Extremal Einstein–Born–Infeld black holes in dilaton gravity

Motivated by considerable interests of Myers–Perry black holes, we employ the perturbative method to obtain a family of extremal charged rotating black hole solutions in odd dimensional Einstein–Born–Infeld-dilaton gravity. We start with an extremal Myers–Perry black hole with equal angular momenta, and then by adding the dilaton field and the nonlinear Born–Infeld electrodynamics, we find an extremal nonlinearly charged rotating black holes. The perturbative parameter is assumed to be the electric charge q$q$ and the perturbations are performed up to the third order. We then study the physical properties of these Born–Infeld-dilaton black holes. In particular, we show that the perturbative parameter, q$q$, the dilaton coupling constant, α$\alpha$, and the Born–Infeld parameter, β$\beta$, modify the Smarr formula and the values of the gyromagnetic ratio of the extremal charged rotating black holes.     

Geonic black holes and remnants in Eddington-inspired Born–Infeld gravity

We show that electrically charged solutions within the Eddington-inspired Born–Infeld theory of gravity replace the central singularity by a wormhole supported by the electric field. As a result, the total energy associated with the electric field is finite and similar to that found in the Born–Infeld electromagnetic theory. When a certain charge-to-mass ratio is satisfied, in the lowest part of the mass and charge spectrum the event horizon disappears, yielding stable remnants. We argue that quantum effects in the matter sector can lower the mass of these remnants from the Planck scale down to the TeV scale.     

Magnetic strings in Einstein–Born–Infeld-dilaton gravity

A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. These solutions have no curvature singularity and no horizon, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. Although the asymptotic behavior of these solutions are neither flat nor (A)dS, we calculate the conserved quantities of these solutions by using the counterterm method. We also generalize these four-dimensional solutions to the case of (n+1)$(n+1)$-dimensional rotating solutions with k?[n/2]$k?[n/2]$ rotation parameters, and calculate the conserved quantities and electric charge of them.     

P–V criticality of topological black holes in Lovelock–Born–Infeld gravity

To understand the effect of third order Lovelock gravity, $P$ – $V$ criticality of topological AdS black holes in Lovelock–Born–Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case $\beta \rightarrow \infty $ is performed for the seven-dimensional black holes. It is shown that, for the spherical topology, $P$ – $V$ criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P$ – $V$ criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss–Bonnet black holes. For $k=0$ , there would be no $P$ – $V$ criticality. Interesting findings occur in the case $k=-1$ , in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the $P$ – $v$ diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of $\alpha $ , the entropy is always positive for any specific volume $v$ . Since no $P$ – $V$ criticality exists for $k=-1$ in Einstein gravity and Gauss–Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss–Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and “swallow tail” behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.     

Higher-dimensional black holes with Dirac–Born–Infeld (DBI) global defects

It is well-known that the exact solution of non-linear \(\sigma \) model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein’s equations coupled to a non-linear \(\sigma \) model with Dirac–Born–Infeld (DBI) kinetic term in D dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all D, but they can be expressed as polynomial functions in r only when D is even. We give conditions for the mass M and the scalar charge \(\eta \) in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical \(\eta \). This behavior can also be observed for variation of DBI coupling, \(\beta \). As it gets stronger (\(\beta \ll 1\)) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking–Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.     

N-dimensional non-abelian dilatonic,stable black holes and their Born–Infeld extension

We find large classes of non-asymptotically flat Einstein–Yang–Mills–Dilaton and Einstein–Yang–Mills–Born–Infeld–Dilaton black holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass. Extension of the dilatonic YM solution to N-dimensions has been possible by employing the generalized Wu-Yang ansatz. Another metric ansatz, which aided in finding exact solutions is the functional dependence of the radius function on the dilaton field. These classes of black holes are stable against linear radial perturbations. In the limit of vanishing dilaton we obtain Bertotti–Robinson type metrics with the topology of AdS ₂×S ^N–2. Since connection can be established between dilaton and a scalar field of Brans–Dicke type we obtain black hole solutions also in the Brans–Dicke–Yang–Mills theory as well.     

