Three-dimensional Black Holes Research Articles

Stabilizing Effects of Higher-Order Quantum Corrections on Charged BTZ Black Hole Thermodynamics

In this paper, we study the thermodynamic properties and stability of static charged BTZ black holes with the inclusion of higher-order quantum corrections. The corrections to the entropy, mass, and Helmholtz free energy are derived, revealing the intricate interplay between quantum effects and classical gravitational forces in the context of black hole thermodynamics. The study of the specific heat capacity shows that higher-order corrections stabilize the system by removing the instabilities present at lower orders. The analysis of the van der Waals-like isotherms demonstrates the continuous transition from a highly compressible to an almost incompressible regime as the volume is decreased, akin to the behavior of supercritical fluids. Notably, the isotherms do not exhibit any regions of negative compressibility, indicating the absence of instabilities. Furthermore, the convexity of the Helmholtz free energy as a function of volume confirms the stability of the charged BTZ black hole system. These findings provide valuable insights into the complex thermodynamic landscape of three-dimensional black holes and the role of quantum corrections in shaping their behavior.

Mass fluctuations in non-rotating BTZ black holes

We investigate the impact of oscillations of a black hole's mass around its average value on the three-dimensional black hole geometry. Drawing on a classical framework that conceptualizes fluctuations near an event horizon as mass variations, we introduce a model where the metric of a black hole, formed from the collapse of a massive null shell, exhibits oscillatory behavior in spherical modes. This dynamic is encapsulated by a non-rotating BTZ-Vaidya solution, characterized by the black hole mass fluctuating at a resonant frequency ω and a small amplitude parameter μ0. Using a perturbative approach, solutions to the null geodesic equation are determined up to the second order in μ0. The temporal fluctuations of the event horizon's location induce alterations in the thermodynamic variables' values. Upon calculating the time-averaged values, the mean Hawking temperature experiences a slight decrease due to these fluctuations, while the mean entropy exhibits an increase. Furthermore, the study explores the influence of these fluctuations on the trajectories of null rays near the horizon, which ultimately reach the anti-de Sitter boundary at late times. The analytical computation of the general solution for the perturbed rays up to the second order underscores the novel approach of this study in examining the effects of mass oscillations on black hole thermodynamics and geometry, thereby contributing a unique perspective to the field.

AdS/CFT correspondence with a three-dimensional black hole simulator

AdS/CFT correspondence with a three-dimensional black hole simulator

Thermodynamics of the three-dimensional black hole with torsion

The stationary black hole solution of a Chern-Simons model based on the semi-simple extension of the Poincaré gauge group is studied. The solution resembles the metric properties of the BTZ geometry but contains, in addition, non-vanishing torsion. The global structure of spacetime is characterized by three conserved charges: two associated with the mass and angular momentum and one extra constant triggered by spacetime torsion. Consequently, we show that the entropy deviates from the standard Bekenstein-Hawking value and discuss the implications of torsional charges in the context of black hole thermodynamics.

Black holes in dS3

In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Nariai-type limit. We show explicitly how these solutions arise using braneworld holography, but also compare to a non-holographic, perturbative analysis of backreaction due to conformally coupled scalar fields in conical de Sitter space. We analyze the thermodynamics of this quantum black hole, revealing it behaves similarly to its classical four-dimensional counterpart, where the generalized entropy replaces the classical Bekenstein-Hawking entropy. We compute entropy deficits due to nucleating the three-dimensional black hole and revisit arguments for a possible matrix model description of dS spacetimes. Finally, we comment on the holographic dual description for dS spacetimes as seen from the braneworld perspective.

