arXiv subjects

David Tempo

Publications and source records attributed to David Tempo.

33 records · Page 2Linked to original sources

arXiv2015

Conserved charges and black holes in the Einstein-Maxwell theory on AdS$_{3}$ reconsidered

Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than the standard one for a localized distribution of matter, it is shown that, by virtue of a suitable choice of the electromagnetic Lagrange multiplier, the action attains a bona fide extremum provided the asymptotic form of the electromagnetic field fulfills a nontrivial integrability condition. As a consequence, the mass and the angular momentum become automatically finite, without the need of any regularization procedure, and they generically acquire contributions from the electromagnetic field. Therefore, unlike the higher-dimensional case, it is found that the precise value of the mass and the angular momentum explicitly depends on the choice of boundary conditions. It can also be seen that requiring compatibility of the boundary conditions with the Lorentz and scaling symmetries of the class of stationary solutions, singles out a very special set of "holographic boundary conditions" that is described by a single parameter. Remarkably, in stark contrast with the somewhat pathological behaviour found in the standard case, for the holographic boundary conditions (i) the energy spectrum of an electrically charged (rotating) black hole is nonnegative, and (ii) for a fixed value of the mass, the electric charge is bounded from above.

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arXiv2015

Hypersymmetry bounds and three-dimensional higher-spin black holes

We investigate the hypersymmetry bounds on the higher spin black hole parameters that follow from the asymptotic symmetry superalgebra in higher-spin anti-de Sitter gravity in three spacetime dimensions. We consider anti-de Sitter hypergravity for which the analysis is most transparent. This is a $osp(1\vert 4) \oplus osp(1\vert 4)$ Chern-Simons theory which contains, besides a spin-$2$ field, a spin-$4$ field and a spin-$5/2$ field. The asymptotic symmetry superalgebra is then the direct sum of two-copies of the hypersymmetric extension $W_{(2,\frac52,4)}$ of $W_{(2,4)}$, which contains fermionic generators of conformal weight $5/2$ and bosonic generators of conformal weight $4$ in addition to the Virasoro generators. Following standard methods, we derive bounds on the conserved charges from the anticommutator of the hypersymmetry generators. The hypersymmetry bounds are nonlinear and are saturated by the hypersymmetric black holes, which turn out to possess $1/4$-hypersymmetry and to be "extreme", where extremality can be defined in terms of the entropy: extreme black holes are those that fulfill the extremality bounds beyond which the entropy ceases to be a real function of the black hole parameters. We also extend the analysis to other $sp(4)$-solitonic solutions which are maximally (hyper)symmetric.

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arXiv2014

Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics

A generalized set of asymptotic conditions for higher spin gravity without cosmological constant in three spacetime dimensions is constructed. They include the most general temporal components of the gauge fields that manifestly preserve the original asymptotic higher spin extension of the BMS$_{3}$ algebra, with the same central charge. By virtue of a suitable permissible gauge choice, it is shown that this set can be directly recovered as a limit of the boundary conditions that have been recently constructed in the case of negative cosmological constant, whose asymptotic symmetries are spanned by two copies of the centrally-extended W$_{3}$ algebra. Since the generalized asymptotic conditions allow to incorporate chemical potentials conjugated to the higher spin charges, a higher spin extension of locally flat cosmological spacetimes becomes naturally included within the set. It is shown that their thermodynamic properties can be successfully obtained exclusively in terms of gauge fields and the topology of the Euclidean manifold, which is shown to be the one of a solid torus, but with reversed orientation as compared with one of the black holes. It is also worth highlighting that regularity of the fields can be ensured through a procedure that does not require an explicit matrix representation of the entire gauge group. In few words, we show that the temporal components of generalized dreibeins can be consistently gauged away, which partially fixes the chemical potentials, so that the remaining conditions can just be obtained by requiring the holonomy of the generalized spin connection along a thermal circle to be trivial. The extension of the generalized asymptotically flat behaviour to the case of spins $s\geq2$ is also discussed.

