arXiv subjects

David Kastor

Publications and source records attributed to David Kastor.

At least 37 records · Page 2Linked to original sources

arXiv2013

Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.

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arXiv2012

The Angular Tension of Black Holes

Angular tension is an ADM charge that contributes a work term to the first law of black hole mechanics when the range of an angular coordinate is varied and leads to a new Smarr formula for stationary black holes. A phase diagram for singly-spinning D=5 black holes shows that angular tension resolves the degeneracies between spherical black holes and (dipole) black rings and captures the physics of the black ring balance condition. Angular tension depends on the behavior of the metric at rotational axes and we speculate on its relation to rod/domain structure characterizations of higher dimensional black holes and black hole uniqueness theorems.

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arXiv2012

The Riemann-Lovelock Curvature Tensor

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \le D <4k. In D=2k+1 this identity implies that all solutions of pure kth-order Lovelock gravity are `Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle space times, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D=3, which corresponds to the k=1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature.

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arXiv2011

Dynamics of localized Kaluza-Klein black holes in a collapsing universe

The Clayton Antitrust Act of 1914 prohibits corporate mergers that would result in certain highly undesired end states. We study an exact solution of the Einstein equations describing localized, charged Kaluza-Klein black holes in a collapsing deSitter universe and seek to demonstrate that a similar effect holds, preventing a potentially catastrophic black hole merger. As the collapse proceeds, it is natural to expect that the black hole undergoes a topological transition, wrapping around the shrinking compact dimension to merge with itself and form a black string. However, the putative uniform charged black string end state is singular and such a transition would violate (a reasonable notion of) cosmic censorship. We present analytic and numerical evidence that strongly suggests the absence of such a transition. Based on this evidence, we expect that the Kaluza-Klein black hole horizon stays localized, despite the increasingly constraining size of the compact dimension. On the other hand, the deSitter horizon does change between spherical and cylindrical topologies in a simple way.

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arXiv2011

Mass and Free Energy of Lovelock Black Holes

An explicit formula for the ADM mass of an asymptotically AdS black hole in a generic Lovelock gravity theory is presented, identical in form to that in Einstein gravity, but multiplied by a function of the Lovelock coupling constants and the AdS curvature radius. A Gauss' law type formula relates the mass, which is an integral at infinity, to an expression depending instead on the horizon radius. This and other thermodynamic quantities, such as the free energy, are then analyzed in the limits of small and large horizon radius, yielding results that are independent of the detailed choice of Lovelock couplings. In even dimensions, the temperature diverges in both limits, implying the existence of a minimum temperature for black holes. The negative free energy of sufficiently large black holes implies the existence of a Hawking-Page transition. In odd dimensions the temperature still diverges for large black holes, which again have negative free energy. However, the temperature vanishes as the horizon radius tends to zero and sufficiently small black holes have positive specific heat.

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arXiv2011

Kerr-Schild Ansatz in Lovelock Gravity

We analyze the field equations of Lovelock gravity for the Kerr-Schild metric ansatz, $g_{ab}=\bar g_{ab} +λk_ak_b$, with background metric $\bar g_{ab}$, background null vector $k^a$ and free parameter $λ$. Focusing initially on the Gauss-Bonnet case, we find a simple extension of the Einstein gravity results only in theories having a unique constant curvature vacuum. The field equations then reduce to a single equation at order $λ^2$. More general Gauss-Bonnet theories having two distinct vacua yield a pair of equations, at orders $λ$ and $λ^2$ that are not obviously compatible. Our results for higher order Lovelock theories are less complete, but lead us to expect a similar conclusion. Namely, the field equations for Kerr-Schild metrics will reduce to a single equation of order $λ^p$ for unique vacuum theories of order $p$ in the curvature, while non-unique vacuum theories give rise to a set of potentially incompatible equations at orders $λ^n$ with $1\le n \le p$. An examination of known static black hole solutions also supports this conclusion.

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arXiv2010

Smarr Formula and an Extended First Law for Lovelock Gravity

We study properties of static, asymptotically AdS black holes in Lovelock gravity. Our main result is a Smarr formula that gives the mass in terms of geometrical quantities together with the parameters of the Lovelock theory. As in Einstein gravity, the Smarr formula follows from applying the first law to an infinitesimal change in the overall length scale. However, because the Lovelock couplings are dimensionful, we must first prove an extension of the first law that includes their variations. Key ingredients in this construction are the Killing-Lovelock potentials associated with each of the the higher curvature Lovelock interactions. Geometric expressions are obtained for the new thermodynamic potentials conjugate to variation of the Lovelock couplings.

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arXiv2010

An Extended Kerr-Schild Ansatz

We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr-Schild ansatz that includes a spacelike vector field as well as the usual Kerr-Schild null vector. We show that many, although not all, of the simplifications that occur in the Kerr-Schild case continue to hold for the extended ansatz. In particular, we find a simple set of sufficient conditions on the vectors such that the vacuum field equations truncate beyond quadratic order in an expansion around a general vacuum background solution. We extend our analysis to the electrovac case with a related ansatz for the gauge field.

