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## Full-Text Articles in Physics

Non-Vacuum Ads Cosmologies And The Approach To Equilibrium Of Entanglement Entropy, Sebastian Fischetti, David Kastor, Jennie Traschen

#### Non-Vacuum Ads Cosmologies And The Approach To Equilibrium Of Entanglement Entropy, Sebastian Fischetti, David Kastor, Jennie Traschen

*David Kastor*

We extend standard results for vacuum asymptotically locally AdS (AlAdS) spacetimes, showing that such spacetimes can be constructed as foliations where the induced metric on each hypersurface satisfies Einstein's equation with stress-energy. By an appropriate choice of stress-energy on the hypersurfaces, the resulting AlAdS spacetime satisfies Einstein's equation with a negative cosmological constant and physical stress tensor. We use this construction to obtain AlAdS solutions whose boundaries are FRW cosmologies sourced by a massless scalar field or by a perfect fluid obeying the strong energy condition. We focus on FRW universes that approach Minkowski spacetime at late times ...

Magnetic Fields In An Expanding Universe, David Kastor, Jennie Traschen

#### Magnetic Fields In An Expanding Universe, David Kastor, Jennie Traschen

*David Kastor*

We find a solution to 4D Einstein-Maxwell theory coupled to a massless dilaton field describing a Melvin magnetic field in an expanding universe with 'stiff matter' equation of state parameter w=+1. As the universe expands, magnetic flux becomes more concentrated around the symmetry axis for dilaton coupling a<1/3√ and more dispersed for a>1/3√. An electric field circulates around the symmetry axis in the direction determined by Lenz's law. For a=0 the magnetic flux through a disk of fixed comoving radius is proportional to the proper area of the disk. This result disagrees with the usual expectation based on a test ...

Sum Rule For The Adm Mass And Tensions In Planar Ads Spacetimes, Basem M. El-Menoufi, Benjamin Ett, David Kastor, Jennie Traschen

#### Sum Rule For The Adm Mass And Tensions In Planar Ads Spacetimes, Basem M. El-Menoufi, Benjamin Ett, David Kastor, Jennie Traschen

*David Kastor*

An asymptotically planar AdS spacetimes is characterized by its ADM mass and tensions. We define an additional ADM charge Q associated with the scaling Killing vector of AdS, show that Q is given by a certain sum over the ADM mass and tensions and that Q vanishes on solutions to the Einstein equation with negative cosmological constant. The sum rule for the mass and tensions thus established corresponds in an AdS/CFT context to the vanishing of the trace of the boundary stress tensor. We also show that an analogous sum rule holds for local planar sources of stress-energy sources ...

Conformal Tensors Via Lovelock Gravity, David Kastor

#### Conformal Tensors Via Lovelock Gravity, David Kastor

*David Kastor*

Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D=4k dimensions, based on the squares of the higher curvature Weyl tensors.

On The Universality Of Inner Black Hole Mechanics And Higher Curvature Gravity, Alejandra Castro, Nima Dehmami, Gaston Giribet, David Kastor

#### On The Universality Of Inner Black Hole Mechanics And Higher Curvature Gravity, Alejandra Castro, Nima Dehmami, Gaston Giribet, David Kastor

*David Kastor*

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 ...

Gravitational Tension And Thermodynamics Of Planar Ads Spacetimes, Basem M. El-Menoufi, Benjamin Ett, David Kastor, Jennie Traschen

#### Gravitational Tension And Thermodynamics Of Planar Ads Spacetimes, Basem M. El-Menoufi, Benjamin Ett, David Kastor, Jennie Traschen

*David Kastor*

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 ...

Thermodynamic Volumes And Isoperimetric Inequalities For De Sitter Black Holes, Brian P. Dolan, David Kastor, David KubiznˇA´K, Robert B. Mann, Jennie Traschen

#### Thermodynamic Volumes And Isoperimetric Inequalities For De Sitter Black Holes, Brian P. Dolan, David Kastor, David KubiznˇA´K, Robert B. Mann, Jennie Traschen

*David Kastor*

We consider the thermodynamics of rotating and charged asymptotically de Sitter black holes. Using Hamiltonian perturbation theory techniques, we derive three different first law relations including variations in the cosmological constant, and associated Smarr formulas that are satisfied by such spacetimes. Each first law introduces a different thermodynamic volume conjugate to the cosmological constant. We examine the relation between these thermodynamic volumes and associated geometric volumes in a number of examples, including Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in D=4. We also show that the Chong-Cvetic-Lu-Pope solution of D=5 minimal supergravity, analytically continued to ...