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arXiv2014

Brief review on higher spin black holes

We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-3 fields, being nonperturbatively described by a Chern-Simons theory of two independent sl(3,R) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.

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arXiv2014

Generalized Black Holes in Three-dimensional Spacetime

Three-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of freedom, the asymptotic symmetries become all the more crucial. For pure (2+1) gravity they consist of two copies of the Virasoro algebra. There exists a black hole which may be endowed with all the corresponding charges. The pure (2+1) gravity theory may be reformulated in terms of two Chern-Simons connections for sl(2,R). An immediate generalization containing gravity and a finite number of higher spin fields may be achieved by replacing sl(2,R) by sl(3,R) or, more generally, by sl(N,R). The asymptotic symmetries are then two copies of the so-called W_N algebra, which contains the Virasoro algebra as a subalgebra. The question then arises as to whether there exists a generalization of the standard pure gravity (2+1) black hole which would be endowed with all the W_N charges. The original pioneering proposal of a black hole along this line for N=3 turns out, as shown in this paper, to actually belong to the so called "diagonal embedding" of sl(2,R) in sl(3,R), and it is therefore endowed with charges of lower rather than higher spins. In contradistinction, we exhibit herein the most general black hole which belongs to the "principal embedding". It is endowed with higher spin charges, and possesses two copies of W_3 as its asymptotic symmetries. The most general diagonal embedding black hole is studied in detail as well, in a way in which its lower spin charges are clearly displayed. The extension to N>3 is also discussed. A general formula for the entropy of a generalized black hole is obtained in terms of the on-shell holonomies.

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arXiv2014

Chemical potentials in three-dimensional higher spin anti-de Sitter gravity

We indicate how to introduce chemical potentials for higher spin charges in higher spin anti-de Sitter gravity in a manner that manifestly preserves the original asymptotic W-symmetry. This is done by switching on a non-vanishing component of the connection along the temporal (thermal) circles. We first recall the procedure in the pure gravity case (no higher spin) where the only "chemical potentials" are the temperature and the chemical potential associated with the angular momentum. We then generalize to the higher spin case. We find that there is no tension with the W(N) or W(infinity) asymptotic algebra, which is obviously unchanged by the introduction of the chemical potentials. Our argument is non-perturbative.

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arXiv2013

Higher spin black hole entropy in three dimensions

A generic formula for the entropy of three-dimensional black holes endowed with a spin-3 field is found, which depends on the horizon area A and its spin-3 analogue, given by the reparametrization invariant integral of the induced spin-3 field at the spacelike section of the horizon. From this result it can be shown that the absolute value of the spin-3 analogue of the area has to be bounded from above by A/3^(1/2). The entropy formula is constructed by requiring the first law of thermodynamics to be fulfilled in terms of the global charges obtained through the canonical formalism. For the static case, in the weak spin-3 field limit, our expression for the entropy reduces to the result found by Campoleoni, Fredenhagen, Pfenninger and Theisen, which has been recently obtained through a different approach.

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arXiv2013

Higher spin gravity in 3D: black holes, global charges and thermodynamics

Global charges and thermodynamic properties of three-dimensional higher spin black holes that have been recently found in the literature are revisited. Since these solutions possess a relaxed asymptotically AdS behavior, following the canonical approach, it is shown that the global charges, and in particular the mass, acquire explicit nontrivial contributions given by nonlinear terms in the deviations with respect to the reference background. It is also found that there are cases for which the first law of thermodynamics is fulfilled in the canonical ensemble, i.e., without work terms associated to the presence of higher spin fields, and remarkably, the semiclassical higher spin black hole entropy is exactly reproduced from Cardy formula.

