Neutral Black Holes Research Articles

Global geometry of two-dimensional charged black holes

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation.

Semiclassical geometry of charged black holes

At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstr\"om black holes, including multiple asymptotic regions, timelike curvature singularities, and Cauchy horizons. The black hole spacetime is, however, significantly modified by quantum effects, which can be systematically studied in this two-dimensional context. In particular, the back-reaction on the geometry due to pair-creation of charged fermions destabilizes the inner horizon and replaces it with a spacelike curvature singularity. The semiclassical geometry has the same global topology as an electrically neutral black hole.

New phases of thermal SYM and LST from Kaluza‐Klein black holes

AbstractWe review the recently found map that takes any static and neutral Kaluza‐Klein black hole, i.e. any static and neutral black hole on Minkowski‐space times a circle ℳ︁d × S1, and maps it to a corresponding solution for a non‐ and near‐extremal brane on a circle. This gives a precise connection between phases of Kaluza‐Klein black holes and the thermodynamic behavior of the non‐gravitational theories dual to near‐extremal branes on a circle. In particular, for the thermodynamics of strongly‐coupled supersymmetric Yang‐Mills theories on a circle we predict the existence of a new non‐uniform phase and find new information about the localized phase. We also find evidence for the existence of a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

Topological G2 strings

AbstractWe review the recently found map that takes any static and neutral Kaluza‐Klein black hole, i.e. any static and neutral black hole on Minkowski‐space times a circle ℳ︁d × S1, and maps it to a corresponding solution for a non‐ and near‐extremal brane on a circle. This gives a precise connection between phases of Kaluza‐Klein black holes and the thermodynamic behavior of the non‐gravitational theories dual to near‐extremal branes on a circle. In particular, for the thermodynamics of strongly‐coupled supersymmetric Yang‐Mills theories on a circle we predict the existence of a new non‐uniform phase and find new information about the localized phase. We also find evidence for the existence of a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

New phases of thermal SYM and LST from Kaluza‐Klein black holes

AbstractWe review the recently found map that takes any static and neutral Kaluza‐Klein black hole, i.e. any static and neutral black hole on Minkowski‐space times a circle ℳ︁d × S1, and maps it to a corresponding solution for a non‐ and near‐extremal brane on a circle. This gives a precise connection between phases of Kaluza‐Klein black holes and the thermodynamic behavior of the non‐gravitational theories dual to near‐extremal branes on a circle. In particular, for the thermodynamics of strongly‐coupled supersymmetric Yang‐Mills theories on a circle we predict the existence of a new non‐uniform phase and find new information about the localized phase. We also find evidence for the existence of a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

Global embedding ofD-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).

SIGNATURES OF QUANTIZED TeV SCALE BLACK HOLES IN SCATTERING PROCESSES

In this paper we shall study the phenomenology of a doubly charged and neutral exchange black hole in an (n+3) extra-dimensional scenario, where the black hole shall be treated as a normal quantum field.

Instability of a four-dimensional de Sitter black hole with a conformally coupled scalar field

We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always unstable. The charged black holes are also shown analytically to be unstable for the vast majority of the parameter space of solutions, and we argue using numerical techniques that the configurations corresponding to the remainder of the parameter space are also unstable.

New Phases of Near-Extremal Branes on a Circle

We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle d × S1, and map it to a corresponding solution for a near-extremal brane on a circle. The map is derived using first a combined boost and U-duality transformation on the Kaluza-Klein black hole, transforming it to a solution for a non-extremal brane on a circle. The resulting solution for a near-extremal brane on a circle is then obtained by taking a certain near-extremal limit. As a consequence of the map, we can transform the neutral non-uniform black string branch into a new non-uniform phase of near-extremal branes on a circle. Furthermore, we use recently obtained analytical results on small black holes in Minkowski-space times a circle to get new information about the localized phase of near-extremal branes on a circle. This gives in turn predictions for the thermal behavior of the non-gravitational theories dual to these near-extremal branes. In particular, we give predictions for the thermodynamics of supersymmetric Yang-Mills theories on a circle, and we find a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.

