We extend the black hole/qudit correspondence by identifying five and six-dimensional 1/2-BPS black string and hole charge vectors in N=8 and N=2 magic supergravities with qubits and qutrits over composition algebras. In D=6, this is accomplished via Hopf fibrations, which map qubits over composition algebras to rank one elements of Jordan algebras of degree two. An analogous procedure maps qutrits over composition algebras to D=5 charge vectors, which are rank one elements of Jordan algebras of degree three. In both cases, the U-duality groups are interpreted as qudit SLOCC transformation groups. We provide explicit gates for such transformations and study their applications in toroidally compactified M-theory.
We recover the properties of a wide class of far from extremal charged black branes from the properties of near extremal black branes, generalizing the results of Danielsson, Guijosa and Kruczenski.
We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treatment is based on the following conjecture: extremal and non-extremal black holes ae qualitatively distinct entities. We show that only the latter method yields regularity and consistency at the one-loop …
Taking the extremal limit of a non-extremal Reissner-Nordström black hole (by externally varying the mass or charge), the region between the inner and outer event horizons experiences an interesting fate -- while this region is absent in the extremal case, it does not disappear in the extremal limit but rather approaches a patch of $AdS_2\times S^2$. In other words, the approach to extremality is not continuous, as the non-extremal Reissner-Nordström solution splits into two spacetimes at extremality: an extremal black hole and a disconnected $AdS$ space. We suggest that the unusual nature of …
We investigate the five and six-dimensional black strings within Einstein-Maxwell theory. The extremal black strings are endowed with the null Killing symmetry. We study the propagation of Einstein-Maxwell modes in the extremal black string background by using this symmetry. It turns out that one graviton is a propagating mode, while both the Maxwell $F$ and three-form $H$ fields are non-propagating modes. Further we discuss the stability and classical hair of the extremal black strings.
We show that the entropy of extremal $D=4$ Reissner--Nordstrom black holes can be computed from horizon CFTs with central charges and conformal weights fixed by the dimensionless Rindler energy. This is possible in the simultaneous extremal and near horizon limit of the black hole which takes the geometry to an $AdS_2$ Rindler space with finite temperature. The CFT description of dilatonic $AdS_2$ black holes, obtained from extremal ones by dimensional reduction, lead to exactly the same CFT states.
We present a new formulation of deriving Hawking temperature for near-extremal black holes using distributions. In this paper the near-extremal Reissner-Nordstrom and Kerr black holes are discussed. It is shown that the extremal solution as a limit of non-extremal metric is well-defined. The pure extremal case is also discussed separately.
We discuss the two-dimensional (2D), $ε<2$ extremal ground states of charged black hole. Here $ε$ is the dilaton coupling parameter for the Maxwell term. The complete analysis of stability is carried out for all these extremal black holes. It is found that they are all unstable. To understand this instability, we study the non-extremal charged black hole with two (inner and outer) horizons. The extremal black holes appear when two horizons coalesce. It conjectures that the instability originates from the inner horizon.
We use the relation between extremal black hole solutions in five- and in four-dimensional N=2 supergravity theories with cubic prepotentials to define the entropy function for extremal black holes with one angular momentum in five dimensions. We construct two types of solutions to the associated attractor equations.
In a recent paper (hep-th/0111091), the near-extremal thermodynamics of a 4-dimensional Reissner-Nordstrom black hole had been considered. In the current letter, we extend this prior treatment to the more general case of a spherically symmetric, charged black hole of arbitrary dimensionality. After summarizing the earlier work, we demonstrate a duality that exists between the near-extremal sector of spherically symmetric black holes and Jackiw-Teitelboim theory. On the basis of this correspondence, we argue that back-reaction effects prohibit any of these ``RN-like'' black holes from reaching …
The AdS_2\timesS^2 geometry of near-extremal Reissner-Nordstrom black holes can be described by an effective solvable model which allows to follow analytically the evaporation process including the backreaction. We find that an infinite amount of time is required for the black hole to decay to extremality.
We present a consolidated manual of Euclidean gravity approaches for finding the logarithmic corrections to the entropy of the full Kerr-Newman family of black holes in both extremal and non-extremal limits. Seeley-DeWitt coefficients for the quadratic fluctuations of a concern gravity theory appear to be the key ingredients in this manual. Following the manual, we calculate the first three Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes in a generalized Einstein-Maxwell theory minimally-coupled to additional massless scalar, vecto…
We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.
