Extremal Limit Research Articles

Where is the extremal Kerr ISCO?

Although the circular photon orbit and ISCO for the Kerr black hole remain distinct from each other and from the horizon in the extremal spin limit on a constant Boyer–Lindquist time slice, on a horizon-crossing slice they both coincide with the null generators of the horizon.Communicated by E Poisson

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.

Holographic Description of Rotating Charged Black Holes in Extremal Limit

We show that extremal rotating charged black holes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in rotating charged spacetimes and find in the “near region”, the wave equation in extremal limit can be written in terms of SL(2,R) Casimir invariants. Moreover, we obtain the microscopic entropy of the rotating charged black holes and find the correlation function of a near-region scalar field matches to the microscopic greybody factor of the dual 2D CFT. Subject Index: 121, 122, 124, 129, 454

Rotating charged cylindrical black holes as particle accelerators

It has recently been pointed out that arbitrary center-of-mass energies may be obtained for particle collisions near the horizon of an extremal Kerr black hole. We investigate this mechanism in cylindrical topology. In particular we consider the center-of-mass energies of a cylindrical black hole with an extremal rotation and charge parameter. The geodesics are first derived with a rotating charged cylindrical black hole producing the background gravitational field. Finally the center-of-mass is determined for this background and its extremal limit is taken.

HIDDEN CONFORMAL SYMMETRY OF ROTATING NS5-BRANES IN EXTREMAL LIMIT

We show that extremal rotating NS5-branes space–times have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal NS5-branes space–times and find in the "near region," the wave equation in extremal limit can be written in terms of the SL (2, R) quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal NS5-branes space–times, also we calculate the correlation function of a near-region scalar field and find perfect agreement with the dual 2D CFT.

Gravitational perturbation of the BTZ black hole induced by test particles and weak cosmic censorship in AdS spacetime

We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ringlike distribution of test particles in the BTZ background. This setup ensures that the $U(1)$ symmetry of the background is preserved. The nonasymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the best of our knowledge, has never been addressed in the literature. We confirm that the naive expressions for energy and angular momentum are the correct definitions. Finally, we put an asymptotically AdS version of the weak cosmic censorship to a test: by attempting to overspin the BTZ black hole with test particles it is found that the black hole cannot be spun-up past its extremal limit.

Hidden Conformal Symmetry of Extremal BMPV Black Hole

We show that extremal BMPV black holes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal BMPV spacetime and find in the “near region”, the wave equation in extremal limit could be written in terms of the SL(2, R) quadratic Casimir. From the new conformal coordinates, the temperatures of the dual CFTs could be read directly. For the extremal black hole, the Hawking temperature is vanishing. Correspondingly, only the left (right) temperature of the dual CFT is non-vanishing and the excitations of the other sector are suppressed. Moreover, we obtain the microscopic entropy of the extremal BMPV black hole and find that the correlation function of a near-region scalar field matches to the microscopic greybody factor of the dual 2D CFT.

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.

Energy scales in a holographic black hole and conductivity at finite momentum

In this work we discuss the low temperature (T) behavior of gauge field correlators with finite momentum (k) in a AdS4 black hole background. At low temperature, a substantial nonzero conductivity is only possible for a frequency range ω > ωg = k. This tallies with the simple fact that at least an amount of energy ωg is needed to create an excitation of momentum k. Due to the existence of this “gap”, one may expect that at the zero frequency limit the real part of momentum-dependent conductivity falls exponentially with 1/T. Using analytic methods, we found a exp(–ωc/T) falloff of the real part of conductivity with inverse temperature. Interestingly, ωg ≠ ωc. From the above results, we speculate that the “degrees of freedom”, say carriers, different than quasiparticle excitation determines conductivity at the low temperature and the low-frequency limit. Here ωc < ωg, and we may calculate their ratios analytically. We also discuss similar issues at a finite chemical potential. The situation is rather different for an extremal blackhole. A zero temperature extremal blackhole does not show a sharp gap for the finite momentum excitations, and the real part of the conductivity is always nonzero for any nonzero frequency ω. However, the real part of the conductivity goes to zero at the ω → 0 limit. Not surprisingly, we find a power-law decay with temperature for the same quantity, as the extremal limit is approached.

Holographic description of Kerr–Bolt–AdS–dS spacetimes

We show that there exists a holographic 2D CFT description of a Kerr–Bolt–AdS–dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr–Bolt–AdS–dS spacetimes and find in the “near region”, the wave equation in extremal limit could be written in terms of the SL ( 2 , R ) quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four-dimensional non-extremal Kerr–Bolt–AdS–dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the SL ( 2 , R ) quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the super-radiant scattering, the retarded Greenʼs functions and the corresponding absorption cross sections are in perfect match with CFT prediction.