Angular Tension Of Black Holes, David Kastor, Jennie Traschen

#### Angular Tension Of Black Holes, David Kastor, Jennie Traschen

*David Kastor*

Angular tension is an Arnowitt-Deser-Misner 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 ...

Smarr Formula And An Extended First Law For Lovelock Gravity, David Kastor, Sourya Ray, Jennie Traschen

#### Smarr Formula And An Extended First Law For Lovelock Gravity, David Kastor, Sourya Ray, Jennie Traschen

*David Kastor*

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 ...

The Thermodynamics Of Kaluza–Klein Black Hole/Bubble Chains, David Kastor, Sourya Ray, Jennie Traschen

#### The Thermodynamics Of Kaluza–Klein Black Hole/Bubble Chains, David Kastor, Sourya Ray, Jennie Traschen

*David Kastor*

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 ...

U Duality, D-Branes, And Black Hole Emission Rates: Agreements And Disagreements, F Dowker, David Kastor, Jennie Traschen

#### U Duality, D-Branes, And Black Hole Emission Rates: Agreements And Disagreements, F Dowker, David Kastor, Jennie Traschen

*David Kastor*

An expression for the spacetime absorption coefficient of a scalar field in a five-dimensional, near-extremal black hole background is derived, which has the same form as that presented by Maldacena and Strominger, but is valid over a larger, U-duality invariant region of parameter space and in general disagrees with the corresponding D-brane result. We develop an argument, based on D-brane thermodynamics, which specifies the range of parameters over which agreement should be expected. For neutral emission, the spacetime and D-brane results agree over this range. However, for charged emission, we find disagreement in the “fat black hole” regime, in which ...

Breaking Cosmic Strings Without Monopoles, D Eardley, G Horowitz, David Kastor, Jennie Traschen

#### Breaking Cosmic Strings Without Monopoles, D Eardley, G Horowitz, David Kastor, Jennie Traschen

*David Kastor*

It is shown that topologically stable cosmic strings can, in fact, appear to end or to break, even in theories without monopoles. This can occur whenever the spatial topology of the universe is nontrivial. For the case of Abelian-Higgs strings, we describe the gauge and scalar field configurations necessary for a string to end on a black hole. We give a lower bound for the rate at which a cosmic string will break via black hole pair production, using an instanton calculation based on the Euclidean C-metric.

Very Effective String Model?, David Kastor, Jennie Traschen

#### Very Effective String Model?, David Kastor, Jennie Traschen

*David Kastor*

Additional evidence is presented for a recently proposed effective string model, conjectured to hold throughout the parameter space of the basic 5 dimensional, triply charged black holes, which includes the effects of brane excitations, as well as momentum modes. We compute the low energy spacetime absorption coefficient σ for the scattering of a triply charged scalar field in the near extremal case, and conjecture an exact form for σ. It is shown that this form of σ arises simply from the effective string model. This agreement encompasses both statistical factors coming from the Bose distributions of string excitations and a ...

Enthalpy And The Mechanics Of Ads Black Holes, David Kastor, Sourya Ray, Jennie Traschen

#### Enthalpy And The Mechanics Of Ads Black Holes, David Kastor, Sourya Ray, Jennie Traschen

*David Kastor*

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 Λ 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 ...

Positivity Bounds For The Yano-Arnowitt-Deser-Misner Mass Density, David Kastor, T Shiromizu, S Tomizawa, Jennie Traschen

#### Positivity Bounds For The Yano-Arnowitt-Deser-Misner Mass Density, David Kastor, T Shiromizu, S Tomizawa, Jennie Traschen

*David Kastor*

Killing-Yano tensors are natural generalizations of Killing vectors to arbitrary rank antisymmetric tensor fields. It was recently shown that Killing-Yano tensors lead to conserved gravitational charges, called Yano-Arnowitt-Deser-Misner (Y-ADM) charges. These new charges are interesting because they measure e.g. 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 ...