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arXiv2011

Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes

Field theories with anisotropic scaling in 1+1 dimensions are considered. It is shown that the isomorphism between Lifshitz algebras with dynamical exponents z and 1/z naturally leads to a duality between low and high temperature regimes. Assuming the existence of gap in the spectrum, this duality allows to obtain a precise formula for the asymptotic growth of the number of states with a fixed energy which depends on z and the energy of the ground state, and reduces to the Cardy formula for z=1. The holographic realization of the duality can be naturally inferred from the fact that Euclidean Lifshitz spaces in three dimensions with dynamical exponents and characteristic lengths given by z, l, and 1/z, l/z, respectively, are diffeomorphic. The semiclassical entropy of black holes with Lifshitz asymptotics can then be recovered from the generalization of Cardy formula, where the ground state corresponds to a soliton. An explicit example is provided by the existence of a purely gravitational soliton solution for BHT massive gravity, which precisely has the required energy that reproduces the entropy of the analytic asymptotically Lifshitz black hole with z=3. Remarkably, neither the asymptotic symmetries nor central charges were explicitly used in order to obtain these results.

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arXiv2011

Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity

Hairy black holes and gravitational solitons in three dimensions for the new massive gravity theory proposed by Bergshoeff, Hohm and Townsend (BHT) are considered at the special case when there is a unique maximally symmetric solution. Following the Brown-York approach with suitable counterterms, it is shown that the soliton possesses a fixed negative mass which coincides with the one of AdS spacetime regardless the value of the integration constant that describes it. Hence, the soliton can be naturally regarded as a degenerate ground state labeled by a single modulus parameter. The Euclidean action, endowed with suitable counterterms, is shown to be finite and independent of modulus and hair parameters for both classes of solutions, and in the case of hairy black holes the free energy in the semiclassical approximation is reproduced. Modular invariance allows to show that the gravitational hair turns out to be determined by the modulus parameter. According to Cardy's formula, it is shown that the semiclassical entropy agrees with the microscopic counting of states provided the modulus parameter of the ground state is spontaneously fixed, which suggests that the hairy black hole is in a broken phase of the theory. Indeed, it is found that there is a critical temperature characterizing a first order phase transition between the static hairy black hole and the soliton which, due to the existence of gravitational hair, can take place in the semiclassical regime.

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arXiv2009

Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity

Asymptotically AdS rotating black holes for the Bergshoeff-Hohm-Townsend (BHT) massive gravity theory in three dimensions are considered. In the special case when the theory admits a unique maximally symmetric solution, apart from the mass and the angular momentum, the black hole is described by an independent "gravitational hair" parameter, which provides a negative lower bound for the mass. This bound is saturated at the extremal case and, since the temperature and the semiclassical entropy vanish, it is naturally regarded as the ground state. The absence of a global charge associated with the gravitational hair parameter reflects through the first law of thermodynamics in the fact that the variation of this parameter can be consistently reabsorbed by a shift of the global charges, giving further support to consider the extremal case as the ground state. The rotating black hole fits within relaxed asymptotic conditions as compared with the ones of Brown and Henneaux, such that they are invariant under the standard asymptotic symmetries spanned by two copies of the Virasoro generators, and the algebra of the conserved charges acquires a central extension. Then it is shown that Strominger's holographic computation for general relativity can also be extended to the BHT theory; i.e., assuming that the quantum theory could be consistently described by a dual conformal field theory at the boundary, the black hole entropy can be microscopically computed from the asymptotic growth of the number of states according to Cardy's formula, in exact agreement with the semiclassical result.

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arXiv2009

Static wormholes in vacuum for conformal gravity

A static spherically symmetric wormhole solution for conformal gravity in vacuum is found. The solution possesses a single integration constant which determines the size of the neck connecting two static homogeneous universes of constant spatial curvature. Time runs at different rates on each side of the neck, and depending on the value of the parameter, the wormhole can develop a cosmological horizon only at one side. It is shown that the wormholes correspond to the matching of different Einstein spacetimes by means of improper conformal transformations.

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arXiv2009

Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, are obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the ones of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, $dS_{2}\times S^{1}$. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the $t-ϕ$ plane.

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arXiv2009

Static spherically symmetric solutions for conformal gravity in three dimensions

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be constructed from suitable identifications of a static universe of negative spatial curvature, and it is shown that they correspond to the conformal matching of two black hole solutions with the same mass.

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arXiv2009

Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions

As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a=b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a different than b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.

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