Twisted strings in three-dimensional black holes

We revisit the classical dynamics of fundamental strings in BTZ black holes with NSNS flux. We analyze probe strings in the black hole background and determine their classical energy using a Nambu–Goto action. Three-dimensional gravity has a non-local effect on the metric surrounding a massive object which can be measured by winding strings. We also study the behaviour of short and long strings in the Wess–Zumino–Witten orbifold and show that their energy matches the long string probe analysis. In the process, we fix subtleties in the Lorentzian choice of NSNS flux. In Euclidean signature, we analyze the one-loop fundamental string partition function on the BTZ black hole and interpret the off-shell degrees of freedom as those of a coset orbifold. Finally, we speculate on how to identify the quantum Lorentzian string spectrum from the Euclidean orbifold partition function.

Three-dimensional black holes with scalar hair coupled to a Maxwell-like electrodynamics

By consideration of an Einstein-dilaton nonlinear charged gravitating system, it has been shown that this theory is confronted with the problem of indeterminacy. It means that the number of independent differential equations is one less than the number of unknowns. To overcome this problem, the power-law and exponential ansatz functions have been used, separately. Through solving the field equations, in the presence of a Coulomb-like electric field, it has been found that this theory includes two novel classes of charged black holes (BHs) with unusual asymptotic behavior, for each ansatz. It has been found that, under some circumstances, both of the ansatz functions lead to the same results. The novel exact solutions show BHs with one horizon, two horizons and without horizon. Using a Smarr-type mass formula, the validity of the first law of BH thermodynamics (FLT) has been proved, after calculating the thermodynamic and conserved quantities. Making use of thermodynamical and geometrical approaches, thermal stability of the BHs has been analyzed. Results of the aforementioned methods have been compared by use of the plots.

Quantum tunneling from accelerating three-dimensional black hole

Hawking radiation as a quantum tunneling phenomena from accelerating BTZ black holes is presented in this work. We have calculated the Dirac particle's Hawking radiation from the horizon of the accelerating BTZ black hole. WKB approximation is applied to Dirac equation in the background of three dimensional black holes. This procedure gives us the tunneling probability, which we have used to calculate the Hawking temperature of the background three-dimensional black hole. Our study is consistent with the previous studies in the absence of the acceleration parameter. We have also studied the quantum corrections to the Hawking temperature of accelerating BTZ black hole.

Charged black hole solutions with Toroidal horizons in f(R)-gravity surrounded by quintessence and cloud of strings: Effective potential barrier, quasinormal modes

We construct a new class of [Formula: see text]-dimensional black hole solutions with Toroidal horizons in [Formula: see text] gravity framework which is surrounded by quintessence and string cloud configuration, whose asymptotic structures are determined by the quintessential state parameter [Formula: see text] and dimension’s parameter [Formula: see text]. We point out that the asymptotic behavior of the obtained solutions is neither asymptotically flat nor (A)dS when we have [Formula: see text] and [Formula: see text]. Regarding the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we investigate the critical behavior of our black hole solutions. In [Formula: see text] and [Formula: see text], the P–V diagrams are more complex than that of the standard Van der Waals. These diagrams behave like the Born–Infeld-AdS P–V diagrams. When [Formula: see text] and [Formula: see text], the P–V diagrams behave like the standard Van der Waals system (In this work [S. Gunasekaran, D. Kubiznaak and R. B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012).] [S. Gunasekaran, D. Kubiznaak and R.B. Mann, Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization, J. High Energy Phys. (2012)], the authors believe that the BTZ black holes, contrary to the higher-dimensional case, do not show any critical behavior. In this work, we have showed that the three-dimensional (3D) black holes can also have critical behavior and coincide with those of the Van der Waals system). Besides, we have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. We figure out the effect of the coupling constant [Formula: see text], the string parameter b, and the quintessential state parameter [Formula: see text] on the height of the potential barrier and the other thermodynamical quantities like temperature and heat capacity. Then, we study the quasinormal modes (QNMs) of 3D black holes in the [Formula: see text] context. For this purpose, we use the WKB approximation method upto third-order corrections. We have shown the perturbation’s decay in corresponding diagrams when the string parameter b changes.