We show that the correct entropy, temperature (and absorption probability) of non-extremal black p-brane can be reproduced by a certain thermodynamical model when maximizing its entropy. We show that the form of the model is related to the geometrical similarity of non-extremal and near extremal black p-brane at near horizon region, and argue about the appropriateness of the model.
Freudenthal duality (F-duality), an anti-involution of charge vectors keep the entropy and attractor solutions invariant for an extremal supersymmetric black hole. In this paper, we analyze the effect of F-duality on the entropy of a near-extremal $STU$ black hole in $\mathcal{N}=2$ ungauged, four-dimensional supergravity. We consider double-extremal black holes, whose attractor solutions are fixed in terms of the black hole charges throughout the moduli space. It is well known that JT gravity governs the dynamics of the near-horizon regions of higher dimensional, near-extremal black holes. Ow…
String theory is used to count microstates of four-dimensional extremal black holes in compactifications with $N=4$ and $N=8$ supersymmetry. The result agrees for large charges with the Bekenstein-Hawking entropy.
Entropy for two dimensional extremal black holes is computed explicitly in a finite-space formulation of the black hole thermodynamics and is shown to be zero {\it locally}. Our results are in conformity with the recent one by Hawking et al in four dimensions.
We provide a realization of the AdS$_2$/CFT$_1$ correspondence in terms of asymptotic symmetries of the AdS$_2\times$S$^1$ and AdS$_2\times$S$^2$ geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality.
We derive a general form of first-order flow equations for extremal and non-extremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squares a la Bogomol'nyi, we identify the function governing the first-order gradient flow, the `generalised superpotential', which reduces to the `fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we …
We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N=2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five- and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.
We have learnt that the Bekenstein-Hawking entropy of supersymmetric black holes in five-dimensional minimal supergravity can be reproduced from microstate counting via the AdS/CFT and Kerr/CFT correspondence. In this note, we demostrate the coincidence of both formalisms for extremal and near-extremal black holes in five-dimensional minimal supergravity. Connection to AdS_2 gravity is also mentioned.
Using the quasi-normal modes frequency of extremal Reissner-Nordström black holes, we obtain area spectrum for these type of black holes. We show that the area and entropy black hole horizon are equally spaced. Our results for the spacing of the area spectrum differ from that of schwarzschild black holes.
We generalize the entropy function formalism to five-dimensional and four-dimensional non-extremal black holes in string theory. In the near horizon limit, these black holes have BTZ metric as part of the spacetime geometry. It is shown that the entropy function formalism also works very well for these non-extremal black holes and it can reproduce the Bekenstein-Hawking entropy of these black holes in ten dimensions and lower dimensions.
We consider N=2 supergravity in four dimensions with small R^2 curvature corrections. We construct large charge extremal supersymmetric and non-supersymmetric black hole solutions in all space, and analyze their thermodynamic properties.
We show that the exact entropy and the temperature (including coeffecient) of non-extremal black p-brane are calculated by maximizing the entropy under several assumptions. We argue the relation of those assumptions and certain Dp-D(p-2) system in compactified space.
Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of near extremal black $3-$branes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the near extremal black $3-$branes. The result for the area of event horizon although discrete, is not equally spaced.
It is believed that extremal black holes do not emit Hawking radiation as understood by taking extremal limits of non-extremal black holes. However, it is debated whether one can make such conclusion reliably starting from an extremal black hole, as the associated Bogoliubov coefficients which relate ingoing and outgoing field modes do not satisfy the required consistency condition. We address this issue in a canonical approach firstly by presenting an exact canonical derivation of the Hawking effect for non-extremal Kerr black holes. Subsequently, for extremal Kerr black holes we show that th…
We construct non-extremal as well as extremal black string solutions in minimal five-dimensional supergravity coupled to vector multiplets using dimensional reduction to three Euclidean dimensions. Our method does not assume that the scalar manifold is a symmetric space, and applies as well to a class of non-supersymmetric theories governed by a generalization of special real geometry. We find that five-dimensional black string solutions correspond to geodesics in a specific totally geodesic para-Kähler submanifold of the scalar manifold of the dimensionally reduced theory, and identify the su…
It is demonstrated that the near-horizon geometry of general non-extremal black holes can be described by a portion of AdS space. We show that the reason why hidden conformal symmetries near horizons of general non-extremal black holes are achieved in previous works is that the near-horizon geometries have been equivalently taken as these AdS segments rather than simply the Rindler space.