Perturbative Uniqueness of Black Holes near the Static Limit in All Dimensions

The behaviour of stationary gravitational perturbations is studied for generalised static black holes in spacetimes of greater than three dimensions, using the formulation developed by the present author and Ishibashi. For the case in which the horizon has a spatial section with constant curvature, it is proved that irrespective of the value of the cosmological constant, there exists no stationary perturbation that is regular at the horizon(s) and falls off at infinity in the case of negative cosmological constant, except for those corresponding to the stationary rotation of black holes and the variation of the background parameters. This result indicates that regular neutral black hole solutions that are either asymptotically flat, de Sitter or anti-de Sitter can be parametrised by mass, (multiple component) angular momentum and the cosmological constant near the spherically symmetric and static limit. A similar conclusion is obtained for topological black holes. It is also pointed out that this perturbative uniqueness near the static limit may not hold in the case in which the horizon geometry is described by a generic Einstein space with non-constant sectional curvature. Further, non-uniqueness in the asymptotically anti-de Sitter case under a weaker boundary condition at infinity related to the AdS/CFT argument is discussed.

Pair creation of anti–de Sitter black holes on a cosmic string background

We analyze the quantum process in which a cosmic string breaks in an anti-de Sitter (AdS) background, and a pair of charged or neutral black holes is produced at the ends of the strings. The energy to materialize and accelerate the pair comes from the strings tension. In an AdS background this is the only study done in the process of production of a pair of correlated black holes with spherical topology. The acceleration $A$ of the produced black holes is necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant. Only in this case the virtual pair of black holes can overcome the attractive background AdS potential well and become real. The instantons that describe this process are constructed through the analytical continuation of the AdS C-metric. Then, we explicitly compute the pair creation rate of the process, and we verify that (as occurs with pair creation in other backgrounds) the pair production of nonextreme black holes is enhanced relative to the pair creation of extreme black holes by a factor of exp(Area/4), where Area is the black hole horizon area. We also conclude that the general behavior of the pair creation rate with the mass and acceleration of the black holes is similar in the AdS, flat and de Sitter cases, and our AdS results reduce to the ones of the flat case when L=0.

Nonsingular solutions fors-branes

Exact, non-singular, time-dependent solutions of Maxwell-Einstein gravity with and without dilatons are constructed by double Wick rotating a variety of static, axisymmetric solutions. This procedure transforms arrays of charged or neutral black holes into s-brane (spacelike brane) solutions, i.e. extended, short-lived spacelike defects. Along the way, new static solutions corresponding to arrays of alternating-charge Reissner-Nordstrom black holes, as well as their dilatonic generalizations, are found. Their double Wick rotation yields s-brane solutions which are periodic in imaginary time and potential large-N duals for the creation/decay of unstable D-branes in string theory.

Small black holes on cylinders

We find the metric of small black holes on cylinders, i.e. neutral and static black holes with a small mass in d-dimensional Minkowski-space times a circle. The metric is found using an ansatz for black holes on cylinders proposed in hep-th/0204047. We use the new metric to compute corrections to the thermodynamics which is seen to deviate from that of the (d+1)-dimensional Schwarzschild black hole. Moreover, we compute the leading correction to the relative binding energy which is found to be non-zero. We discuss the consequences of these results for the general understanding of black holes and we connect the results to the phase structure of black holes and strings on cylinders.

Pair creation of de Sitter black holes on a cosmic string background

We analyze the quantum process in which a cosmic string breaks in a de Sitter (dS) background, and a pair of neutral or charged black holes is produced at the ends of the string. The energy to materialize and accelerate the pair comes from the positive cosmological constant and, in addition, from the string tension. The compact saddle point solutions without conical singularities (instantons) or with conical singularities (sub-maximal instantons) that describe this process are constructed through the analytical continuation of the dS C-metric. Then, we explicitly compute the pair creation rate of the process. In particular, we find the nucleation rate of a cosmic string in a dS background, and the probability that it breaks and a pair of black holes is produced. Finally we verify that, as occurs with pair production processes in other background fields, the pair creation rate of black holes is proportional to exp(S), where the gravitational entropy of the black hole, S, is given by one quarter of the area of the horizons present in the saddle point solution that mediates the process.

Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings

We present new self-gravitating solutions in five dimensions that describe circular strings, i.e., rings, electrically coupled to a two-form potential (as e.g., fundamental strings do), or to a dual magnetic one-form. The rings are prevented from collapsing by rotation, and they create a field analogous to a dipole, with no net charge measured at infinity. They can have a regular horizon, and we show that this implies the existence of an infinite number of black rings, labeled by a continuous parameter, with the same mass and angular momentum as neutral black rings and black holes. We also discuss the solution for a rotating loop of fundamental string. We show how more general rings arise from intersections of branes with a regular horizon (even at extremality), closely related to the configurations that yield the four-dimensional black hole with four charges. We reproduce the Bekenstein-Hawking entropy of a large extremal ring through a microscopic calculation. Finally, we discuss some qualitative ideas for a microscopic understanding of neutral and dipole black rings.

Black holes in Gödel universes and pp waves.

We find exact solutions for rotating and nonrotating neutral black holes in the Gödel universe of five-dimensional minimal supergravity theory. We also describe the embedding of this solution in M-theory. After dimensional reduction and T-duality, we obtain a supergravity solution corresponding to placing a black string in a pp-wave background.

Thermal fluctuations and black-hole entropy

In this paper, we consider the effect of thermal fluctuations on the entropy of both neutral and charged black holes. We emphasize the distinction between fixed and fluctuating charge systems, using a canonical ensemble to describe the former and a grand canonical ensemble to study the latter. Our novel approach is based on the philosophy that the black-hole quantum spectrum is an essential component in any such calculation. For definiteness, we employ a uniformly spaced area spectrum, which has been advocated by Bekenstein and others in the literature. The generic results are applied to some specific models, in particular, various limiting cases of an (arbitrary-dimensional) AdS–Reissner–Nordstrom black hole. We find that the leading-order quantum correction to the entropy can consistently be expressed as the logarithm of the classical quantity. For a small AdS curvature parameter and zero net charge, it is shown that, independent of the dimension, the logarithmic prefactor is +1/2 when the charge is fixed but +1 when the charge is fluctuating. We also demonstrate that, in the grand canonical framework, the fluctuations in the charge are large, ΔQ ∼ ΔA ∼ S1/2BH, even when ⟨Q⟩ = 0. A further implication of this framework is that an asymptotically flat, non-extremal black hole can never achieve a state of thermal equilibrium.

Black holes and black strings on cylinders

AbstractWe review the recently discovered ansatz that describes non‐extremal charged dilatonic branes of string/M‐theory with a transverse circle. The ansatz involves a new coordinate system that interpolates between the spherical and cylindrical case, and reduces the equations of motion to a set of equations on one unknown function of two variables. The function is independent of the charge, so that the ansatz can also be used to construct neutral black holes on cylinders and near‐extremal charged dilatonic branes with a transverse circle. The construction enables us to argue that, for sufficiently large mass, there exists a neutral solution that breaks translational invariance in the circle direction, and has larger entropy than that of the neutral black string of the same mass.

Quantum mechanical spectra of charged black holes

It has been argued by several authors, using different formalisms, that the quantum mechanical spectrum of black hole horizon area is discrete and uniformly spaced. Recently it was shown that two such approaches, namely the one involving quantization on a reduced phase space, and the algebraic approach of Bekenstein and Gour are equivalent for spherically symmetric, neutral black holes (hep-th/0202076). That is, the observables of one can be mapped to those of the other. Here we extend that analysis to include charged black holes. Once again, we find that the ground state of the black hole is a Planck size remnant.

Many accelerating black holes

We show how the Weyl formalism allows metrics to be written down which correspond to arbitrary numbers of collinear accelerating neutral black holes in 3 + 1 dimensions. The black holes have arbitrary masses and different accelerations and share a common acceleration horizon. In the general case, the black holes are joined by cosmic strings or struts that provide the necessary forces that, together with the inter black-hole gravitational attractions, produce the acceleration. In the cases of two and three black holes, the parameters may be chosen so that the outermost black hole is pulled along by a cosmic string and the inner black holes follow behind accelerated purely by gravitational forces. We conjecture that similar solutions exist for any number of black holes.