Three-dimensional black holes via Noether symmetries

We investigate the Noether symmetries of the Lagrangian for the stationary rotating BTZ-type three-dimensional spacetimes in $f(R)$ theory of gravity. A detailed analysis of Noether symmetries of (2+1)-dimensional rotating BTZ-type black hole spacetime model is presented. Applying the Noether symmetry approach, the first integrals (constants of motion) for each of Noether symmetries are obtained to look for the exact solutions. After solving the first integral equations depending on the form of the function $f(R)$, we derived some new (2+1)-dimensional rotating BTZ-type black hole solutions. We discussed the physical implications of the derived exact solutions. The thermodynamical properties of the obtained BTZ-type black hole solutions are analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of $r_{\pm}$, where $r_+$ is the event horizon and $r_{-}$ is the inner horizon. Further, it is shown that thermodynamic quantities obey the first law, and the Smarr-like formulas of the solutions we found are obtained.

Entropies and the first laws of black hole thermodynamics in Einstein-aether-Maxwell theory

Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including three-dimensional static charged quasi-BTZ black hole, two four-dimensional static charged black holes and three-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universal horizons of three-dimensional black holes, the entropies have a corrected term in addition to the one proportional to the horizon area.

Three-dimensional static black hole with Λ and nonlinear electromagnetic fields and its thermodynamics

Static black hole with the Power Maxwell invariant (PMI), Born–Infeld (BI), logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional spacetime with cosmological constant was studied. It was shown that the LN and EN fields represent the Born–Infeld type of nonlinear electrodynamics. It the framework of General Relativity the exact solutions of the field equations were obtained, corresponding thermodynamic functions were calculated and the [Formula: see text] criticality of the black holes in the extended phase-space thermodynamics was investigated.

Holographic subregion complexity of a (1+1)-dimensional $p$-wave superconductor

Abstract We analyze the holographic subregion complexity in a three-dimensional black hole with vector hair. This three-dimensional black hole is dual to a (1+1)-dimensional $p$-wave superconductor. We probe the black hole by changing the size of the interval and by fixing $q$ or $T$. We show that the universal part is finite across the superconductor phase transition and has competitive behaviors different from the finite part of the entanglement entropy. The behavior of the subregion complexity depends on the gravitational coupling constant divided by the gauge coupling constant. When this ratio is less than the critical value, the subregion complexity increases as temperature becomes low. This behavior is similar to that of the holographic (1+1)-dimensional $s$-wave superconductor [M. K. Zangeneh, Y. C. Ong, and B. Wang, Phys. Lett. B 771, 130 (2014)]. When the ratio is larger than the critical value, the subregion complexity has a non-monotonic behavior as a function of $q$ or $T$. We also find a discontinuous jump of the subregion complexity as a function of the size of the interval. The subregion complexity has a maximum when it wraps almost the entire spatial circle. Due to competitive behaviors between the normal and condensed phases, the universal term in the condensed phase becomes even smaller than that of the normal phase by probing the black hole horizon at a large interval. This implies that the condensate formed decreases the subregion complexity as in the case of the entanglement entropy.

Tunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiation

We analyse the local behaviour of the two-point correlation function of a quantum state for a scalar field in a neighbourhood of a Killing horizon in a 2+1-dimensional spacetime, extending the work of Moretti and Pinamonti in a 3+1-dimensional scenario. In particular we show that, if the state is of Hadamard form in such neighbourhood, similarly to the 3+1-dimensional case, under a suitable scaling limit towards the horizon, the two-point correlation function exhibits a thermal behaviour at the Hawking temperature. Since the whole analysis rests on the assumption that a Hadamard state exists in a neighbourhood of the Killing horizon, we show that this is not an empty condition by verifying it for a massive, real scalar field subject to Robin boundary conditions in the prototypic example of a three-dimensional black hole background: the non-extremal, rotating BTZ spacetime.