Using the blackfold effective theory applied to extremal Kerr branes we provide evidence for the existence of new stationary extremal black hole solutions in asymptotically flat spacetime with both single and multiple disconnected horizons. These include extremal doubly-spinning black rings, black saturns, di-rings and bi-rings in five spacetime dimensions as well as extremal Myers-Perry black holes and black saturns in dimensions greater than five. Some of these constructions constitute the first examples of black hole solutions with extremal disconnected horizons in vacuum Einstein gravity.
The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordstr$\ddot{o}$m anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordstr$\ddot{o}$m anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function $f$ at their final states. It is found that both of the near-extremal and extremal …
Analytic solutions to low-energy string theory, which describe arbitrary numbers of extreme `black holes (strings)' in linear dilaton vacua, are found.
We discuss the microscopic states of the extremal BTZ black holes. Degeneracy of the primary states corresponding to the extremal BTZ black holes in the boundary N=(4,4) SCFT is obtained by utilizing the elliptic genus and the unitary representation theory of N=4 SCA. The degeneracy is consistent with the Bekenstein-Hawking entropy.
The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black…
The extreme limit of a class of D-dimensional black holes is revisited. In the static limit, it is shown that well defined extremal limiting procedure exists and it leads to new solutions of the type AdS2 times constant curvature symmetric spaces.
We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.
Using the superpotential approach we generalize Denef's method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional N = 2 supergravity to allow non-supersymmetric solutions. We illustrate the general results with an explicit example of the stu model.
We construct the Euclidean on-shell action for the five-dimensional non-extremal black hole with multiple electric charges. We show that this thermal action agrees with one half of the entropy. This agreement is argued to be related to the generalized Smarr formula of the five-dimensional black hole mass. Through the calculation of the specific heat far off extremality we observe that a phase transition occurs.
We investigate the black string in the context of the string theories. It is shown that the graviton is the only propagating mode in the (2+1)--dimensional extremal black string background. Both the dilation and axion turn out to be non-propagating modes.
We study stationary black brane solutions in the context of N = 2, U(1) gauged supergravity in five dimensions. Using the formalism of first-order flow equations, we construct examples of extremal black brane solutions that include Nernst branes, i.e. extremal black brane solutions with vanishing entropy density, as well as black branes with cylindrical horizon topology, whose entropy density can be computed from a Cardy formula of the dual CFT.
We consider N=2 supergravity in four dimensions with small R^2 curvature corrections. We construct large charge non-extremal black hole solutions in all space, with either a supersymmetric or a non-supersymmetric extremal limit, and analyze their thermodynamic properties. This generalizes some of the extremal solutions presented in [arXiv:0902.0831]. The indexed entropy of the non-extremal extension of the supersymmetric black hole, has the form of the extremal entropy, with the charges replaced by a function of the charges, the moduli at infinity and the non-extremality parameter. This is the…
We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature showing that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extremal stringy black holes obeys the area law. An attempt is made to reconcile these arguments.
In this short note we extend the work of 1401.3746 about gravity waves by a massive orbiting star in an extremal Kerr black hole to an extremal Kerr- Newman black hole for scalar radiation, and still find that it has a CFT interpretation from Kerr-Newman/CFT. In addition, we investigate on electromagnetic radiation with Kerr/CFT, which a detailed analysis isn't given by 1401.3746.
After summarizing the development of black hole thermodynamics in the seventies, we describe a recent microscopic model. This model suggests that the Bekenstein-Hawking area formula holds for extremal black holes as well as for ordinary (non-extremal) ones. On the other hand, semiclassical studies have suggested a discontinuity between non-extremal and extremal cases. We indicate how a reconciliation has been brought about by summing over topologies.
We examine in details the entropy function formalism for non-extremal D3, M2, and M5-branes that their throat approximation is given by Schwarzschild black hole in AdS_{p+2} \times S^{D-(p+2)}. We show that even though there is no attractor mechanism in the non-extremal black holes/branes, the entropy function formalism does work and the entropy is given by the entropy function at its saddle point.
