Higher-dimensional Black Holes Research Articles

Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes

In a recent publication we studied the decay rate of primordial black holes perceiving the dark dimension, an innovative five-dimensional (5D) scenario that has a compact space with characteristic length scale in the micron range. We demonstrated that the rate of Hawking radiation of 5D black holes slows down compared to 4D black holes of the same mass. Armed with our findings we showed that for a species scale of O(1010 GeV), an all-dark-matter interpretation in terms of primordial black holes should be feasible for black hole masses in the range 1014≲M/g≲1021. As a natural outgrowth of our recent study, herein we calculate the Hawking evaporation of near-extremal 5D black holes. Using generic entropy arguments we demonstrate that Hawking evaporation of higher-dimensional near-extremal black holes proceeds at a slower rate than the corresponding Schwarzschild black holes of the same mass. Assisted by this result we show that if there were 5D primordial near-extremal black holes in nature, then a primordial black hole all-dark-matter interpretation would be possible in the mass range 105β≲M/g≲1021, where β is a parameter that controls the difference between mass and charge of the associated near-extremal black hole. Published by the American Physical Society 2024

Island formula from Wald-like entropy with backreaction

We propose a Lorentzian derivation of the generalized entropy associated with the island formula for black holes as a Wald-like entropy without reference to the exterior non-gravitating region or field-theoretic von Neumann entropy of Hawking radiation in a fixed curved spacetime background. We illustrate this idea by studying two-dimensional black holes in the Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model in which Hawking radiation is represented by conformal scalars. With some prescriptions assumed, we show that the generalized entropy for the island formula can be reproduced as the Wald-like entropy of the two-dimensional dilaton-gravity theories upon the inclusion of the backreaction from Hawking radiation described by conformal anomaly. We give a discussion on how a similar idea can be applied to higher-dimensional black holes. It is emphasized that the generalized entropy is obtained in a fully gravitational fashion, yet it yields the same Page curve as that of the half-gravitational set-up. We argue that the results in this paper exacerbate the issues raised in the work of massive islands and inconsistency of islands in theories of long-range gravity.

Solutions with a Flat Horizon in D Dimensions within the Cubic Form of f(Q) Gravity

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from f(Q)’s field equations prevents it from deriving spherically symmetric black hole solutions, the result is either Q′=0 or fQQ=0. Utilizing the cylindrical coordinate system within the context the cubic form of f(Q) theory while imposing the condition of a coincident gauge, we establish the existence of static solutions in D-dimensions. The power-law ansatz, which is the most practical based on observations, will be used in this study, where f(Q)=Q+12γQ2+13γQ3−2Λ and the condition D≥4 are met. These solutions belong to a new solution class, the properties of which are derived only from the non-metricity Q modification, since they do not have a general relativity limit. We examine the singularities present in the solutions by calculating the non-metricity and curvature invariant values. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.

Thermodynamic topological classification of higher dimensional and massive gravity black holes

In this work, we investigate the thermodynamic properties of black holes (BHs) that have non-trivial topological features in their phase diagrams. We consider three different models of BHs: (1) a class of BHs in dRGT massive gravity, which adds a mass term to general relativity; (2) a class of BHs in 5D Yang–Mills massive gravity, which combines dRGT massive gravity with a non-Abelian gauge field; and (3) a D-dimensional RN-AdS BH surrounded by Quintessence and a cloud of strings, which are strange forms of matter that change the thermodynamics of the BH. Our goal is to find the critical points of these BHs, which provide the location of first-order phase transitions, and figure out their corresponding topological charges. Topological charges are numbers that show how complicated the BH topology is. Then, we look at these BHs as topological defects in the thermodynamic domain, which is the space of thermodynamic variables like pressure and temperature. We calculate winding numbers to analyze topology on a global and local scale at these defects, which are integers that indicate how many times a curve encircling the defect wraps around the origin. Our analysis reveals that the total topological charge is either equal to 0 or 1 for all models, meaning that the BHs have either a trivial or simple topology. In some cases, we see that the BHs’ topology belongs to a different thermodynamic topological class. This means that the BHs can go through topological phase transitions.