Nonlinearly charged three-dimensional black holes in the Einstein-dilaton gravity theory

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a three-dimensional space time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a spherically symmetric geometry and it has been shown that the dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, two new classes of charged dilatonic BTZ black hole solutions, in the presence of power-law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. The consistency of the results of these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions. The black holes stability or phase transitions have been studied, making use of the canonical ensemble method. The points of type one and type two phase transitions as well as the ranges at which the black holes are stable have been indicated by considering the heat capacity of the new black hole solutions.

Three-dimensional black holes with quintessence

We study a quintessential black hole solution in three dimensions, with mass and quintessence charge. By exploring the Carter-Penrose diagram, we show the presence of spacelike and lightlike singularities in the metric, given different values for the quintessence parameter, as well as an AdS-like spatial infinity and event horizon encapsulating the singularity. We also study the propagation of scalar and Dirac (Weyl) fields around the black hole solutions with different quintessence charges obtaining the quasinormal spectra for both fields using two different numerical methods with good agreement between the data. In both cases, the presence of quintessence increases the imaginary part of the quasinormal mode, since this is related to the event horizon of the solution, preserving the interpretation of this quantity as relaxation time in the corresponding CFT. We also investigate the behavior of high-temperature scalar field modes, demonstrating the presence of the so-called hydrodynamical limit, differently from the BTZ black hole, for which no such modes exist.

Thermodynamic properties of charged three-dimensional black holes in the scalar-tensor gravity theory

Making use of the suitable transformation relations, the action of three-dimensional Einstein-Maxwell-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory coupled to the Maxwell's electrodynamics as the matter field. Two new classes of the static three-dimensional charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained in the Einstein frame. Also, it has been found that the scalar potential can be written in the form of a generalized Liouville-type potential. The conserved black hole charge and masses as well as the black entropy, temperature, and electric potential have been calculated from the geometrical and thermodynamical approaches, separately. Through comparison of the results arisen from these two alternative approaches, the validity of the thermodynamical first law has been proved for both of the new black hole solutions in the Einstein frame. Making use of the canonical ensemble method, a black hole stability or phase transition analysis has been performed. Regarding the black hole heat capacity, with the black hole charge as a constant, the points of type-1 and type-2 phase transitions have been determined. Also, the ranges of the black hole horizon radius at which the Einstein black holes are thermally stable have been obtained for both of the new black hole solutions. Then making use of the inverse transformation relations, two new classes of the string black hole solutions have been obtained from their Einstein counterpart. The thermodynamics and thermal stability of the new string black hole solutions have been investigated. It has been found that thermodynamic properties of the new charged black holes are identical in the Einstein and Jordan frames.

Throat quantization of the Schwarzschild-Tangherlini(-AdS) black hole

By the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area/entropy spectra for the Schwarzschild-Tangherlini-type asymptotically flat or AdS vacuum black hole in arbitrary dimensions. Using the WKB approximation for black holes with large mass, we show that area/entropy is equally spaced for asymptotically flat black holes, while mass is equally spaced for asymptotically AdS black holes. Exact spectra can be obtained for toroidal AdS black holes in arbitrary dimensions including the three-dimensional BTZ black hole.

Log corrections to entropy of three dimensional black holes with soft hair

We calculate log corrections to the entropy of three-dimensional black holes with “soft hairy” boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories with anisotropic scaling of Lifshitz type with dynamical exponent z at the boundary. On the gravity side such scalings arise for KdV-type boundary conditions, which provide a specific 1-parameter family of multi-trace deformations of the usual AdS3/CFT2 setup, with Brown-Henneaux corresponding to z = 1 and soft hairy boundary conditions to the limiting case z → 0+. Both approaches agree in the case of BTZ black holes for any non-negative z. Finally, for soft hairy boundary conditions we show that not only the leading term, but also the log corrections to the entropy of black flowers endowed with affine û (1) soft hair charges exclusively depend on the zero modes and hence coincide with the ones for BTZ black holes.

Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities.

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the rôle of quantum mechanics as a cosmic censor in nature.