Results 1  10
of
862
Some properties of Noether charge and a proposal for dynamical black hole entropy
 Phys. Rev
, 1994
"... We consider a general, classical theory of gravity with arbitrary matter fields in n dimensions, arising from a diffeomorphism invariant Lagrangian, L. We first show that L always can be written in a “manifestly covariant ” form. We then show that the symplectic potential current (n − 1)form, Θ, an ..."
Abstract

Cited by 342 (4 self)
 Add to MetaCart
(Show Context)
We consider a general, classical theory of gravity with arbitrary matter fields in n dimensions, arising from a diffeomorphism invariant Lagrangian, L. We first show that L always can be written in a “manifestly covariant ” form. We then show that the symplectic potential current (n − 1)form, Θ, and the symplectic current (n − 1)form, ω, for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current (n − 1)form, J, and corresponding Noether charge (n − 2)form, Q. We derive a general “decomposition formula ” for Q. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, Sdyn, of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of L, Θ, and Q. However, the issue of whether this dynamical entropy in general obeys a “second law ” of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stressenergy pseudotensors. PACS #: 04.20.q, 0.4.20.Fy, 97.60.Lf 1 1
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
Abstract

Cited by 299 (25 self)
 Add to MetaCart
We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior antide Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N = 4 gauged supergravity theory holographically dual to a sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a cfunction that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the cfunction coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.
The generally covariant locality principle  A new paradigm for local quantum physics
 COMMUN.MATH.PHYS
, 2001
"... A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally cova ..."
Abstract

Cited by 147 (21 self)
 Add to MetaCart
(Show Context)
A new approach to the modelindependent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity, thus giving rise to the concept of a locally covariant quantum field theory. Such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories, on one side, of globally hyperbolic spacetimes with isometric embeddings as morphisms and, on the other side, of ∗algebras with unital injective ∗endomorphisms as morphisms. Moreover, locally covariant quantum fields can be described in this framework as natural transformations between certain functors. The usual HaagKastler framework of nets of operatoralgebras over a fixed spacetime backgroundmanifold, together with covariant automorphic actions of the isometrygroup of the background spacetime, can be regained from this new approach as a special case. Examples of this new approach are also outlined. In case that a locally covariant quantum field theory obeys the
A Covariant Entropy Conjecture
 JHEP
, 1999
"... We conjecture the following entropy bound to be valid in all spacetimes admitted by Einstein’s equation: Let A be the area of any twodimensional surface. Let L be a hypersurface generated by surfaceorthogonal null geodesics with nonpositive expansion. Let S be the entropy on L. Then S ≤ A/4. We pre ..."
Abstract

Cited by 112 (21 self)
 Add to MetaCart
(Show Context)
We conjecture the following entropy bound to be valid in all spacetimes admitted by Einstein’s equation: Let A be the area of any twodimensional surface. Let L be a hypersurface generated by surfaceorthogonal null geodesics with nonpositive expansion. Let S be the entropy on L. Then S ≤ A/4. We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited selfgravity it reduces to Bekenstein’s bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. It thus places a fundamental limit on the number of degrees of freedom in nature.
Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
, 2008
"... In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities h ..."
Abstract

Cited by 111 (10 self)
 Add to MetaCart
In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and Köhler, and by Brunetti and Fredenhagen, but they did not impose any “locality ” or “covariance ” condition in their constructions. As a consequence, their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters. In this paper, we construct an “extended Wick polynomial algebra”—large enough to contain the Wick polynomials and their time ordered products—by generalizing a construction of Dütsch and Fredenhagen to curved spacetime. We then define the notion of a local, covariant quantum field, and seek a definition of local Wick polynomials and their time ordered products as local, covariant quantum fields. We introduce a new notion of the scaling behavior of a local, covariant quantum field, and impose scaling requirements on our local Wick polynomials and their time ordered products as well as certain additional requirements—such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric. For a given polynomial order in powers of the field, we prove that these conditions uniquely determine the local Wick polynomials and their time ordered products up to a finite number of parameters. (These parameters correspond to the usual renormalization ambiguities occurring in Minkowski spacetime together with
The gravitational action in asymptotically AdS and flat spacetimes,” Nucl
 Phys. B
, 1999
"... The divergences of the gravitational action are analyzed for spacetimes that are asymptotically antide Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discus ..."
Abstract

Cited by 101 (5 self)
 Add to MetaCart
(Show Context)
The divergences of the gravitational action are analyzed for spacetimes that are asymptotically antide Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discussed. For AdS, an iterative procedure is devised that determines the counterterms efficiently. For asymptotically flat space, we use a different method to derive counterterms which are sufficient to remove divergences in most cases. Postdoctoraal Onderzoeker FWO, Belgium
The prebig bang scenario in string cosmology
 Phys. Rept
, 2003
"... We review physical motivations, phenomenological consequences, and open problems of the socalled prebig bang scenario in superstring cosmology. Contents 1 ..."
Abstract

Cited by 90 (3 self)
 Add to MetaCart
(Show Context)
We review physical motivations, phenomenological consequences, and open problems of the socalled prebig bang scenario in superstring cosmology. Contents 1
Special geometry of euclidean supersymmetry I: vector multiplets
 J. High Energy Phys
"... Abstract: We construct two new versions of the cmap which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N = 2 supersymmetry. While the Minkowskian paracmap is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, ..."
Abstract

Cited by 88 (16 self)
 Add to MetaCart
(Show Context)
Abstract: We construct two new versions of the cmap which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N = 2 supersymmetry. While the Minkowskian paracmap is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean paracmap corresponds to the dimensional reduction of the Euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are parahyperKähler manifolds. We review and prove the relevant results of paracomplex and parahypercomplex geometry. In particular, we give a second, purely geometrical construction of both cmaps, by proving that
NonTuring computations via MalamentHogarth spacetimes
 Int. J. Theoretical Phys
, 2002
"... We investigate the Church–Kalmár–Kreisel–Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turingtype Theses (not only ..."
Abstract

Cited by 79 (8 self)
 Add to MetaCart
(Show Context)
We investigate the Church–Kalmár–Kreisel–Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there are several distinguished Church–Turingtype Theses (not only one) and (ii) validity of some of these theses depend on the background physical theory we choose to use. In particular, if we choose classical general relativity theory as our background theory, then the above mentioned limitations (predicted by these Theses) become no more necessary, hence certain forms of the Church– Turing Thesis cease to be valid (in general relativity). (For other choices of the background theory the answer might be different.) We also look at various “obstacles ” to computing a nonrecursive function (by relying on relativistic phenomena) published in the literature and show that they can be avoided (by improving the “design ” of our future computer). We also ask ourselves, how all this reflects on the arithmetical hierarchy and the analytical hierarchy of uncomputable functions.