Electric Dipole Moment Of A Bps Monopole, David Kastor, Euy Na

#### Electric Dipole Moment Of A Bps Monopole, David Kastor, Euy Na

*David Kastor*

Monopole “superpartner” solutions are constructed by acting with finite, broken supersymmetry transformations on a bosonic N=2 BPS monopole. The terms beyond first order in this construction represent the back reaction of the fermionic zero-mode state on the other fields. Because of the quantum nature of the fermionic zero modes, the superpartner solution is necessarily operator valued. We extract the electric dipole moment operator and show that it is proportional to the fermion zero-mode angular momentum operator with a gyroelectric ratio g=2. The magnetic quadrupole operator is shown to vanish identically on all states. We comment on the usefulness ...

Spin Of The M2-Brane And Spin-Spin Interactions Via Probe Techniques, Balasubramanian, David Kastor, Jennie Traschen, K.Z. Win

#### Spin Of The M2-Brane And Spin-Spin Interactions Via Probe Techniques, Balasubramanian, David Kastor, Jennie Traschen, K.Z. Win

*David Kastor*

The 256-dimensional M2-brane multiplet contains solitons of many different intrinsic spins. Using the broken supersymmetry transformations of the M2-brane, we find supergravity solutions which explicitly display these spins. This amounts to quantizing the fermionic zero modes and computing the back reaction on the metric and gauge potential. These spacetime fields are therefore operator valued and acquire a conventional classical meaning only after taking expectations in given BPS states. Our spinning spacetimes are not of the standard Kerr form—there is a nonvanishing gravitino. Nevertheless, the solutions have angular momentum and magnetic dipole moments with a g factor of 2. We ...

Do Killing–Yano Tensors Form A Lie Algebra?, David Kastor, Sourya Ray, Jennie Traschen

#### Do Killing–Yano Tensors Form A Lie Algebra?, David Kastor, Sourya Ray, Jennie Traschen

*David Kastor*

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 Poincaré and (A)dS symmetry algebras.

An Extended Kerr–Schild Ansatz, Benjamin Ett, David Kastor

#### An Extended Kerr–Schild Ansatz, Benjamin Ett, David Kastor

*David Kastor*

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 ...

Non-Extreme Calabi-Yau Black Holes, David Kastor, K.Z Win

#### Non-Extreme Calabi-Yau Black Holes, David Kastor, K.Z Win

*David Kastor*

Non-extreme black hole solutions of four dimensional, N = 2 supergravity theories with Calabi-Yau prepotentials are presented, which generalize certain known double-extreme and extreme solutions. The boost parameters characterizing the nonextreme solutions must satisfy certain constraints, which effectively limit the functional independence of the moduli scalars. A necessary condition for being able to take certain boost parameters independent is found to be block diagonality of the gauge coupling matrix. We present a number of examples aimed at developing an understanding of this situation and speculate about the existence of more general solutions.

Fully Localized Brane Intersections: The Plot Thickens, A Gomberoff, David Kastor, D Marolf, Jennie Traschen

#### Fully Localized Brane Intersections: The Plot Thickens, A Gomberoff, David Kastor, D Marolf, Jennie Traschen

*David Kastor*

We study fully localized Bogomol’nyi-Prasad-Sommerfield brane solutions in classical supergravity using a perturbative approach to the coupled Born-Infeld or bulk supergravity system. We derive first order bulk supergravity fields for world-volume solitons corresponding to intersecting M2-branes and to a fundamental string ending on a D3-brane. One interesting feature is the appearance of certain off-diagonal metric components and the corresponding components of the gauge potentials. Making use of a supersymmetric ansatz for the exact fields, we formulate a perturbative expansion which applies to M2⊥M2(0), M5⊥M5(3) and Dp⊥Dp (p-2) intersections. We find that perturbation theory qualitatively ...

Calibrations And Fayyazuddin-Smith Spacetimes, Hyunji Cho, Moataz Emam, David Kastor, Jennie Traschen

#### Calibrations And Fayyazuddin-Smith Spacetimes, Hyunji Cho, Moataz Emam, David Kastor, Jennie Traschen

*David Kastor*

We show that a class of spacetimes introduced by Fayyazuddin and Smith to describe intersecting M5-branes admits a generalized Kähler calibration. Equipped with this understanding, we are able to construct spacetimes corresponding to further classes of calibrated p-brane world-volume solitons. We note that these classes of spacetimes also describe the fields of p-branes wrapping certain supersymmetric cycles of Calabi-Yau manifolds.