We study the low temperature expansion of the first law of thermodynamics for near-extremal black holes. We show that for extremal black holes with non-vanishing entropy, the leading order contribution yields an expression for their extremal entropy in agreement with the entropy function result and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and…
We construct a four-dimensional BPS saturated heterotic string solution from the Taub-NUT solution. It is a non-extremal black hole solution since its Euler number is non-zero. We evaluate its black hole entropy semiclassically. We discuss the relation between the black hole entropy and the degeneracy of string states. The entropy of our string solution can be understood as the microscopic entropy which counts the elementary string states without any complications.
We present a simple and yet rigorous derivation of the flow equations for the supersymmetric black-hole solutions of all 4-dimensional supergravities based on the recently found general form of all those solutions.
We consider the entropy of four-dimensional near-extremal N=2 black holes. Without R^2-terms, the Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We derive a generalized Wald entropy formula for non-extremal N=2 black holes with R^2-terms. We construct a class of small near-extremal horizon solutions with R^2-terms. In this case the entropy is the same as in the extremal case to order O(mu^2), and does not exhibit the charge shift behavior.
We consider Kerr-Newman-AdS-dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U(1)_L x U(1)_R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well defined and non-vanishing and to yield central charges c_L\neq0 and c_R=0. The Cardy formula subsequently reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr-New…
We obtain the $ε<2$ new extremal ground states of a two-dimensional (2D) charged black hole where $ε$ is the dilaton coupling parameter for the Maxwell term. The stability analysis is carried out for all these extremal black holes. It is found that the shape of potentials to an on-coming tachyon (as a spectator) take all barrier-well types. These provide the bound state solutions, which imply that they are unstable. We conclude that the 2D, $ε<2$ extremal black holes should not be considered as a toy model for the stable endpoint of the Hawking evaporation.
The problem of asymptotic density of quantum states of fundamental extended objects is revised in detail. We argue that in the near-extremal regime the fundamental $p$-brane approach can yield a microscopic interpretation of the black hole entropy. The asymptotic behavior of partition functions, associated with the $p$-branes, and the near-extremal entropy of five-dimensional black holes are explicitly calculated.
We study extremal cohomogeneity one five-dimensional asymptotically flat black holes of minimal supergravity in terms of the geodesics generated by nilpotent elements of the Lie algebra g2(2) on the coset manifold G2(2)/SO(2,2). There are two branches of regular extremal black holes with these properties: (i) the supersymmetric BMPV branch, and (ii) the non-supersymmetric extremal branch. We show that both of these branches are reproduced by nilpotent SO(2,2)-orbits. Furthermore, we show that the partial ordering of nilpotent orbits of G2(2) is in one-to-one correspondence with the phase diagr…
We take the method of anomaly cancellation for the derivation of Hawking radiation initiated by Robinson and Wilczek, and apply it to the non-extremal five-dimensional D1-D5 black hole in string theory. The fluxes of the electric charge flow and the energy-momentum tensor from the black hole are obtained. They are shown to match exactly with those of the two-dimensional black body radiation at the Hawking temperature.
We consider the perturbation of tachyon about the extremal ground state of a two-dimensional (2D) electrically charged black hole. It is found that the presenting potential to on-coming tachyonic wave takes a double-humped barrier well. This allows an exponentially growing mode with respect to time. This extremal ground state is classically unstable. We conclude that the 2D extremal electrically charged black hole cannot be a candidate for the stable endpoint of the Hawking evaporation.
Extremal black holes have vanishing Hawking temperatures. In this article, we argue that for asymptotically AdS black holes, at extremality, a particular class of correlators in the dual CFT can exhibit exponential, maximally chaotic growth with a non-vanishing temperature. Our approach, at extremality, is two-fold. First, we geometrically investigate the modes that are responsible for chaos. Secondly, we study the dynamics of a probe string to capture chaos in worldsheet correlators. For rotating BTZ at extremality, the corresponding Lyapunov exponent is determined by the left-moving temperat…
We review various properties of the exceptional Euclidean Jordan algebra of degree three. Euclidean Jordan algebras of degree three and their corresponding Freudenthal triple systems were recently shown to be intimately related to extremal black holes in N=2, d=4 homogeneous supergravities. Using a novel type of eigenvalue problem with eigenmatrix solutions, we elucidate the rich matrix geometry underlying the exceptional N=2, d=4 homogeneous supergravity and explore the relations to extremal black holes.
