Kastor, David
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Senior Lecturer, Department of Physics
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Kastor
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David
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Physics
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Publication Do Killing–Yano tensors form a Lie algebra?(2007-01-01) Kastor, David; Ray, Sourya; Traschen, JennieKilling–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.Publication On black strings & branes in Lovelock gravity(2006-01-01) Kastor, David; Mann, RobertIt 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.Publication Conserved gravitational charges from Yano tensors(2004-01-01) Kastor, David; Traschen, JennieThe 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 an integral over only the sphere SD−(p+2) surrounding the brane and may be regarded as an intensive property of the brane.Publication Stresses and strains in the first law for Kaluza-Klein black holes(2006-01-01) Kastor, David; Traschen, JennieWe 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 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 S1 case.Publication Testing cosmic censorship with black hole collisions(1994) Brill, D; Horowitz, G; Kastor, David; Traschen, JennieThere 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 smooth. Generically, there is a mild curvature singularity, which still allows geodesics to be extended. The implications of these results for cosmic censorship are discussed.Publication The first law for boosted Kaluza-Klein black holes(2007-01-01) Kastor, David; Ray, Sourya; Traschen, JennieWe 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.Publication Electric dipole moment of a BPS monopole(1999) Kastor, David; Na, EuyMonopole “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 of the monopole superpartner solution for a study of the long-range spin-dependent dynamics of BPS monopoles.Publication A positive energy theorem for asymptotically de Sitter spacetimes(2002-01-01) Kastor, David; Traschen, JennieWe construct a set of conserved charges for asymptotically de Sitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of de Sitter. Using a spinor construction, we show that the charge associated with conformal time translations is necessarily positive and hence may provide a useful definition of energy for these spacetimes. A similar spinor construction shows that the charge associated with the time translation Killing vector of de Sitter in static coordinates has both positive and negative definite contributions. For Schwarzschild–de Sitter the conformal energy we define is given by the mass parameter times the cosmological scale factor. The time dependence of the charge is a consequence of a nonzero flux of the corresponding conserved current at spatial infinity. For small perturbations of de Sitter, the charge is given by the total comoving mass density.Publication The thermodynamics of Kaluza–Klein black hole/bubble chains(2008-01-01) Kastor, David; Ray, Sourya; Traschen, JennieA 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.Publication C-functions in Lovelock gravity(2008-01-01) Anber, Mohamed; Kastor, DavidWe 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.