Supersymmetric Self-Gravitating Solitons, G Gibbons, David Kastor, L London, P Townsend, Jennie Traschen

#### Supersymmetric Self-Gravitating Solitons, G Gibbons, David Kastor, L London, P Townsend, Jennie Traschen

*David Kastor*

We show that the “instantonic” soliton of five-dimensional Yang-Mills theory and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs theory continue to be exact static, and stable, solutions of these field theories even after the inclusion of gravitational, electromagnetic and, in the four-dimensional case, dilatonic interactions, provided that certain non-minimal interactions are included. With the inclusion of these interactions, which would be required by supersymmetry, these exact self-gravitating solitons saturate a gravitational version of the Bogomol'nyi bound on the energy of an arbitrary field configuration.

The Attractor Mechanism In Gauss-Bonnet Gravity, Mohamed Anber, David Kastor

#### The Attractor Mechanism In Gauss-Bonnet Gravity, Mohamed Anber, David Kastor

*David Kastor*

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 ...

Conserved Gravitational Charges From Yano Tensors, David Kastor, Jennie Traschen

#### Conserved Gravitational Charges From Yano Tensors, David Kastor, Jennie Traschen

*David Kastor*

The defining properties of Yano tensors naturally generalize those of Killing vectors to anti-symmetric tensor fields of arbitrary rank. We show how the Yano tensors of flat spacetime can be used to construct new, conserved gravitational charges for transverse asymptotically flat spacetimes. The relationship of these new charges to Yano tensors parallels that of ordinary ADM conserved charges to Killing vectors. Hence, we call them Y-ADM charges. A rank n Y-ADM charge is given by an integral over a co-dimension n slice of spatial infinity. In particular, a rank (p+1) Y-ADM charge in a p-brane spacetime is given by ...

From Wrapped M-Branes To Calabi-Yau Black Holes And Strings, David Kastor

#### From Wrapped M-Branes To Calabi-Yau Black Holes And Strings, David Kastor

*David Kastor*

We study a class of D = 11 BPS spacetimes that describe M-branes wrapping supersymmetric 2 and 4-cycles of Calabi-Yau 3-folds. We analyze the geometrical significance of the supersymmetry constraints and gauge field equations of motion for these spacetimes. We show that the dimensional reduction to D = 5 yields known BPS black hole and black string solutions of D = 5, N = 2 supergravity. The usual ansatz for the dimensional reduction is valid only in the linearized regime of slowly varying moduli and small gauge field strengths. Our identification of the massless D = 5 modes with D = 11 quantities extends beyond this ...

Horizons Inside Classical Lumps, David Kastor, Jennie Traschen

#### Horizons Inside Classical Lumps, David Kastor, Jennie Traschen

*David Kastor*

We investigate the possibility of having horizons inside various classical field configurations. Using the implicit function theorem, we show that models satisfying a certian set of criteria allow for (at least) small horizons within extended matter fields. Gauge and global monopoles and Skyrmions satisfy these criteria. Q balls and boson stars are examples which do not and can be shown not to allow for horizons. In examples that do allow for horizons, we show how standard "no hair" arguments are avoided.

The First Law For Boosted Kaluza-Klein Black Holes, David Kastor, Sourya Ray, Jennie Traschen

#### The First Law For Boosted Kaluza-Klein Black Holes, David Kastor, Sourya Ray, Jennie Traschen

*David Kastor*

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 ...

Stresses And Strains In The First Law For Kaluza-Klein Black Holes, David Kastor, Jennie Traschen

#### Stresses And Strains In The First Law For Kaluza-Klein Black Holes, David Kastor, Jennie Traschen

*David Kastor*

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 S1 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 ...

Testing Cosmic Censorship With Black Hole Collisions, D Brill, G Horowitz, David Kastor, Jennie Traschen

#### Testing Cosmic Censorship With Black Hole Collisions, D Brill, G Horowitz, David Kastor, Jennie Traschen

*David Kastor*

There exists an upper limit on the mass of black holes when the cosmological constant Λ is positive. We study the collision of two black holes whose total mass exceeds this limit. Our investigation is based on a recently discovered exact solution describing the collision of Q=M black holes with Λ>0. The global structure of this solution is analyzed. We find that if the total mass is less than the extremal limit, then the black holes coalesce. If it is greater, then a naked singularity forms to the future of a Cauchy horizon. However, the horizon is not ...