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We propose homogeneous metrics of Petrov type III that describe gyrating Schrödinger geometries as duals to some nonrelativistic field theories, in which the Schrödinger symmetry is broken further so that the phase space has a linear dependence of the momentum in a selected direction. We show that such solutions can arise in four-dimensional Einstein-Weyl supergravity as well as higher-dimensional extended gravities with quadratic curvature terms coupled to a massive vector. In Einstein-Weyl supergravity, the gyrating Schrödinger solutions can be supersymmetric, preserving ¼ of the supersymmetry. We obtain the exact Green function in the phase space associated with a bulk free massive scalar [ABSTRACT FROM AUTHOR]

Many of the useful features of supergravities, such as admitting supersymmetric bosonic backgrounds governed by first-order Bogomol'nyi-Prasad-Sommerfield equations, can be realized in a much broader setting by relaxing the requirement of closure of the superalgebra beyond the level of quadratic fermion terms. The resulting pseudo-supersymmetric theories can be defined in arbitrary spacetime dimensions. We focus here on the N=1 pseudo-supersymmetric extensions of the arbitrary-dimensional bosonic string action, which were constructed a few years ago. In this paper, we recast these in the language of double field theory. More precisely, we construct the action and the corresponding pseudo-supersymmetry transformation rules in terms of O(D)×O(D) covariant derivatives, and we discuss consistent truncations on manifolds with generalized G structure. We thereby obtain a natural generalization of the previously known results for N=1 supersymmetric double field theory in D=10 to arbitrary dimensions. As explicit examples, we discuss Minkowski×G vacuum solutions and their corresponding pseudo-supersymmetry. We also briefly discuss squashed group manifold solutions, including an example with a Lorentzian signature metric on the group manifold G. [ABSTRACT FROM AUTHOR]

The extremal Reissner-Nordström black hole admits a conformal inversion symmetry, in which the metric is mapped into itself under an inversion of the radial coordinate combined with a conformal rescaling. In the rotating generalization, Couch and Torrence showed that the Kerr-Newman metric no longer exhibits a conformal inversion symmetry, but the radial equation arising in the separation of the massless Klein-Gordon equation admits a mode-dependent inversion symmetry, where the radius of inversion depends upon the energy and azimuthal angular momentum of the mode. It was more recently shown that the static four-charge extremal black holes of STU supergravity (i.e., N=2 supergravity in four dimension coupled to three vector multiplets) admit a generalization of the conformal inversion symmetry, in which the conformally inverted metric is a member of the same four-charge black hole family but with transformed charges. In this paper we study further generalizations of these inversion symmetries, within the general class of extremal STU supergravity black holes. For the rotating black holes, where again the massless Klein-Gordon equation is separable, we show that examples with four electric charges exhibit a generalization of the Couch-Torrence symmetry of the radial equation. Now, as in the conformal inversion of the static specializations, the inversion of the radial equation maps it to the radial equation for a rotating black hole with transformed electric charges. We also study the inversion transformations for the general case of extremal Bogomol'nyi-Prasad-Sommerfield STU black holes carrying eight charges (four electric plus four magnetic), and argue that analogous generalizations of the inversion symmetries exist for both the static and the rotating cases. [ABSTRACT FROM AUTHOR]

Motivated by the study of conserved Aretakis charges for a scalar field on the horizon of an extremal black hole, we construct the metrics for certain classes of four-dimensional and five-dimensional extremal rotating black holes in Gaussian null coordinates. We obtain these as expansions in powers of the radial coordinate, up to sufficient order to be able to compute the Aretakis charges. The metrics we consider are for 4-charge black holes in four-dimensional STU supergravity (N=2 supergravity coupled to three vector multiplets) (including the Kerr-Newman black hole in the equal-charge case) and the general 3-charge black holes in five-dimensional STU supergravity. We also investigate the circumstances under which the Aretakis charges of an extremal black hole can be mapped by conformal inversion of the metric into Newman-Penrose charges at null infinity. We show that while this works for four-dimensional static black holes, a simple radial inversion fails in rotating cases because a necessary conformal symmetry of the massless scalar equation breaks down. We also discuss that a massless scalar field in dimensions higher than four does not have any conserved Newman-Penrose charge, even in a static asymptotically flat spacetime. [ABSTRACT FROM AUTHOR]