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arXiv2009

Enthalpy and the Mechanics of AdS Black Holes

We present geometric derivations of the Smarr formula for static AdS black holes and an expanded first law that includes variations in the cosmological constant. These two results are further related by a scaling argument based on Euler's theorem. The key new ingredient in the constructions is a two-form potential for the static Killing field. Surface integrals of the Killing potential determine the coefficient of the variation of the cosmological constant in the first law. This coefficient is proportional to a finite, effective volume for the region outside the AdS black hole horizon, which can also be interpreted as minus the volume excluded from a spatial slice by the black hole horizon. This effective volume also contributes to the Smarr formula. Since the cosmological constant is naturally thought of as a pressure, the new term in the first law has the form of effective volume times change in pressure that arises in the variation of the enthalpy in classical thermodynamics. This and related arguments suggest that the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime.

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arXiv2008

Komar Integrals in Higher (and Lower) Derivative Gravity

The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given for black holes in pure Lovelock gravities of all orders and in general Gauss-Bonnet theories.

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arXiv2008

The Thermodynamics of Kaluza-Klein Black Hole/Bubble Chains

A Killing bubble is a minimal surface that arises as the fixed surface of a spacelike Killing field. We compute the bubble contributions to the Smarr relations and the mass and tension first laws for spacetimes containing both black holes and Killing bubbles. The resulting relations display an interesting interchange symmetry between the properties of black hole horizons and those of KK bubbles. This interchange symmetry reflects the underlying relation between static bubbles and black holes under double analytic continuation of the time and Kaluza-Klein directions. The thermodynamics of bubbles involve a geometrical quantity that we call the bubble surface gravity, which we show has several properties in common with the black hole surface gravity.

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arXiv2008

C-Functions in Lovelock Gravity

We present C-functions for static and spherically symmetric spacetimes in Lovelock gravity theories. These functions are monotonically increasing functions of the outward radial coordinate and acquire their minima when evaluated on the horizon. Unlike the case of Einstein gravity, where there is a single C-function, we find that this function is non-unique in the case of Lovelock gravity. We define two C-functions, which agree at the horizon giving the black hole entropy, and state the different energy conditions that must hold in order for these functions to satisfy the monotonicity condition.

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arXiv2007

The Attractor Mechanism in Gauss-Bonnet Gravity

We study extremal black hole solutions of D=5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.

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arXiv2007

Do Killing-Yano tensors form a Lie Algebra?

Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing-Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincare and (A)dS symmetry algebras.

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arXiv2007

The First Law for Boosted Kaluza-Klein Black Holes

We study the thermodynamics of Kaluza-Klein black holes with momentum along the compact dimension, but vanishing angular momentum. These black holes are stationary, but non-rotating. We derive the first law for these spacetimes and find that the parameter conjugate to variations in the length of the compact direction is an effective tension, which generally differs from the ADM tension. For the boosted black string, this effective tension is always positive, while the ADM tension is negative for large boost parameter. We also derive two Smarr formulas, one that follows from time translation invariance, and a second one that holds only in the case of exact translation symmetry in the compact dimension. Finally, we show that the `tension first law' derived by Traschen and Fox in the static case has the form of a thermodynamic Gibbs-Duhem relation and give its extension in the stationary, non-rotating case.

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arXiv2006

Stresses and Strains in the First Law for Kaluza-Klein Black Holes

We consider how variations in the moduli of the compactification manifold contribute pdV type work terms to the first law for Kaluza-Klein black holes. We give a new proof for the circle case, based on Hamiltonian methods, which demonstrates that the result holds for arbitrary perturbations around a static black hole background. We further apply these methods to derive the first law for black holes in 2-torus compactifications, where there are three real moduli. We find that the result can be simply stated in terms of constructs familiar from the physics of elastic materials, the stress and strain tensors. The strain tensor encodes the change in size and shape of the 2-torus as the moduli are varied. The role of the stress tensor is played by a tension tensor, which generalizes the spacetime tension that enters the first law in the circle case.

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arXiv2006

On black strings & branes in Lovelock gravity

It is well known that black strings and branes may be constructed in pure Einstein gravity simply by adding flat directions to a vacuum black hole solution. A similar construction holds in the presence of a cosmological constant. While these constructions fail in general Lovelock theories, we show that they carry over straightforwardly within a class of Lovelock gravity theories that have (locally) unique constant curvature vacua.

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arXiv2004

Positivity Bounds for the Y-ADM Mass Density

Killing-Yano tensors are natural generalizations of Killing vectors to arbitrary rank anti-symmetric tensor fields. It was recently shown that Killing-Yano tensors lead to conserved gravitational charges, called Y-ADM charges. These new charges are interesting because they measure, for example, the mass density of a p-brane, rather than the total ADM mass which may be infinite. In this paper, we show that the spinorial techniques used by Witten, in his proof of the positive energy theorem, may be straightforwardly extended to study the positivity properties of the Y-ADM mass density for p-brane spacetimes. Although the resulting formalism is quite similar to the ADM case, we show that establishing a positivity bound in the higher rank Y-ADM case requires imposing a condition on the Weyl tensor in addition to an energy condition. We find appropriate energy conditions for spacetimes that are conformally flat or algebraically special, and for spacetimes that have an exact Killing vector along the brane. Finally we discuss our expression for the Y-ADM mass density from the Hamiltonian point of view.

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