Annals of physics

Black Holes and Membranes in Higher Dimensional Theories with Dilaton Fields

We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali-Gabadadze-Porrati model, cascading gravity and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware-Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally we present alternative and related models of massive gravity such as new massive gravity, Lorentz-violating massive gravity and non-local massive gravity.

Massive Gravity

We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

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Black Holes in Higher Dimensions

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents (γ, δ) that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the (γ, δ) plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when γ = δ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole (γ, δ) plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T = 0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

/pdf/effective-holographic-theories-for-low-temperature-condensed-3jl1tvu7sh.pdf

Effective Holographic Theories for low-temperature condensed matter systems

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.

Black hole mass and angular momentum in topologically massive gravity

We show that an analytical continuation of the Vuorio solution to three-dimensional topologically massive gravity leads to a two-parameter family of black-hole solutions, which are geodesically complete and causally regular within a certain parameter range. No observers can remain static in these spacetimes. We discuss their global structure, and evaluate their mass, angular momentum and entropy, which satisfy a slightly modified form of the first law of thermodynamics.

https://iopscience.iop.org/article/10.1088/0264-9381/20/24/L01/pdf

The Black holes of topologically massive gravity

We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS3 black holes, and (for a critical value of the cosmological constant) AdS2 × S1 as solutions. The entropy, mass and angular momentum of these black holes are computed.

https://iopscience.iop.org/article/10.1088/0264-9381/26/10/105015/pdf

Warped AdS(3) black holes in new massive gravity

We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS_3 black holes, and (for a critical value of the cosmological constant) AdS_2 x S^1 as solutions. The entropy, mass and angular momentum of these black holes are computed.

Warped AdS_3 black holes in new massive gravity

We present new solutions to Einstein-Maxwell-dilaton-axion (EMDA) gravity in four dimensions describing black holes which asymptote to the linear dilaton background. In the non-rotating case they can be obtained as the limiting geometry of dilaton black holes. The rotating solutions (possibly endowed with a NUT parameter) are constructed using a generating technique based on the Sp(4,R) duality of the EMDA system. In a certain limit (with no event horizon present) our rotating solutions coincide with supersymmetric Israel-Wilson-Perjes type dilaton-axion solutions. In presence of an event horizon supersymmetry is broken. The temperature of the static black holes is constant, and their mass does not depend on it, so the heat capacity is zero. We investigate geodesics and wave propagation in these spacetimes and find superradiance in the rotating case. Because of the non-asymptotically flat nature of the geometry, certain modes are reflected from infinity, in particular, all superradiant modes are confined. This leads to classical instability of the rotating solutions. The non-rotating linear dilaton black holes are shown to be stable under spherical perturbations.

Gérard Clément

Papers

Black hole mass and angular momentum in topologically massive gravity

The Black holes of topologically massive gravity

Warped AdS(3) black holes in new massive gravity

Warped AdS_3 black holes in new massive gravity

Linear dilaton black holes