Non-extremal Black Holes Research Articles

Hawking radiation of asymptotically nonflat dyonic black holes in Einstein-Maxwell-dilaton gravity

In the present paper, we investigate the Hawking radiation of asymptotically nonflat dyonic black holes in 4D Einstein-Maxwell-dilaton gravity in semiclassical approximation. We show that the problem allows an exact analytical treatment and we compute exactly the semiclassical radiation spectrum of both nonextremal and extremal black holes under consideration. In the high-frequency regime, we find that the Hawking temperature does not agree with the surface gravity when the magnetic charge is nonzero. Even more surprisingly, the Hawking temperature is independent of the black hole intrinsic characteristics, as the mass and magnetic charge, and depends only on the linear dilaton background parameter.

Static nonextremal AdS4 black hole solutions

We find new static nonextremal black hole solutions that asymptote to AdS4 in D = 4 gauged $ \mathcal{N} $ = 2 supergravity. Solutions include electric and magnetic black holes with constant scalars that in the BPS limit reduce to naked singularities, but also magnetic black holes with running scalars that at extremality reduce to BPS black holes with finite horizon area. For all these solutions we compute area product formulae and show they are independent of the mass. Finally, we also find new examples of nonextremal magnetic black branes.

Black hole uniqueness theorems and new thermodynamic identities in eleven dimensional supergravity

We consider stationary, non-extremal black holes in 11-dimensional supergravity having isometry group . We prove that such a black hole is uniquely specified by its angular momenta, its electric charges associated with the 7-cycles in the manifold, together with certain moduli and vector valued winding numbers characterizing the topological nature of the spacetime and group action. We furthermore establish interesting, non-trivial, relations between the thermodynamic quantities associated with the black hole. These relations are shown to be a consequence of the hidden E8( + 8) symmetry in this sector of the solution space, and are distinct from the usual ‘Smarr-type’ formulas that can be derived from the first law of black hole mechanics. We also derive the ‘physical process’ version of this first law applicable to a general stationary black hole spacetime without any symmetry assumptions other than stationarity, allowing in particular arbitrary horizon topologies. The work terms in the first law exhibit the topology of the horizon via the intersection numbers between cycles of various dimension.

Subtracted geometry from Harrison transformations

We consider the rotating non-extremal black hole of N=2 D=4 STU supergravity carrying three magnetic charges and one electric charge. We show that its subtracted geometry is obtained by applying a specific SO(4,4) Harrison transformation on the black hole. As previously noted, the resulting subtracted geometry is a solution of the N=2 S=T=U supergravity.

STATE-SPACE GEOMETRY, NONEXTREMAL BLACK HOLES AND KALUZA–KLEIN MONOPOLES

We examine the statistical nature of the charged anticharged nonextremal black holes in string theory. From the perspective of the intrinsic Riemannian geometry, the first principle of the statistical mechanics shows that the stability properties of general nonextremal nonlarge charged black brane solutions are divulged from the positivity of the corresponding principle minors of the space-state metric tensor. Under the addition of the Kaluza–Klein monopoles, a novel aspect of the Gaussian fluctuations demonstrates that the canonical fluctuations can be ascertained without any approximation. We offer the state-space geometric implication for the most general nonextremal black brane configurations in string theory.

Metastable supertubes and non-extremal black hole microstates

Abstract We study the dynamics of supertubes in smooth bubbling geometries with three charges and three dipole charges that can describe black holes, black rings and their microstates. We find the supertube Hamiltonian in these backgrounds and show that there exist metastable supertube configurations, that can decay into supersymmetric and nonsupersymmetric ones via brane-flux annihilation. We also find stable non-supersymmetric configurations. Both the metastable and the stable non-supersymmetric configuration are expected to describe microstate geometries for non-extremal black holes, and we discuss the implication of their existence for the fuzzball proposal.

Holographic description of three-dimensional Gödel black hole

Three-dimensional G\"odel black hole is a solution to Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We have studied the hidden conformal symmetry for massive scalar field without any additional condition in the background of three-dimensional nonextremal and extremal G\"odel black holes. This conformal symmetry is uncovered by the observation that the radial wave equations in both cases can all be rewritten in the form of $SL(2,R)$ Casimir operators through introducing two sets of conformal coordinates to write the $SL(2,R)$ generators. At last, we give the holographic dual descriptions of Bekenstein-Hawking entropies of nonextremal and extremal black holes from Cardy formula of conformal field theory.

New instability of non-extremal black holes: spitting out supertubes

Abstract We search for stable bound states of non-extremal rotating three-charge black holes in five dimensions (Cvetic-Youm black holes) and supertubes. We do this by studying the potential of supertube probes in the non-extremal black hole background and find that generically the marginally bound state of the supersymmetric limit becomes metastable and disappears with non-extremality (higher temperature). However near extremality there is a range of parameters allowing for stable bound states, which have lower energy than the supertube-black hole merger. Angular momentum is crucial for this effect. We use this setup in the D1-D5 decoupling limit to map a thermodynamic instability of the CFT (a new phase which is entropically dominant over the black hole phase) to a tunnelinginstability of the black hole towards the supertube-black hole bound state. This generalizes the results of [1], which mapped an entropy enigma in the bulk to the dual CFT in a supersymmetric setup.