We study a free scalar field ϕ in a fixed curved background spacetime subject to a higher derivative field equation of the form F(□)ϕ=0, where F is a polynomial of the form F(□)=∏i(□-mi²) and all masses mi are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantization and briefly discuss the issue of negative energy vs negative norm and its relation to reflection positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish nonexistence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background and show how the Hubble friction may eliminate what would otherwise be unstable behavior when interactions are included. [ABSTRACT FROM AUTHOR]

The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, e.g., the S7 reduction of 11-dimensional supergravity, such a consistent "Pauli reduction" does exist. In this paper, we study this existence question in two examples of S² reductions of supergravities. We do this by making use of a relation between certain S² reductions and group manifold S³=SU(2) reductions of a theory in one dimension higher. By this means, we establish the nonexistence of a consistent S² Pauli reduction of five-dimensional minimal supergravity. We also show that a previously discovered consistent Pauli reduction of six-dimensional Salam-Sezgin supergravity can be elegantly understood via a group-manifold reduction from seven dimensions. [ABSTRACT FROM AUTHOR]

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type "no-hair" theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to "vacuum" solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as "wormholes," which can match symmetrically onto another sheet of spacetime at finite radius. [ABSTRACT FROM AUTHOR]

We study the shear viscosity to entropy ratio η/S in the boundary field theories dual to black-hole backgrounds in theories of gravity coupled to a scalar field, and generalizations including a Maxwell field and nonminimal scalar couplings. Motivated by the observation in simple examples that the saturation of the η/S ≥ 1 / (4π) bound is correlated with the existence of a generalized Smarr relation for the planar black-hole solutions, we investigate this in detail for the general black-hole solutions in these theories, focusing especially on the cases where the scalar field plays a nontrivial role and gives rise to an additional parameter in the space of solutions. We find that a generalized Smarr relation holds in all cases, and in fact it can be viewed as the bulk gravity dual of the statement of the saturation of the viscosity to entropy bound. We obtain the generalized Smarr relation, whose existence depends upon a scaling symmetry of the planar black-hole solutions, by two different but related methods, one based on integrating the first law of thermodynamics, and the other based on the construction of a conserved Noether charge. [ABSTRACT FROM AUTHOR]

The thermodynamics of a magnetized Kerr-Newman black hole is studied to all orders in the appended magnetic field B. The asymptotic properties of the metric and other fields are dominated by the magnetic flux that extends to infinity along the axis, leading to subtleties in the calculation of conserved quantities such as the angular momentum and the mass. We present a detailed discussion of the implementation of a Wald-type procedure to calculate the angular momentum, showing how ambiguities that are absent in the usual asymptotically flat case may be resolved by the requirement of gauge invariance. We also present a formalism from which we are able to obtain an expression for the mass of the magnetized black holes. The expressions for the mass and the angular momentum are shown to be compatible with the first law of thermodynamics and a Smarr-type relation. Allowing the appended magnetic field B to vary results in an extra term in the first law of the form --μB where μ is interpreted as an induced magnetic moment. Minimizing the total energy with respect to the total charge Q at fixed values of the angular momentum and energy of the seed metric allows an investigation of Wald's process. The Meissner effect is shown to hold for electrically neutral extreme black holes. We also present a derivation of the angular momentum for black holes in the four-dimensional STU model, which is N = 2 supergravity coupled to three vector multiplets. [ABSTRACT FROM AUTHOR]

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 nonzero charges that the Reissner-Nordström black hole arises under an appropriate specialization of the charges. (The definition can be relaxed somewhat in charged anti-de Sitter black holes in D = 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. [ABSTRACT FROM AUTHOR]

We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformai theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschi Id-AdS metric and its conformai scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions [ABSTRACT FROM AUTHOR]

