Charged Black Holes In Higher Dimensions Research Articles

Black hole evaporation process and Tangherlini–Reissner–Nordström black holes shadow

In this article, we study the black hole evaporation process and shadow property of the Tangherlini-Reissner-Nordström (TRN) black holes. The TRN black holes are the higher-dimensional extension of the Reissner-Nordström (RN) black holes and are characterized by their mass M, charge q, and spacetime dimensions D. In higher-dimensional spacetime, the black hole evaporation occurs rapidly, causing the black hole’s horizon to shrink. We derive the rate of mass loss for the higher-dimensional charged black hole and investigate the effect of higher-dimensional spacetime on charged black hole shadow. We derive the complete geodesic equations of motion with the effect of spacetime dimensions D. We determine impact parameters by maximizing the black hole’s effective potential and estimate the critical radius of photon orbits. The photon orbits around the black hole shrink with the effect of the increasing number of spacetime dimensions. To visualize the shadows of the black hole, we derive the celestial coordinates in terms of the black hole parameters. We use the observed results of M87 and Sgr A∗ black hole from the Event Horizon Telescope and estimate the angular diameter of the charge black hole shadow in the higher-dimensional spacetime. We also estimate the energy emission rate of the black hole. Our finding shows that the angular diameter of the black hole shadow decreases with the increasing number of spacetime dimensions D.

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.

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.

Higher-dimensional charged black holes in f(R)-gravity's rainbow surrounded by cloud of strings: Exact solution, shadow, and effective potential barrier

We construct a new class of spherically symmetric black hole solutions in f(R)-gravity's rainbow1 framework which is surrounded by string cloud configuration. In the thermodynamic analysis, we show that the black hole's temperature grows up for such small values of b parameter and also big values of it, graphically. In addition to the mass and charge of the black holes, we show that the presence of the rainbow function gr(ε) and cloud's strength b can also affect the size of the shadow. For the black hole solution, it is shown that the shadow size increases with the parameter b, but decreases with the parameter gr(ε). In addition, we have shown that the energy emission rate decreases with increase in gr(ε) and decrease in b parameter. We have analyzed the concept of effective potential barrier by transforming the radial equation of motion into standard Schrodinger form. The most important result derived from this study is that the height of this potential increases with decrease in gr(ε) parameter and increases in the coupling constant λ and the b parameter. We also investigate the impact of these parameters on the other thermodynamical quantities like temperature and heat capacity. There is a minimum on that between for one special value of b. From the temperature diagram versus the b parameter (T−b) and analogy with T−r+ diagrams, we can say that the b parameter behaves as the event horizon radius r+. 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 d=5, 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 d=6, the P-V diagrams are also more complex than that of the standard Van der Waals and we decompose them into two parts. One part behaves like the standard Van der Waals system. The other part is similar to the Schwarzschild-AdS black hole P-V diagrams where the isotherms turn and enter a region with negative pressures. The null geodesic equations are computed in d=5 spacetime dimensions by using the concept of symmetries and Hamilton-Jacobi equation and Carter separable method. With the null geodesics in hand, we then evaluate the celestial coordinates (x, y) and the radius Rs of the black hole shadow and represent it graphically.

Weak cosmic censorship conjecture in higher-dimensional black holes with nonlinear electrodynamic sources

The new version of the gedanken experiments proposed by Sorce and Wald are designed to test the validity of the weak cosmic censorship conjecture (WCCC) by overspinning or overcharging the Kerr-Newman black hole in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the WCCC in the higher-dimensional charged black hole with a nonlinear electrodynamics source. We derive the first and seconder order perturbation inequalities of the charged collision matter based on the Iyer-Wald formalism as well as the null energy conditions, and show that they share the similar form as that in Einstein-Maxwell gravity. As a result, we find that the static higher-dimensional nonlinear electrodynamics (HDNL) black holes cannot be overcharged after considering these two inequalities. Our result might indicate the validity of WCCC for more general HNDL and related systems.

Higher dimensional charged black hole surrounded by quintessence in massive gravity

In this paper, we have found a D-dimensional static and spherically symmetric charged black hole solution with the quintessence matter surrounding in the context of the massive gravity. We studied the horizon properties of this black hole solution, which depend crucially on the sign of the coupling parameters of the massive gravity. In addition, we investigated the black hole thermodynamics in details from the local and global viewpoints at which various thermodynamic quantities are computed. The thermodynamic stability and phase transition of the black hole are analyzed by studying the behavior of the heat capacity at constant normalization factor which is related to the energy density of the quintessence matter.

Interior volume and entropy of higher-dimensional charged black holes

The study of the black holes in higher-dimensional space-time has got the focus mainly after developments of string theory or M-theory. Beside this, construction of brane world scenario also motivates to study the properties of higher-dimensional black holes. In this letter, we calculate the maximal interior volume of higher-dimensional charged black holes which is actually the extension of a previous work (Ong Y. C., Gen. Relativ. Gravit., 47 (2015) 88 (arXiv:gr-qc/1503.08245)) in addition to the study of entropy of the same class of black holes' interior. The actual detail investigation and proof have been shown in Christodoulou M. and Lorenzo T. D., Phys. Rev. D, 94 (2016) 104002 (arXiv:gr-qc/1604.07222). We try in this letter, to establish a generalized form which is not only the maximal interior volume but also the entropy of the black hole in its interior for Schwarzschild like regular black holes. We also show how their behaviors depend on the mass parameter m considering the constant valued horizon and for the charge parameter q = 0 and q > 0.

