108 research outputs found

    Non-analyticity of holographic Rényi entropy in Lovelock gravity

    Get PDF
    We compute holographic Rényi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points corresponds to a dual boundary conformal field theory whose Rényi entropy exhibits a kink at a certain critical index n.This research was supported in part by the Icelandic Research Fund under contracts 163419-051 and 163422-051, and by grants from the University of Iceland Research Fund.Peer Reviewe

    Slowly rotating and the accelerating α\alpha'-corrected black holes in four and higher dimensions

    Full text link
    We consider the low-energy effective action of string theory at order α\alpha ', including R2R^2-corrections to the Einstein-Hilbert gravitational action and non-trivial dilaton coupling. By means of a convenient field redefinition, we manage to express the theory in a frame that enables us to solve its field equations analytically and perturbatively in α\alpha ' for a static spherically symmetric ansatz in an arbitrary number of dimensions. The set of solutions we obtain is compatible with asymptotically flat geometries exhibiting a regular event horizon at which the dilaton is well-behaved. For the 4-dimensional case, we also derive the stationary black hole configuration at first order in α\alpha ' and in the slowly rotating approximation. This yields string theory modifications to the Kerr geometry, including terms of the form aa, a2a^2, α\alpha ' and aαa\alpha '. In addition, we obtain the first α\alpha' correction to the C-metrics, which accommodates accelerating black holes. We work in the string frame and discuss the connection to the Einstein frame, for which rotating black holes have already been obtained in the literature.Comment: 19 pages, no figures. v2 21 pages, rotating solution added and title modified, one author added. v3 26 pages, accelerating solution added and title accordingly modified. We have also included the explicit mapping to the Einstein frame that allows to relate our solutions with the ones appearing in previous literature. To appear in PR

    Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theories

    Get PDF
    Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied

    Stirring a black hole

    Get PDF
    We present novel asymptotically global AdS4 solutions, constructed by turning on a dipolar differential rotation at the conformal boundary. At fixed energy and boundary profile, we find two different geometries: a horizonless spacetime, and a deformed, hourglass shaped black hole with zero net angular momentum. Both solutions exist up to some maximum amplitudes of the boundary profile, and develop an ergoregion attached to the boundary before the maximum amplitude is reached. We show that both spacetimes develop hair as soon as the ergoregion develops. Furthermore, we discuss the full phase diagram, including the possibility of phases with disconnected horizons, by considering the Mathisson-Papapetrou equations for a spinning test particle. Finally, we provide a first principle derivation of the superradiant bound purely from CFT data, and outline possible scenarios for the late time evolution of the system.JM is supported by an STFC studentship. JES was supported in part by STFC grants PHY-1504541 and ST/P000681/1 ... The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by CENTRA/IST. Part of the computations were performed at the cluster \Baltasar-Sete-S ois" and supported by the H2020 ERC Consolidator Grant \Matter and strong eld gravity: New frontiers in Einstein's theory" grant agreement no. MaGRaTh-646597. Part of this work was undertaken on the COSMOS Shared Memory system at DAMTP, University of Cambridge operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital grant ST/J005673/1 and STFC grants ST/H008586/1, ST/K00333X/1

    Lovelock gravity, black holes and holography

    Get PDF
    Lovelock theory is the natural extension of General Relativity to higher di- mensions and can also be thought of as a toy model for ghost-free higher curvature gravity. These gravity theories capture some of the de ning fea- tures of higher curvature gravities, namely the existence of more than one (A)dS vacuum and an intricate dynamics, more general black hole solutions and instabilities; while avoiding some of their problems. In particular, Love- lock gravities yield second order eld equations so that they can be considered beyond the perturbative regime and are free of higher derivative ghosts. This provides an appealing arena to explore di erent gravitational and holographic aspects of higher curvature gravity. Most of the vacua of the theory support black holes that display inter- esting features. Besides, black holes with maximally symmetric horizons are subject to a version of Birkho 's theorem and their solutions can be found analytically. Most e orts in the literature have been devoted however to one particular branch of solutions, often restricted to a speci c combination of the Lovelock couplings. The branch usually chosen for the analysis is the so- called EH-branch, as it actually reduces to the general relativistic solution as we turn o the higher order couplings. In this thesis we have presented some tools that allow for the description of Lovelock black holes for arbitrary values of the whole set of couplings, dimensionality and order of the theory. Despite the fact of the solution being implicit, it is possible to extract most relevant information and discuss all possible cases in the general situation, analyze the number of horizons, the thermodynamic stability of the solution, phase transitions, etc. Furthermore, this approach has been generalized to the case of charged and cosmological solutions, and also to the so called quasi-topological gravities, that share the same functional form of the black hole solutions with the Lovelock family while being lower dimensional. Our method is very useful to gain intuition about physical processes in- volving black holes. One can easily visualize the evolution of the position and number of horizons as the mass of the solution varies, this providing crucial information about, for instance, the possible appearance of naked singulari- ties or the violation of the third law of thermodynamics. We have seen that the rigid symmetry imposed on the solution naively allows such problematic behavior which is avoided once the stability of the solution is taken into full consideration

    The Gregory-Laflamme Instability of Black Strings and Violation of the Weak Cosmic Censorship Conjecture

    Get PDF
    Einstein's general relativity is a remarkably successful theory of space, time and gravitation. Over a hundred years since its birth, it has been verified by all of the experiments and observations with incredibly high accuracy. It has shown us its power in predicting exotic objects such as gravitational waves and black holes. Despite its great success, its predictive power has been questioned due to the existence of the singularities which would break down the theory. This brings out the weak cosmic censorship conjecture, suggesting that singularities are always hidden inside black hole horizons so that they cannot cause any problem to the outside. Whether the conjecture is true or false remains as one of the biggest open questions in the field. Although a rigorous mathematical proof or disproof to the conjecture is still lacking, there have been evidence against it arising from a family of numerical studies on the Gregory-Laflamme instability. The most studied case that has tuned our current understanding of the conjecture is about the five-dimensional black strings. The first full numerical work done by Lehner and Pretorius suggests a pinch-off of the horizon at the endpoint of the Gregory-Laflamme instability of black strings, which provides solid evidence against the conjecture. However, their study is more than ten years old and has not been reproduced independently in any other literature. The development in numerical techniques and computer power facilitate us to have an independent study on the black strings. In this thesis, we revisit the previous study by Lehner and Pretorius on the endpoint of the Gregory-Laflamme instability of the five-dimensional black strings. We not only reproduce and confirm their results with a different and independent formalism, but also improve the simulation with better resolution and extend the evolution much closer to the endpoint. The simulations in the thesis are conducted by using our own \textsc{GRChombo} code. Our results provide further evidence about the fractal structure that the horizon develops into in the late-time dynamics of the black string instability. Moreover, we investigate unstable black strings with fixed thickness but different lengths and provide a more general picture of the development of the instability. In all cases, we confirm that the intermediate dynamics of the evolution can be described by a quasi-stationary sequence of spherical black holes of various sizes connected by string segments on different scales. In particular, with better resolution, our results respect the particular symmetry of the problem. However, our numerical results do not support the existence of a global timescale relating subsequent generations as stated in the previous study. Instead, our results indicate that, due to the non-uniform development of the string, the late-time dynamics are governed by the joint effect from the Gregory-Laflamme instability and the local dynamics of the bulges. Finally, we confirm that the endpoint of the instability is the pinch off of the horizon in finite asymptotic time, which constitutes to the violation of the weak cosmic censorship conjecture
    corecore