Non-extremal black holes of [formula omitted], [formula omitted] supergravity

We study the generalization of the Ansatz of Galli et al. (2011) [1] for non-extremal black holes of N=2, d=4 supergravities for a simple model of N=2, d=5 supergravity with a vector multiplet whose moduli space has two branches. We use the formalism of Ferrara, Gibbons and Kallosh (1997) [2], which we generalize to any dimension d. We find that the equations of motion of the model studied can be completely integrated without the use of our Anstaz (which is, nevertheless, recovered in the integration). The family of solutions found (common to both branches) is characterized by five independent parameters: the mass M, the electric charges q0, q1, the asymptotic value of the scalar at infinity ϕ∞ and the scalar charge Σ. The solutions have a singular horizon whenever Σ differs from a specific expression Σ0(M,q0,q1,ϕ∞) (i.e. when there is primary scalar hair Σ−Σ0≠0). The family of regular black holes interpolates between its two extremal limits. The supersymmetry properties of the extremal solutions depend on the choice of branch: one is always supersymmetric and the other non-supersymmetric in one branch and the reverse in the other one.

Particle acceleration in Kerr–(anti-)de Sitter black hole backgrounds

Banãdos, Silk and West (BSW) proved that Kerr black holes could act as particle accelerators with arbitrarily high center-of-mass energy, if two conditions are satisfied: (1) these black holes are extremal; (2) one of the colliding particles has critical angular momentum. In this paper, we extend the research to the cases of Kerr–(anti-)de Sitter black holes and find that the cosmological constant has an important effect on the result. In order for the case of Kerr–anti-de Sitter black holes (with negative cosmological constant) to get arbitrary high center-of-mass energy, we need an additional condition besides the above two for Kerr ones. While, for the case of general Kerr–de Sitter black holes (with positive cosmological constant), the collision of two particles can take place on the outer horizon of the black holes and the center-of-mass energy of collision can blow up arbitrarily if the above second condition is satisfied. Hence, non-extremal Kerr-de Sitter black holes could also act as particle accelerators with arbitrarily high center-of-mass energy.

HIGH ENERGY PROCESSES IN THE VICINITY OF THE KERR'S BLACK HOLE HORIZON

Two particle collisions close to the horizon of the rotating nonextremal black hole are analyzed. It is shown that high energy of the order of the Grand Unification scale in the centre of mass of colliding particles can be obtained when there is a multiple collision – the particle from the accretion disc gets the critical momentum in first collision with the other particle close to the horizon and then there is a second collision of the critical particle with the ordinary one. High energy occurs due to a great relative velocity of two particles and a large Lorentz factor. The dependence of the relative velocity on the distance to horizon is analyzed, the time of movement from the point in the accretion disc to the point of scattering with large energy as well as the time of back movement to the Earth are calculated. It is shown that they have reasonable order.

Euclidean dilaton black hole vortex and Dirac fermions

We considered the behaviour of Dirac fermion modes in the background of Euclidean dilaton black hole with an Abelian Higgs vortex passing through it. Fermions were coupled to the fields due to the superconducting string model. The case of nonextremal and extremal charged black hole in the theory with arbitrary coupling constant between dilaton field and U(1)-gauge field were considered. We elaborated the cases of zero and non-zero Dirac fermion modes. One finds the evidence that the system under consideration can support fermion fields acting like superconducting hair on black hole in the sence that nontrivial spinor field configuration can be carried by Euclidean spherically symmetric charged dilaton black hole. It was revealed that the localization of Dirac fermion modes depended on the cosmic string winding number and the value of black hole surface gravity.

Non-extremal Kerr black holes as particle accelerators

It has been shown that extremal Kerr black holes can be used as particle accelerators and arbitrarily high energy may be obtained near the event horizon. We study particle collisions near the event horizon (outer horizon) and Cauchy horizon (inner horizon) of a non-extremal Kerr black hole. Firstly, we provide a general proof showing that particles cannot collide with arbitrarily high energies at the outter horizon. Secondly, we show that ultraenergetic collisions can occur near the inner horizon of a Kerr black hole with any spin parameter $a$.

General hidden conformal symmetry of 4D Kerr-Newman and 5D Kerr black holes

There are two known CFT duals, namely the J-picture and the Q-picture, for a four-dimensional Kerr-Newman black hole, corresponding to the angular momentum J and the electric charge Q respectively. In our recent study we found a one-parameter class of CFT duals for extremal Kerr-Newman black hole, connecting these two pictures. In this paper we study these novel CFT duals for the generic non-extremal Kerr-Newman black hole. We investigate the hidden conformal symmetry in the low frequency scattering off Kerr-Newman black hole, from which the dual temperatures could be read. We find that there still exists a hidden conformal symmetry for a general CFT dual. We reproduce the correct Bekenstein-Hawking entropy from the Cardy formula, assuming the form of the central charge being invariant. Moreover we compute the retarded Green’s function in the general CFT dual picture and find it is in good match with the CFT prediction. Furthermore we discuss the hidden conformal symmetries of the five dimensional Kerr black hole and obtain the similar evidence to support the general dual CFT pictures.