Higher-order curvature corrections involving the conformally invariant Weyl-squared action have played a role in two recent investigations of four-dimensional gravity: in critical gravity, where they are added to the standard cosmological Einstein-Hilbert action with a coefficient tuned to make the massive ghostlike spin-2 excitations massless, and in a pure Weyl-squared action considered by Maldacena, where the massive spin-2 modes are removed by the imposition of boundary conditions. We exhibit the connections between the two approaches, and we also generalize critical gravity to a wider class of Weyl-squared modifications to cosmological Einstein gravity where one can eliminate the massive ghostlike spin-2 modes by means of boundary conditions. The cosmological constant plays a crucial role in the discussion, since there is then a "window" of negative mass-squared spin-2 modes around AdS4 that are not tachyonic. We also construct analogous conformal and nonconformal gravities in six dimensions. [ABSTRACT FROM AUTHOR]

We show that there are a further infinite number of, previously unknown, supertranslation charges. These can be viewed as duals of the known Bondi-Metzner-Sachs (BMS) charges corresponding to supertranslations. In Newman-Penrose language, these new supertranslation charges roughly correspond to the imaginary part of the leading term in ψ2. We find these charges by dualizing the Barnich-Brandt asymptotic charges and argue that this prescription gives rise to new bona fide charges at null infinity. [ABSTRACT FROM AUTHOR]

We construct a relation between the Aretakis charge of any extreme black hole and the Newman-Penrose charge. This is achieved by constructing a conformal correspondence between extreme black holes and what we call weakly asymptotically flat space-times. Under this correspondence, the Newman-Penrose charge of the weakly asymptotically flat space-time maps onto the Aretakis charge of the extreme black hole. Furthermore, we generalize the conformal isometry displayed by the extreme Reissner-Nordström solution to a novel conformal symmetry that acts within a class of static STU supergravity black holes. [ABSTRACT FROM AUTHOR]

A new branch of black hole solutions occurs along with the standard Schwarzschild branch in n-dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard n = 4 dimensional general relativity. This static eigenfunction has two roles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point. [ABSTRACT FROM AUTHOR]

We study closed photon orbits in spherically symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. These orbits lie in what we shall call a photon sphere (antiphoton sphere) if the orbit is unstable (stable). We show that in all the asymptotically flat solutions we examine that admit a regular event horizon, and whose energy-momentum tensor satisfies the strong energy condition, there is one and only one photon sphere outside the event horizon. We give an example of a Horndeski theory black hole (whose energy-momentum tensor violates the strong energy condition) whose metric admits both a photon sphere and an antiphoton sphere. The uniqueness and nonexistence also holds for asymptotically anti-de Sitter solutions in gauged supergravity. The latter also exhibits the projective symmetry that was first discovered for the Schwarzschild-de Sitter metrics: the unparametrized null geodesics are the same as when the cosmological or gauge coupling constant vanishes. We also study the closely related problem of accretion flows by perfect fluids in these metrics. For a radiation fluid, Bondi's sonic horizon coincides with the photon sphere. For a general polytropic equation of state this is not the case. Finally we exhibit counterexamples to a conjecture of Hod's. [ABSTRACT FROM AUTHOR]

Off-shell formulations of supergravities allow one to add closed-form higher-derivative super-invariants that are separately supersymmetric to the usual lower-derivative actions. In this paper we study four-dimensional off-shell N = 1 supergravity where additional super-invariants associated with the square of the Weyl tensor and the square of the Ricci scalar are included. We obtain a variety of solutions where the metric describes domain walls, Lifshitz geometries, and also solutions of a kind known as gyratons. We find that in some cases the solutions can be supersymmetric for appropriate choices of the parameters. In some solutions the auxiliary fields may be imaginary. One may reinterpret these as real solutions in an analytically continued theory. Since the supersymmetry transformation rules now require the gravitino to be complex, the analytically continued theory has a "fake supersymmetry" rather than a genuine supersymmetry. Nevertheless, the concept of pseudosupersymmetric solutions is a useful one, since the Killing spinor equations provide first-order equations for the bosonic fields. [ABSTRACT FROM AUTHOR]

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual anti-de Sitter (AdS) vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Lifshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a nonrelativistic Lifshitz system. [ABSTRACT FROM AUTHOR]