Dimensionally continued black holes sourced by a conformally coupled scalar field and Chaplygin-like dark fluid

In this paper, we study the higher dimensional black holes of Lovelock gravity coupled with a conformal scalar field. The matter source of gravity is suggested to come from the Chaplygin-like dark fluid, i.e., the hybrid of a dark matter and dark energy. We primarily focus on dimensionally continued gravity where the coupling parameters are reduced into two independent parameters, i.e., the Newtonian and cosmological constants. In this specific case of Lovelock gravity, we derive the metric function that describes the hairy black holes surrounded by dark fluid. For these objects, the basic thermodynamic quantities are worked out. We discuss how the unified dark fluid affects both local and global thermodynamic stabilities. We also demonstrate that the radiation spectrum is proportional to the change in entropy of the hairy black holes. Lastly, the hairy black holes in the presence of Chaplygin-like dark fluid are briefly investigated within the context of generic Lovelock gravity.

Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics.

This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the Trautman-Bondi mass in terms of the hyperboloidal metric functions. Moreover, we apply this formalism to a class of wave equations commonly used in black-hole perturbation theory. Additionally, we provide a comprehensive derivation of the hyperboloidal minimal gauge, introducing two alternative approaches within this conceptual framework: the in-out and out-in strategies. Specifically, we demonstrate that the height function in the in-out strategy follows from the well-known tortoise coordinate by changing the sign of the terms that become singular at future null infinity. Similarly, for the out-in strategy, a sign change also occurs in the tortoise coordinate's regular terms. We apply the methodology to the following spacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensional black holes, black hole with matter halo, and Reissner-Nordström-de Sitter. From this heuristic study, we conjecture that the out-in strategy is best adapted for black hole geometries that account for environmental or effective quantum effects. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

Thermodynamics of higher dimensional charged black holes: nonperturbative study

In this paper, we consider higher dimensional charged black holes to study nonperturbative corrected thermodynamics. This correction is dominant when the black hole size decreases due to the Hawking radiation. The nonperturbative correction on the black hole entropy is proportional to the exponential of the original entropy with a negative sign. We calculate some thermodynamics quantities such as the internal Helmholtz free energies, and obtain the effect of the exponential correction. We study the first law of thermodynamics and investigate how it satisfies. We also study the stability of the black hole through specific heat analysis and investigate the possible phase transition. We find a second-order phase transition that is interpreted as the unstable/stable phase transition. Then, we find a first-order phase transition that makes it unstable. Hence, the final stage of the Reissner–Nordström black holes may be an unstable phase, which means that black hole evaporation at the quantum scale. It may be a cause that we never find a black hole in accelerators.

Thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions

We investigate thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions, namely higher-dimensional charged black holes in which the electromagnetic sector exhibits the same properties with that of the usual three-dimensional BTZ solution. We first present the Euclidean on-shell action in arbitrary dimensions, inserting a radial cutoff. We then extract the corresponding thermodynamic quantities from the semi-classical partition function in different ensembles and find that there exist two possible thermodynamic schemes, with different outcomes. Regarding the traditional scheme (scheme I), where the length cutoff is identified with the AdS radius, we show that charged BTZ-like black holes are super-entropic, namely they violate the reverse isoperimetric inequality conjecture, and their super-entropicity is strongly connected to a fundamental thermodynamic instability. This class of solutions is the first demonstration of super-entropic black holes which possess second-order critical points and, since thermodynamic instabilities always arise, it is not possible to physically interpret the corresponding van der Waals critical phenomenon in this scheme. In the second scheme (II) where the length cutoff is considered as an independent variable, namely the system respects the conjectured reverse isoperimetric inequality, we show that the solutions are thermodynamically stable in an ensemble where the length cutoff is kept fixed, and hence one can provide an explanation for the van der Waals critical phenomenon. Furthermore, in order to verify the consistency of the second scheme, we study the Joule–Thomson expansion and we extract the Joule–Thomson coefficient, the inversion temperature, the inversion curves, and the isenthalpic curves. The results indicate that this class of AdS black holes can be considered as interacting statistical systems. Additionally, in the D→3 limit we recover the conventional charge BTZ black holes, as well as their thermodynamic properties. Finally, we report a new thermodynamic instability for charged BTZ black holes, as well as their generalization to higher dimensions, which implies that working in an ensemble with fixed length cutoff is mandatory to consistently examine the thermodynamic processes.

