge, which acts as an irrelevant deformation of the dual CFT with W_3 x W_3 symmetry. The smoothness or holonomy conditions admit four branches of solutions describing a flow between two AdS_3 backgrounds corresponding to two different CFTs. The dominant branch at low temperatures, connected to the BTZ black hole, merges smoothly with a thermodynamically unstable branch and disappears at higher temperatures. We confirm that the UV region of the flow satisfies the Ward identities of a CFT with W_3^(2) x W_3^(2) symmetry deformed by a spin-3/2 current. This allows to identify the precise map between UV and IR thermodynamic variables. We find that the high temperature regime is dominated by a black hole branch whose thermodynamics can only be consistently inferred with reference to this W_3^(2) x W_3^(2) CFT.

Instability of the Reissner-Nordström solution and new hairy black holes ind=5dimensions

The $d=5$ Reissner-Nordstr\"om black hole becomes unstable when considered as a solution of Einstein--Yang-Mills--Chern-Simons theory. The existence of a marginally stable mode gives rise to a new branch of black holes with non-Abelian magnetic fields outside the horizon. These solutions carry a nonzero electric charge and have finite mass. We argue that these features manifest themselves both for Minkowski and (anti-)de Sitter asymptotics. The properties of solutions in a de Sitter background are new to the present work and are emphasized. All solutions constructed have finite mass by virtue of the presence of the Chern-Simons term, which in $d=5$ plays the role of a higher order term scaling appropriately for this purpose.