A holographic description of extremal black holes

We show that the extremal Einstein–Maxwell–Dilaton–Axion (EMDA) black hole and the extremal Kaluza–Klein black hole have a hidden conformal symmetry. In this regard, we consider the wave equations of a massless scalar field propagating in EMDA and Kaluza–Klein spacetimes and find in the ‘near region', the wave equations in the extremal limit can be written in terms of SL(2, R) Casimir invariants. Moreover, we obtain the microscopic entropy of the extremal EMDA black hole and extremal Kaluza–Klein black hole and find that the correlation function of a near-region scalar field matches the microscopic graybody factor of the dual 2D CFT.

Thermodynamic stability of warped [formula omitted] black holes

We study the thermodynamic stability of warped black holes in three-dimensional topologically massive gravity. The spacelike stretched black hole is parametrized by its mass and angular momentum. We determine the local and global stability properties in the canonical and grand canonical ensembles. The presence of a Hawking–Page type transition is established, and the critical temperature is determined. The thermodynamic metric of Ruppeiner is computed, and the curvature is shown to diverge in the extremal limit. The consequences of these results for the classical stability properties of warped black holes are discussed within the context of the correlated stability conjecture.

Test Bodies and Naked Singularities: Is the Self-Force the Cosmic Censor?

Jacobson and Sotiriou showed that rotating black holes could be spun up past the extremal limit by the capture of nonspinning test bodies, if one neglects radiative and self-force effects. This would represent a violation of the cosmic censorship conjecture in four-dimensional, asymptotically flat spacetimes. We show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.

Circular orbits in extremal Reissner–Nordstrom spacetime

Circular null geodesic orbits, in extremal Reissner–Nordstrom spacetime, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely on the event horizon which coincides with the null geodesic generator. Such a null orbit on the horizon is also indicated by the global minimum of the effective potential for circular timelike orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry.

A general black string and its microscopics

Using G2(2) dualities we construct the most general black string solution of minimal five-dimensional ungauged supergravity. The black string has five independent parameters, namely, the magnetic one-brane charge, smeared electric zero-brane charge, boost along the string direction, energy above the BPS bound, and rotation in the transverse space. In one extremal limit it reduces to the three parameter supersymmetric string of five-dimensional minimal supergravity; in another extremal limit it reduces to the three parameter non-supersymmetric non-rotating extremal string of five-dimensional minimal supergravity. It also admits an extremal limit when it has maximal rotation in the four-dimensional transverse space. The decoupling limit of our general black string is a BTZ black hole times a two sphere. The macroscopic entropy of the string is reproduced by the Maldacena-Strominger-Witten CFT in appropriate ranges of the parameters. When the pressureless condition is imposed, our string describes the infinite radius limit of the most general class of black rings of minimal supergravity. We discuss implications our solution has for extremal and non-extremal black rings of minimal supergravity.

Hidden conformal symmetry of extremal Kerr-Bolt spacetimes

We show that extremal Kerr-Bolt spacetimes have a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt spacetimes and find in the ”near region”, the wave equation in extremal limit can be written in terms of the SL(2,R) quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal Kerr-Bolt spacetimes also we calculate the correlation function of a near-region scalar field and find perfect agreement with the dual 2D CFT.

Vector unparticle enhanced black holes: Exact solutions and thermodynamics

Tensor and scalar unparticle couplings to matter have been shown to enhance gravitational interactions and provide corrections to the Schwarzschild metric and associated black hole structure. We derive an exact solution to the Einstein equations for vector unparticles, and conclusively demonstrate that these induce Riessner–Nordström (RN)-like solutions where the role of the “charge” is defined by a composite of unparticle phase space parameters. These black holes admit double-horizon structure, although unlike the RN metric these solutions have a minimum inner horizon value. In the extremal limit, the Hawking temperature is shown to vanish. As with the scalar/tensor case, the (outer) horizon is shown via entropy considerations to behave like a fractal surface of spectral dimension dH=2dU.

Three dimensional origin of AdS 2 quantum gravity

We study AdS2 quantum gravity with emphasis on consistency with results from AdS3. We lift AdS2 black holes to three dimensions and map fluctuations around the solutions. Comparison with near extremal BTZ are discussed, with due emphasis on global aspects. The results confirm that parameters like central charges and conformal weights computed directly in 2D are consistent with standard results in 3D. Applying our results to the thermodynamics of near extreme Kerr black holes, we show that AdS2 quantum gravity gives the correct central charge c = 12J, and the entropy of excitations above the extremal limit is captured correctly.

Physical properties of the double-Kerr solution

We analysed two special cases of the double-Kerr solution describing a system of two stationary co-axial Kerr black holes, with equal mass and either the same or opposite angular momentum. These cases are asymptotically flat and obey the axis condition, but there is always a strut (i.e. a conical singularity) between the black holes, preventing the collapse of the system. Studying the force associated to the strut, we show that the force between the two black holes is more attractive in the counter-rotating than in the co-rotating case. We also show that, for both the counter-rotating and co-rotating cases, 1) the angular velocity of the two black holes decreases as they approach one another, for fixed mass and angular momentum; 2) the extremal limit J/M2 varies with the distance between the black holes and may even be larger than one. These results are interpreted in terms of rotational dragging effects.

Destroying black holes with test bodies

If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.