In a theory where the cosmological constant Λ or the gauge coupling constant g arises as the vacuum expectation value, its variation should be included in the first law of thermodynamics for black holes. This becomes dE = TdS + ΩidJi + ΦαdQα + ΘdΛ, where E is now the enthalpy of the spacetime, and Θ, the thermodynamic conjugate of Λ, is proportional to an effective volume V = -16#x03C0;Θ/D-2 "inside the event horizon." Here we calculate Θ and V for a wide variety of D-dimensional charged rotating asymptotically anti-de Sitter (AdS) black hole spacetimes, using the first law or the Smarr relation. We compare our expressions with those obtained by implementing a suggestion of Kastor, Ray, and Traschen, involving Komar integrals and Killing potentials, which we construct from conformal Killing-Yano tensors. We conjecture that the volume V and the horizon area A satisfy the inequality R≡ ((D-1)V/AD-2)1/(D-1)(AD-2/A)1/(D-2) ≥ 1, where AD-2 is the volume of the unit (D - 2) sphere, and we show that this is obeyed for a wide variety of black holes, and saturated for Schwarzschild-AdS. Intriguingly, this inequality is the "inverse" of the isoperimetric inequality for a volume V in Euclidean (D - 1) space bounded by a surface of area A, for which R ≤ 1. Our conjectured reverse isoperimetric inequality can be interpreted as the statement that the entropy inside a horizon of a given "volume" V is maximized for Schwarzschild-AdS. The thermodynamic definition of V requires a cosmological constant (or gauge coupling constant). However, except in seven dimensions, a smooth limit exists where Λ or g goes to zero, providing a definition of V even for asymptotically flat black holes. [ABSTRACT FROM AUTHOR]

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D>4 there are in general two distinct (anti)-de Sitter vacua. We show that, for an appropriate choice of the parameters, there exists a critical point for one of the vacua, with only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have formally vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl2 model with a unique vacuum, whose Λ is determined. [ABSTRACT FROM AUTHOR]

Many discussions in the literature of spacetimes with more than one Killing horizon note that some horizons have positive and some have negative surface gravities, but assign to all a positive temperature. However, the first law of thermodynamics then takes a nonstandard form. We show that if one regards the Christodoulou and Ruffini formula for the total energy or enthalpy as defining the Gibbs surface, then the rules of Gibbsian thermodynamics imply that negative temperatures arise inevitably on inner horizons, as does the conventional form of the first law. We provide many new examples of this phenomenon, including black holes in STU supergravity. We also give a discussion of left and right temperatures and entropies, and show that both the left and right temperatures are non-negative. The left-hand sector contributes exactly half the total energy of the system, and the right-hand sector contributes the other half. Both the sectors satisfy conventional first laws and Smarr formulas. For spacetimes with a positive cosmological constant, the cosmological horizon is naturally assigned a negative Gibbsian temperature. We also explore entropy-product formulas and a novel entropy-inversion formula, and we use them to test whether the entropy is a super-additive function of the extensive variables. We find that super-additivity is typically satisfied, but we find a counterexample for dyonic Kaluza-Klein black holes. [ABSTRACT FROM AUTHOR]

The consistency of the embedding of four-dimensional SO(8) gauged N = 8 supergravity into eleven-dimensional supergravity, where the internal directions are compactified on a seven-sphere, was established by de Wit and Nicolai in the 1980s. The reduction Ansatz for the eleven-dimensional metric, and for some of the components of the 4-form field strength, were found at that time, and recently the complete expression for the 4-form reduction has been obtained. The expressions are quite complicated, and in many practical applications it would be sufficient to know the Ansatz for a subset of the four-dimensional fields. In this paper, we obtain explicit expressions for the embedding of the truncation of the full N = 8 gauged theory to the N = 2 gauged STU supergravity. This corresponds, in the bosonic sector, to a consistent truncation of the N = 8 supergravity fields to those that are singlets under the U(1)4 Cartan subalgebra of SO(8). This truncation to STU supergravity, which comprises N = 2 supergravity coupled to three vector multiplets, suffices, for example, for lifting the general 8-charge asymptotically anti-de Sitter rotating black holes to eleven dimensions. We also give two distinct further truncations to N = 2 supergravities coupled to single vector multiplets. [ABSTRACT FROM AUTHOR]