Higher-dimensional charged black holes cannot be over-charged by gedanken experiments

We reconsider over-charging the higher-dimensional nearly extremal charged black holes using the new version of gedanken experiment proposed recently by Sorce and Wald. As a result, we find that cosmic censorship conjecture associated with such black holes is restored by taking into account the second-order correction, albeit violated by the first-order perturbation. Namely, the higher-dimensional nearly extremal charged black holes cannot be over-charged.

Thermodynamics of higher dimensional black holes with higher order thermal fluctuations

In this paper, we consider higher order corrections of the entropy, which coming from thermal fluctuations, and find their effect on the thermodynamics of higher dimensional charged black holes. Leading order thermal fluctuation is logarithmic term in the entropy while higher order correction is proportional to the inverse of original entropy. We calculate some thermodynamics quantities and obtain the effect of logarithmic and higher order corrections of entropy on them. Validity of the first law of thermodynamics investigated and Van der Waals equation of state of dual picture studied. We find that five-dimensional black hole behaves as Van der Waals, but higher dimensional case have not such behavior. We find that thermal fluctuations are important in stability of black hole hence affect unstable/stable black hole phase transition.

Butterflies with rotation and charge

We explore the butterfly effect for black holes with rotation or charge. We perturb rotating BTZ and charged black holes in 2 + 1 dimensions by adding a small perturbation on one asymptotic region, described by a shock wave in the spacetime, and explore the effect of this shock wave on the length of geodesics through the wormhole and hence on correlation functions. We find the effect of the perturbation grows exponentially at a rate controlled by the temperature; dependence on the angular momentum or charge does not appear explicitly. We comment on issues affecting the extension to higher-dimensional charged black holes.

The Phase Transition of Higher Dimensional Charged Black Holes

We have studied phase transitions of higher dimensional charge black hole with spherical symmetry. We calculated the local energy and local temperature and find that these state parameters satisfy the first law of thermodynamics. We analyze the critical behavior of black hole thermodynamic system by taking state parameters(Q,Φ)of black hole thermodynamic system, in accordance with considering the state parameters(P,V)of van der Waals system, respectively. We obtain the critical point of black hole thermodynamic system and find that the critical point is independent of the dual independent variables we selected. This result for asymptotically flat space is consistent with that for AdS spacetime and is intrinsic property of black hole thermodynamic system.

The relation between [formula omitted] gravity and Einstein-conformally invariant Maxwell source

In this Letter, we consider the special case of F(R) gravity, in which F(R)=RN and obtain its topological black hole solutions in higher dimensions. We show that, the same as higher-dimensional charged black hole, these solutions may be interpreted as black hole solutions with two event horizons, extreme black hole and naked singularity provided the parameters of the solutions are chosen suitably. But, the presented black hole is different from the standard higher-dimensional Reissner–Nordström solutions. Next, we present the conformally invariant Maxwell field coupled to Einstein gravity and discuss about its black hole solutions. Comparing these two class of solutions, shows that there is a correspondence between the Einstein-conformally invariant Maxwell solutions and the solutions of F(R) gravity without matter field in arbitrary dimensions.

A comparative study of Dirac quasinormal modes of charged black holes in higher dimensions

In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner–Nordström type black holes as well as charged black holes in Einstein–Gauss–Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies.

Non-commutative geometry inspired higher-dimensional charged black holes

We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner–Nordström geometry at large distance, and de Sitter spacetime at short distance. Thermodynamical properties of the black hole are investigated and the form of the Area Law is determined. We study pair creation and show that the upper bound on the discharge time increases with the number of extra dimensions.

Higher-dimensional charged black hole solutions with a nonlinear electrodynamics source

We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is derived from a Lagrangian given by an arbitrary power of the Maxwell invariant. The form of the general solution suggests a natural partition for the different ranges of this power. For a particular range, we exhibit a class of solutions whose behavior resembles the standard Reissner–Nordström black holes. There also exists a range for which the black hole solutions approach asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime. We have also found a family of non-asymptotical flat black hole solutions with an asymptotic behavior growing slower than the Schwarzschild–(anti)-de Sitter spacetime. In odd dimensions, there exists a critical value of the exponent for which the metric involves a logarithmic dependence. This critical value corresponds to the transition between the standard behavior and the solution decaying to Minkowski slower than the Schwarzschild spacetime.

COLLAPSING AND STATIC THIN MASSIVE CHARGED DUST SHELLS IN A REISSNER–NORDSTRÖM BLACK HOLE BACKGROUND IN HIGHER DIMENSIONS

The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner–Nordström black hole in d space–time dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First, a derivation of the equation of motion of such a shell in a d-dimensional space–time is given. Then, a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is derived. It is also proved that a shell with total mass equal to charge, i.e. an extremal shell, in an empty interior, can only stay in neutral equilibrium outside its gravitational radius. This implies that it is not possible to generate a regular extremal black hole by placing an extremal dust thin shell within its own gravitational radius. Moreover, it is shown, for an empty interior, that the rest mass of the shell is limited from above. Then, several types of behavior of oscillatory charged shells are studied. In the presence of a horizon, it is shown that an oscillatory shell always enters the horizon and reemerges in a new asymptotically flat region of the extended Reissner–Nordström space–time. On the other hand, for an overcharged interior, i.e. a shell with no horizons, an example showing that the shell can achieve a stable equilibrium position is presented. The results presented have applications in brane scenarios with extra large dimensions, where the creation of tiny higher-dimensional charged black holes in current particle accelerators might be a real possibility, and generalize to higher dimensions previous calculations on the dynamics of charged shells in four dimensions.

Uniqueness theorem of static degenerate and nondegenerate charged black holes in higher dimensions

We prove the uniqueness theorem for static higher dimensional charged black holes spacetime containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon.