Black Hole entropy for two higher derivative theories of gravity

The dark energy issue is focusing the attention of an incresing number of physicists all over the world. Among the possible alternatives in order to explain what as been named the "Mystery of the Millennium" are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). Aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature, little progress being possible along the way which leads to a consistent definition of mass.Comment: 10 pages, 1 figur

Entanglement Island and Page Curve in Wedge Holography

Entanglement islands play an essential role in the recent breakthrough in resolving the black hole information paradox. However, whether entanglement islands can exist in massless gravity theories is controversial. It is found that entanglement islands disappear in the initial model of wedge holography with massless gravity on the brane. As a result, the entanglement entropy of Hawking radiation becomes a time-independent constant, and there is no Page curve. In this paper, we recover massless entanglement islands in wedge holography with suitable DGP gravity or higher derivative gravity on the branes. We study two typical cases. In the first case, we consider a black hole on the strong-gravity brane and a bath on the weak-gravity brane. It is similar to the usual double holography with non-gravitational baths. In the second case, we discuss two black holes on the two branes with the same gravitational strength. We recover massless entanglement islands and non-trivial Page curves in both cases. We also argue that the entanglement island is consistent with massless gravity. Our results strongly support that entanglement islands can exist in long-range theories of gravity.Comment: 42 pages, 20 figures, get a new lower bound for DGP parameter in sect. 2.4, add more discussions, revision published in JHE

Classical and Stringy Properties of Black Holes

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de Lectura: 14-09-2022This thesis is devoted to the study of dynamical and thermodynamical properties of black holes. It has two parts. Part I considers black holes in the context of the low energy effective actions of string theory. The first few higher-derivative corrections induced by finite-size effects in √ the string length ` s ∼ α0 , where α0 is the Regge slope parameter, are well understood for the heterotic superstring (HST). α0-corrected black hole solutions are available and computing their entropy is crucial given its relation to string microstates. However, the Iyer–Wald entropy formula gives a result that is not gauge invariant. This is due to the fact that the original computation assumes that all fields are tensors with no internal gauge freedom. In this thesis, Wald’s derivation is revisited using a formalism that accommodates gauge symmetry conveniently. The main result is a gauge-and Lorentz-invariant entropy formula that includes the first order corrections in α0 . It is also shown, in some particular theories, how magnetic-type terms can be included in the generic proofs of the laws of black hole thermodynamics, even though magnetic charges are not directly associated to gauge symmetry. Part II focuses on dynamical aspects of black holes in different contexts. Rotating black holes in higher-derivative theories are poorly understood due to the complexity of the equations of motion. The problem can be simplified by considering the near horizon geometry of an extremal, charged and rotating black hole. A non-perturbative solution of such a class is presented in a cubic theory called Einsteinian Cubic Gravity. It is the first example in which the entropy of a rotating black hole of higher-order gravity has been exactly computed. In the context of the AdS/CFT correspondence, NUT-charged AdS black holes describe equilibrium states of neutral fluids subject to non-trivial flows at the boundary. Physical transport properties, however, remain largely unexplored. The master equations governing gravitational fluctuations on a class of NUT-charged AdS black holes are derived in this thesis. These exhibit an intriguing relation to Landau quantisation. The gravitational quasinormal mode spectrum of a NUT-charged black hole is computed for the first time, and the spacetime appears to be robustly stable despite the existence of closed causal curves (“time machines”). There is an interesting class of quasi-hydrodynamic modes for which analytic dispersion relations are constructed as a definite holographic prediction for the dual fluid. The last chapter of this thesis deals with the tidal deformability of black holes. Tidal interactions, encoded linearly in the so-called tidal Love numbers, become significant in the last stages of the inspiral phase of a merger. In the case of vacuum, four-dimensional black holes, the tidal Love numbers are zero. The robustness of such a property is investigated by studying the static deformability of charged black holes. It is shown that tidal response coefficients keep on vanishing, in a very non-trivial way, from neutrality all the way down to extremality. This is true not only for gravity (spin-2), but also for spin-0 and spin-1 deformations. In higher dimensions, however, the tidal response is non-trivial and charging up the hole can excite new polarisation modes. One exception is the static response of spin-0 perturbations, which happens to vanish at extremality in any dimension. These results call for further investigation of the tidal deformability properties of black hole

On the Universality of Inner Black Hole Mechanics and Higher Curvature Gravity

Black holes are famous for their universal behavior. New thermodynamic relations have been found recently for the product of gravitational entropies over all the horizons of a given stationary black hole. This product has been found to be independent of the mass for all such solutions of Einstein-Maxwell theory in d=4,5. We study the universality of this mass independence by introducing a number of possible higher curvature corrections to the gravitational action. We consider finite temperature black holes with both asymptotically flat and (A)dS boundary conditions. Although we find examples for which mass independence of the horizon entropy product continues to hold, we show that the universality of this property fails in general. We also derive further thermodynamic properties of inner horizons, such as the first law and Smarr relation, in the higher curvature theories under consideration, as well as a set of relations between thermodynamic potentials on the inner and outer horizons that follow from the horizon entropy product, whether or not it is mass independent.Comment: 26 page

On higher derivative gravity, c-theorems and cosmology

We consider higher derivative gravity lagrangians in 3 and 4 dimensions, which admit simple c-theorems, including upto six derivative curvature invariants. Following a suggestion by Myers, these lagrangians are restricted such that the fluctuations around (anti) de Sitter spaces have second order linearized equations of motion. We study c-theorems both in the context of AdS/CFT and cosmology. In the context of cosmology, the monotonic function is the entropy defined on the apparent horizon through Wald's formula. Exact black hole solutions which are asymptotically (anti) de Sitter are presented. An interesting lower bound for entropy is found in de Sitter space. Some aspects of cosmology in both D=3 and D=4 are discussed.Comment: 23 pages, v3: clarifications added, references adde

Entropy-Product Rules for Charged Rotating Black Holes

We study the universal nature of the product of the entropies of all horizons of charged rotating black holes. We argue, by examining further explicit examples, that when the maximum number of rotations and/or charges are turned on, the entropy product is expressed in terms of angular momentum and/or charges only, which are quantized. (In the case of gauged supergravities, the entropy product depends on the gauge-coupling constant also.) In two-derivative gravities, the notion of the "maximum number" of charges can be defined as being sufficiently many non-zero charges that the Reissner-Nordstrom black hole arises under an appropriate specialisation of the charges. (The definition can be relaxed somewhat in charged AdS black holes in $D\ge 6$.) In higher-derivative gravity, we use the charged rotating black hole in Weyl-Maxwell gravity as an example for which the entropy product is still quantized, but it is expressed in terms of the angular momentum only, with no dependence on the charge. This suggests that the notion of maximum charges in higher-derivative gravities requires further understanding.Comment: References added. 24 page

Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity

We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein's theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic) we use a procedure motivated by earlier work by Pretorius, Vollick and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific m-th order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic) we generalize a procedure, previously introduced by Padmanabhan in the context of GR, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off-shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.Comment: v1: 20 pages, no figures v2: added some discussion, to appear in Phys. Rev.

Entropy Bound and Causality Violation in Higher Curvature Gravity

In any quantum theory of gravity we do expect corrections to Einstein gravity to occur. Yet, at fundamental level, it is not apparent what the most relevant corrections are. We argue that the generic curvature square corrections present in lower dimensional actions of various compactified string theories provide a natural passage between the classical and quantum realms of gravity. The Gauss-Bonnet and $({\rm Riemann})^2$ gravities, in particular, provide concrete examples in which inconsistency of a theory, such as, a violation of microcausality, and a classical limit on black hole entropy are correlated. In such theories the ratio of the shear viscosity to the entropy density, $\eta/s$, can be smaller than for a boundary conformal field theory with Einstein gravity dual. This result is interesting from the viewpoint that the nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme densities and temperatures may violate the conjectured bound $\eta/s\ge 1/4\pi$, {\it albeit} marginally so.Comment: 23 pages, several eps figures; minor changes, references added, published versio