Effect of modified gravity on the Hawking evaporation of charged AdS black holes

We study the impact of rainbow and Einstein bumblebee modified theories of gravity on the Hawking evaporation process of the black holes. After evaluating the basic thermodynamical quantities, we find out impact parameter b = (angular momentum )/(energy of the emitted particles), which control the emission of the particles and the photon orbit of the black hole in modified theories of gravity. We utilize the well-known Stefan-Boltzmann law to obtain the relationship of black hole mass M against its lifetime t. The numerical results of black hole mass versus lifetime t show that initially the mass of black hole in modified gravity decreases rapidly and later evaporation process becomes slower when temperature reduces to zero. The black hole requires huge time to fully evaporate which is consistent result with 3rd law of thermodynamics for black holes. We observe that increasing values of AdS length l increases evaporation time and increasing value of rainbow parameter η results in slowing down the evaporation process. Moreover, we analyze that uncharged black holes evaporate quickly as compared to charged black hole and black hole in higher dimensions required huge time to fully evaporate as compared to black hole in small dimensions.

Thermodynamics of higher-dimensional Brans-Dicke black holes in the presence of a conformal-invariant field inspired by power-Maxwell electrodynamics

Abstract By use of the conformal transformations, in addition to translating the Brans-Dicke (BD) action to the Einstein frame (EF), we introduce an electromagnetic Lagrangian which preserves conformal invariance. We solve the EF field equations, which mathematically are confronted with the problem of indeterminacy, by use of an exponential ansatz function. When the self-interacting potential is absent or is taken constant in the BD action, the exact solution of this theory is just that of Einstein-conformal-invariant theory with a trivial scalar field. This is higher-dimensional (HD) analogues of the same considered in [1]. The EF general solution admits two classes of black holes (BHs) with non-flat and non-AdS asymptotic behavior which can produce extreme and multi-horizon ones. We obtain the exact solutions of BD-conformal-invariant theory, by applying inverse conformal transformations, which show two classes of extreme and multi-horizon BHs too. Based on the fact that thermodynamic quantities remain unchanged under conformal transformations, we show that the first law of BH thermodynamics is valid in the Jordan frame (JF). We analyze thermal stability of the HD BD-conformal-invariant BHs by use of the canonical ensemble method.

Love numbers for rotating black holes in higher dimensions

Love numbers for rotating black holes in higher dimensions

Conformal hairy black holes of quartic quasi-topological gravity with power-Yang–Mills source

We study higher dimensional hairy black holes of quartic quasi-topological gravity in the framework of non-abelian power-Yang–Mills theory. It is shown that real solutions of the gravitational field equations exist only for positive values of quartic quasi-topological coefficient. Depending on the values of the mass, conformal coupling constants, quasi-topological coefficients, Yang–Mills magnetic charge, and nonlinearity parameter, they can be interpreted as black holes with one horizon, at most three horizons and naked singularity. It is also shown that the solution associated with these black holes has an essential curvature singularity at the centre r=0. Thermodynamic and conserved quantities for these hairy black holes are computed and we show that the first law has been verified. We also check thermodynamic stability in both canonical and grand canonical ensembles. In addition to this, we also formulate new power-Yang–Mills hairy black hole solutions in pure quasi-topological gravity. The physical and thermodynamic properties of these black holes are discussed as well. It is concluded that unlike Yang–Mills black holes without scalar hair there exist stability regions for the power-Yang–Mills hairy black holes in grand canonical ensemble. Finally, we discuss the thermodynamics of horizon flat power-Yang–Mills rotating black branes and analyze their thermodynamic and conserved quantities by using the counter-term method inspired by AdS/CFT correspondence.

Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes’ parameters. Since k and c_ 0^2c_2 m^2 appear together in the generalized free energy in the form of k +c_ 0^2c_2 m^2 , where k characterizes the horizon curvature and c_2 m^2 is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime* *Supported by the National Natural Science Foundation of China (11665015), the Guizhou Provincial Science and Technology Planning Project of China (qiankehejichu-ZK[2021]yiban026), and the Guizhou Province ordinary institutions of higher learning top science and technology talents Support plan of China (qianjiaoheKY[2019]062).

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit. We observe that the larger parameters b and q make the condensation of the scalar operator more difficult, and the critical temperature decreases more slowly as the factors increase. In the belt geometry, the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry. At the phase transition point, the discontinuous slope of entanglement entropy is universal for different model factors. It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

Thermodynamics under the extended uncertainty principle background: [formula omitted] criticality analysis

The study of thermodynamics in the background of the “extended uncertainty principle (EUP)” comes into interest in recent eras. In this article, we consider a charged black hole (BH) in higher dimensional space–time and present the thermodynamic parameters, based on a semiclassical framework, initially. Then we extend the same within the EUP background. We also analyze the Q−ϕ criticality and find the critical points (ϕc,Qc and Tc) when Q−ϕ criticality appears. We study the effects of EUP on phase transition for higher dimensions (d=5) by plotting the Q−ϕ diagrams. Further, we investigate the stability (thermal and global) of the BHs by employing the specific heat and the Gibbs free energy without and within EUP correction and compare the results with the Schwarzschild BHs in higher dimensions.

