A note on the hidden conformal structure of non-extremal black holes

We study, following Bertini et al. \cite{Bertini:2011ga}, the hidden conformal symmetry of the massless Klein-Gordon equation in the background of the general, charged, spherically symmetric, static black-hole solution of a class of d-dimensional Lagrangians which includes the relevant parts of the bosonic Lagrangian of any ungauged supergravity. We find that a hidden SL(2,\mathbb{R}) symmetry appears at the near event and Cauchy-horizon limit.Comment: 9 pages. The 2 sl(2) algebras have been extended to two complete Witt algebras. A discussion has been adde

Hairy black holes, scalar charges and extended thermodynamics

We explore the use of the recently defined scalar charge which satisfies a Gauss law in stationary spacetimes, in the context of theories with a scalar potential. We find new conditions that this potential has to satisfy in order to allow for static, asymptotically-flat black-hole solutions with regular horizons and non-trivial scalar field. These conditions are equivalent to some of the known ``no-hair'' theorems (such as Bekenstein's). We study the extended thermodynamics of these systems, deriving a first law and a Smarr formula. As an example, we study the Anabal\'on-Oliva hairy black holeComment: author name correcte

A note on simple applications of the Killing Spinor Identities

We show how the Killing Spinor Identities (KSI) can be used to reduce the number of independent equations of motion that need to be checked explicitly to make sure that a supersymmetric configuration is a classical supergravity solution. We also show how the KSI can be used to compute BPS relations between masses and charges.Comment: 10 pages, latex2e. Comments and references added. Version to be published in Physics Letters

Lie algebra expansions and actions for non-relativistic gravity

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A Note on the D-2-Brane of the Massive Type IIA Theory and Gauged Sigma Models

Gauging the M-2-brane effective action with respect to an Abelian isometry in such a way that the invariance under gauge transformations of the 3-form potential is maintained (slightly modified) we obtain a fully covariant action with 11-dimensional target space that gives the massive D-2-brane effective action upon dimensional reduction in the direction of the gauged isometry.Comment: Latex file. A reference adde

Supersymmetry as a Cosmic Censor

In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in case of Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with the requirement that naked singularities be absent. Here we investigate charged dilaton black holes in this context. We show that the extreme solutions saturate the supersymmetry bound of $N=4\ d=4$ supergravity, or dimensionally reduced superstring theory. Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit super-covariantly constant spinors. The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition. The temperature, entropy and singularity are discussed. The Euclidean action (entropy) of the extreme black hole is given by $2\pi |PQ|$. We argue that this result, as well as the one for Lorentzian signature, is not altered by higher order corrections in the supersymmetric theory. When a black hole reaches its extreme limit, it cannot continue to evaporate by emitting elementary particles, since this would violate the supersymmetric positivity bound. We speculate on the possibility that an extreme black hole may ``evaporate" by emitting smaller extreme black holes.Comment: 42 pages (figures not included

Singular limits of spacetimes and their isometries

We consider spacetime metrics with a given (but quite generic) dependence on a dimensionful parameter such that in the 0 and infinity limits of that parameter the metric becomes singular. We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves.Comment: Latex2e paper, 48 page

Black hole chemistry, the cosmological constant and the embedding tensor

We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald's formalism. The most natural way to deal with these constants is to promote them to scalar fields introducing a (d-1)-form Lagrange multiplier that forces them to be constant on-shell. These (d-1)-form potentials provide a dual description of them and, in the context of superstring/supergravity theories, a higher-dimensional origin/explanation. In the context of gauged supergravity theories, all these constants can be collected in the embedding tensor. We show in an explicit 4-dimensional example that the embedding tensor can also be understood as a thermodynamical variable that occurs in the Smarr formula in a duality-invariant fashion. This establishes an interesting link between black-hole thermodynamics, gaugings and compactifications in the context of superstring/supergravity theories.Comment: References added, 43 pages, no figure

Massless Black Holes as Black Diholes and Quadruholes

Massless black holes can be understood as bound states of a (positive mass) extreme a=\sqrt{3} black hole and a singular object with opposite (i.e. negative) mass with vanishing ADM (total) mass but non-vanishing gravitational field. Supersymmetric balance of forces is crucial for the existence of this kind of bound states and explains why the system does not move at the speed of light. We also explain how supersymmetry allows for negative mass as long as it is never isolated but in bound states of total non-negative mass.Comment: Version to be published in Physical Review Letters. Latex2e fil