Non-extremal black holes of N = 2, d = 4 supergravity

We propose a generic recipe for deforming extremal black holes into non-extremal black holes and we use it to find and study the non-extremal black-hole solutions of several N=2,d=4 supergravity models (SL(2,R)/U(1), CPn and STU with four charges). In all the cases considered, the non-extremal family of solutions smoothly interpolates between all the different extremal limits, supersymmetric and not supersymmetric. This fact can be used to find explicitly extremal non-supersymmetric solutions in the cases in which the attractor mechanism does not completely fix the values of the scalars on the event horizon and they still depend on the boundary conditions at spatial infinity. We compare (supersymmetry) Bogomol'nyi bounds with extremality bounds, we find the first-order flow equations for the non-extremal solutions and the corresponding superpotential, which gives in the different extremal limits different superpotentials for extremal black holes. We also compute the "entropies" (areas) of the inner (Cauchy) and outer (event) horizons, finding in all cases that their product gives the square of the moduli-independent entropy of the extremal solution with the same electric and magnetic charges.

Regular black holes: Electrically charged solutions, Reissner-Nordström outside a de Sitter core

To have the correct picture of a black hole as a whole, it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the physical laws and, as such, should be substituted in one way or another. A proposal that has been around for sometime is to replace the singular region of the spacetime by a region containing some form of matter or false vacuum configuration that can also cohabit with the black hole interior. Black holes without singularities are called regular black holes. In the present work, regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstr\"om, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several types of solutions: regular nonextremal black holes with a null matter boundary, regular nonextremal black holes with a timelike matter boundary, regular extremal black holes with a timelike matter boundary, and regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed.

Electric charge on the brane?

We consider black holes localized on the brane in the Randall-Sundrum infinite braneworld model. These configurations are static and charged with respect to a spherically symmetric, electric Maxwell field living on the brane. We start by attempting to construct vacuum black holes, in which case our conclusions are in agreement with those of Yoshino [J. High Energy Phys. 01 (2009) 068]. Although approximate solutions appear to exist for sufficiently small brane tension, these are likely only numerical artifacts. The qualitative features of the configurations in the presence of a brane U(1) electric field are similar to those in the vacuum case. In particular, we find a systematic unnatural behavior of the metric functions in the asymptotic region in the vicinity of the anti--de Sitter horizon. Our results are most naturally interpreted as evidence for the nonexistence of static, nonextremal charged black holes on the brane. In contrast, extremal black holes are more likely to exist on the brane. We determine their near-horizon form by employing both analytical and numerical methods. For any bulk dimension $d>4$, we find good agreement between the properties of large extremal black holes and the predictions of general relativity, with calculable subleading corrections.

Extremal and nonextremal Kerr/CFT correspondences

I rederive the Kerr/CFT correspondence without first taking the near-horizon extremal Kerr limit. This method extends easily to nonextremal black holes, for which the temperature and central charge behave poorly at the horizon but the entropy remains finite. A computation yields one-half of the standard Bekenstein-Hawking entropy, with hints that the other half may be related to a conformal field theory at the inner horizon. I then present an alternative approach, based on a stretched Killing horizon, in which the full entropy is obtained and the temperature and central charge remain well-behaved even in the nonextremal case.

Tunneling effect of Dirac particles from the non-extremal black hole in D = 5, SO(6) gauged supergravity

Recent research shows that Hawking radiation from black hole horizon can be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man’s fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from the non-extremal black hole in D = 5, SO(6) gauged supergravity by constructing a set of appropriate matrices γ μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods.

Extremal black holes, gravitational entropy and nonstationary metric fields**Based on an essay selected for honorable mention in the 2010 Gravity Research Foundation Essay Competition. This work was partly completed at KITP, Santa Barbara, CA, USA.

We show that extremal black holes have zero entropy by pointing out a simple fact: they are time independent throughout the spacetime and correspond to a single classical microstate. We show that nonextremal black holes, including the Schwarzschild black hole, contain a region hidden behind the event horizon where all their Killing vectors are spacelike. This region is nonstationary and the time t labels a continuous set of classical microstates, the phase space [hab(t), Pab(t)], where hab is a three-metric induced on a spacelike hypersurface Σt and Pab is its momentum conjugate. We determine explicitly the phase space in the interior region of the Schwarzschild black hole. We identify its entropy as a measure of an outside observer's ignorance of the classical microstates in the interior since the parameter t which labels the states lies anywhere between 0 and 2M. We provide numerical evidence from recent simulations of gravitational collapse in isotropic coordinates that the entropy of the Schwarzschild black hole stems from the region inside and near the event horizon where the metric fields are nonstationary; the rest of the spacetime, which is static, makes no contribution. Extremal black holes have an event horizon but in contrast to nonextremal black holes, their extended spacetimes do not possess a bifurcate Killing horizon. This is consistent with the fact that extremal black holes are time independent and therefore have no distinct time reverse.