Gravitational perturbation and quasi-normal modes of charged black holes in Einstein–Born–Infeld gravity

Born–Infeld electrodynamics has attracted considerable interest due to its relation to strings and D-branes. In this paper the gravitational perturbations of electrically charged black holes in Einstein–Born–Infeld gravity are studied. The effective potentials for axial perturbations are derived and discussed. The quasi normal modes for the gravitational perturbations are computed using a WKB method. The modes are compared with those of the Reissner–Nordström black hole. The relation of the quasi normal modes with the non-linear parameter and the spherical index are also investigated. Comments on stability of the black hole and on future directions are madeThis revised version was published online in April 2005. The publishing date was inserted.     

Analytical solutions in a cosmic string Born–Infeld-dilaton black hole geometry: quasinormal modes and quantization

Chargeless massive scalar fields are studied in the spacetime of Born–Infeld dilaton black holes (BIDBHs). We first separate the massive covariant Klein–Gordon equation into radial and angular parts and obtain the exact solution of the radial equation in terms of the confluent Heun functions. Using the obtained radial solution, we show how one gets the exact quasinormal modes for some particular cases. We also solve the Klein–Gordon equation solution in the spacetime of a BIDBHs with a cosmic string in which we point out the effect of the conical deficit on the BIDBHs. The analytical solutions of the radial and angular parts are obtained in terms of the confluent Heun functions. Finally, we study the quantization of the BIDBH. While doing this, we also discuss the Hawking radiation in terms of the effective temperature.     

Tunneling across dilaton–axion black holes

In this work we study both charged and uncharged particles tunneling across the horizon of spherically symmetric dilaton–axion black holes using Parikh–Wilczek tunneling formalism. Such black hole solutions have much significance in string theory based models. For different choices of the dilaton and axion couplings with the electromagnetic field, we show that the tunneling probability depends on the difference between initial and final entropies of the black hole. Our results, which agree with similar results obtained for other classes of black holes, further confirm the usefulness of Parikh–Wilczek formalism to understand Hawking radiation. The emission spectrum is shown to agree with a purely thermal spectrum only in the leading order. The modification of the proportionality factor in the area–entropy relation in the Bekenstein–Hawking formula has been determined.     

Are black holes black?

This work presents a resolution of the causality paradox formulated by T. D. Lee in the theory of the Unruh effect and in the theory of black holes. The basis of the resolution is to take into account the transformation of a pure state into a mixed state in a measurement, which leads to a corresponding modification of the Bogolyubov transformations, so that black holes remain black.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 95–97, May, 1989.The author thanks N. Sh. Urusova for discussion of the work.     

Charged black holes on Kaluza–Klein bubbles

We construct exact solutions of the Einstein–Maxwell field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza–Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza–Klein bubble and also the general charged static black Saturn balanced by a Kaluza–Klein bubble. A straightforward extension of the solution-generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investigate some of the thermodynamic properties of these systems.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

Asymptotic Reissner–Nordström black holes

We consider two types of Born–Infeld like nonlinear electromagnetic fields and obtain their interesting black hole solutions. The asymptotic behavior of these solutions is the same as that of a Reissner–Nordström black hole. We investigate the geometric properties of the solutions and find that depending on the value of the nonlinearity parameter, the singularity covered with various horizons.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.     

Universal properties of distorted Kerr–Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein–Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr–Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.     

Charged fermions tunnelling from Kerr–Newman black holes

We consider the tunnelling of charged spin 1/2 fermions from a Kerr–Newman black hole and demonstrate that the expected Hawking temperature is recovered. We discuss certain technical subtleties related to the obtention of this result.     

Photon emission of extremal Kerr–Newman black holes

In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr–Newman black hole background. In particular, using the matched asymptotic expansion method, we analytically solve the null geodesics near the superradiant bound in the form of algebraic equations. For the case that the photon trajectories are limited in the equatorial plane, the shifts in the azimuthal angle and time are obtained.