Dark matter from higher-dimensional primordial black holes

Dark matter from higher-dimensional primordial black holes

Metric fluctuations in higher-dimensional black holes

We investigated the impact of metric fluctuations on the higher-dimensional black hole geometry. We generalized the four-dimensional model to higher dimensions to treat quantum vacuum fluctuations by the classical approach. A fluctuating black hole is portrayed by a higher-dimensional Vaidya metric with a spherically oscillating mass. Assuming a small fluctuation amplitude, we employed a perturbation method to obtain a radially outgoing null geodesic equation up to the second order in the fluctuation. Furthermore, the fluctuation of the event horizon up to the second order depends on the number of spacetime dimensions. Therefore, the time-averaged values of the thermodynamic variables defined at the horizon also feature dimension-dependent correction terms. A general solution was obtained for rays propagating near the horizon within a fluctuating geometry. Upon examining this in a large D limit, we found that a complete solution can be obtained in a compact form.

Some observable physical properties of the higher dimensional dS/AdS black holes in Einstein-bumblebee gravity theory

We study the greybody factors, quasinormal modes, and shadow of the higher dimensional de-Sitter (dS)/anti de-Sitter (AdS) black hole spacetimes derived from the Einstein-bumblebee gravity theory within the Lorentz symmetry breaking (LSB) framework. We specifically apply the semi-analytical WKB method and the time domain approach to study the scalar and Dirac perturbations of the black hole. In-depth researches are done on the effects of the LSB and dimensionality on the bosonic/fermionic greybody factors, quasinormal modes, and shadow of the higher dimensional bumblebee black hole. The results obtained are discussed, tabulated, and illustrated graphically.

Islands in Generalized Dilaton Theories

This work systematically studies the island formula in the general asymptotically flat eternal black holes in generalized dilaton gravity theories or higher-dimensional spherical black holes. Under some reasonable and mild assumptions, we prove that (the boundary of) the island always appears barely outside the horizon in the late time of Hawking radiation, so the information paradox is resolved. In particular, we find a proper island in the Liouville black hole that solves the previous the puzzle.

Asymptotically locally flat and AdS higher-dimensional black holes of Einstein–Horndeski–Maxwell gravity in the light of EHT observations: shadow behavior and deflection angle

Unification of gravity with other interactions, achieving the ultimate framework of quantum gravity, and fundamental problems in particle physics and cosmology motivate to consider extra spatial dimensions. The impact of these extra dimensions on the modified theories of gravity has attracted a lot of attention. One way to examine how extra dimensions affect the modified gravitational theories is to analytically investigate astrophysical phenomena, such as black hole shadows. In this study, we aim to investigate the behavior of the shadow shapes of higher-dimensional charged black hole solutions including asymptotically locally flat (ALF) and asymptotically locally AdS (ALAdS) in Einstein–Horndeski–Maxwell (EHM) gravitational theory. We utilize the Hamilton–Jacobi method to find photon orbits around these black holes as well as the Carter approach to formulate the geodesic equations. We examine how extra dimensions, negative cosmological constant, electric charge, and coupling constants of the EHM gravity affect the shadow size of the black hole. Then, we constrain these parameters by comparing the shadow radius of these black holes with the shadow size of M87* supermassive black hole captured by the Event Horizon Telescope (EHT) collaborations. We discover that generally the presence of extra dimensions within the EHM gravity results in reducing the shadow size of higher-dimensional ALF and ALAdS charged black holes, whereas the impact of electric charge on the shadow of these black holes is suppressible. Interestingly, we observe that decreasing the negative cosmological constant, i.e., increasing its absolute value, leads to increase the shadow size of the ALAdS charged higher-dimensional black hole in the EHM gravity. Surprisingly, based on the constraints from EHT observations, we discover that only the shadow size of the four dimensional ALF charged black hole lies in the confidence levels of EHT data, whereas owing to the presence of the negative cosmological constant, the shadow radius of the four, five, and seven dimensional ALAdS charged black holes lie within the EHT data confidence levels.