Showing papers on "Stress–energy tensor published in 2001"

Asymptotically Anti-De Sitter Spacetimes and Their Stress Energy Tensor

Abstract: We consider asymptotically anti-de Sitter spacetimes in general dimensions. We review the origin of infrared divergences in the on-shell gravitational action, and the construction of the renormalized on-shell action by the addition of boundary counterterms. In odd dimensions, the renormalized on-shell action is not invariant under bulk diffeomorphisms that yield conformal transformations in the boundary (holographic Weyl anomaly). We obtain formulae for the gravitational stress energy tensor, defined as the metric variation of the renormalized on-shell action, in terms of coefficients in the asymptotic expansion of the metric near infinity. The stress energy tensor transforms anomalously under bulk diffeomorphisms broken by infrared divergences.

Trace anomaly driven inflation

Abstract: This paper investigates Starobinsky's model of inflation driven by the trace anomaly of conformally coupled matter fields. This model does not suffer from the problem of contrived initial conditions that occurs in most models of inflation driven by a scalar field. The universe can be nucleated semiclassically by a cosmological instanton that is much larger than the Planck scale provided there are sufficiently many matter fields. There are two cosmological instantons: the four sphere and a new ``double bubble'' solution. This paper considers a universe nucleated by the four sphere. The AdS/CFT correspondence is used to calculate the correlation function for scalar and tensor metric perturbations during the ensuing de Sitter phase. The analytic structure of the scalar and tensor propagators is discussed in detail. Observational constraints on the model are discussed. Quantum loops of matter fields are shown to strongly suppress short scale metric perturbations, which implies that short distance modifications of gravity would probably not be observable in the cosmic microwave background. This is probably true for any model of inflation provided there are sufficiently many matter fields. This point is illustrated by a comparison of anomaly driven inflation in four dimensions and in a Randall-Sundrum brane-world model.

Comments on the Stress-Energy Tensor Operator in Curved Spacetime

Abstract: Hollands and Wald's technique based on *-algebras of Wick products of field operators is strightforwardly generalized to define the stress-energy tensor operator in curved globally hyperbolic spacetimes. In particular, the locality and covariance requirement is generalized to Wick products of differentiated quantum fields. The proposed stress-energy tensor operator is conserved and reduces to the classical form if field operators are replaced by classical fields satisfying the equation of motion. The definition is based on the existence of convenient counterterms given by certain local Wick products of differentiated fields. They are independent from the arbitrary length scale (and any quantum state) and they classically vanish on solutions of field equation. The averaged stress-energy tensor with respect to Hadamard quantum states can be obtained by an improved point-splitting renormalization procedure which makes use of the nonambiguous part of the Hadamard parametrix only that is completely determined by the local geometry and the parameters which appear in the Klein-Gordon operator. The averaged stress-energy tensor also coincides with that found by employing the local $\zeta$-function approach.

Stress-energy tensor for trans-Planckian cosmology

Abstract: This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian modes in black hole physics and in cosmology. This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their backreaction during inflation. It is shown that gravitational waves of trans-Planckian momenta but subhorizon frequencies cannot account for the form of cosmic vacuum energy density observed at present, contrary to a recent claim. The backreaction effects during inflation are confirmed to be important and generic for those dispersion relations that are liable to induce changes in the power spectrum of metric fluctuations. Finally, it is shown that in pure de Sitter inflation there is no modification of the power spectrum except for a possible magnification of its overall amplitude independently of the dispersion relation.

The role of Eshelby stress in composition-generated and stress-assisted diffusion

Abstract: The chemical potential used in interdiffusion analysis was derived by Li et al. in 1966 and by Larche and Cahn in 1982. It contains the trace of the stress tensor as the essential elasticity contribution to the configurational force conjugate to the material composition. As a result, the underlying diffusion equation is totally independent of any accompanying elastic field. In particular, when an alloy epifilm is annealed, the theory implies that the rather large lattice mismatch has no effect on the ensuing diffusion process. However, it is perhaps intuitively clear by now — almost 50 years since Eshelby published his first paper on energy momentum tensor in 1951 — that the trace of the (canonical) Eshelby stress tensor should be the total elasticity contribution to the desired configurational force. This conjecture is formally established in this paper for an n-component substitutional solid. Since the elastic energy is now a part of the chemical potential, the interplay between a composition-generated deformation and another elastic field may become important via the interaction energy. As an example, the effect of this interaction is calculated for the spinodal decomposition of a binary alloy solid/epifilm. The modification of the critical temperature is such that it is now a function of mismatch.

The theory of gravity

Abstract: In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the gravitational field. The energy-momentum and the angular momentum conservation laws are fulfilled in this theory. Such an approach permits us to unambiguously construct the gravitional field theory as a gauge theory. According to the RTG, the homogeneous and isotropic Universe is to be ``flat''. It evolves cyclewise from some maximal density to the minimal one, etc. The book is designed for scientific workers, post-graduates and upper-year students majoring in theoretical physics.

Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries

Abstract: The vacuum expectation values for the energy-momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on spherically symmetric boundaries in D-dimensional space are investigated. The expressions are derived for the regularized vacuum energy density and radial and azimuthal stress components (i) inside and outside a single spherical surface and (ii) in the intermediate region between two concentric spheres. A regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of cylinder functions. The asymptotic behavior of the vacuum densities near the sphere and at large distances is investigated. A decomposition of the Casimir energy into volumic and surface parts is provided for both cases (i) and (ii). We show that the mode sum energy, evaluated as a sum of the zero-point energy for each normal mode of frequency, and the volume integral of the energy density in general are different, and argue that this difference is due to the existence of an additional surface energy contribution.

Some Cosmological Models in Scalar-Tensor Theory of Gravitation

Abstract: Field equations in a scalar-tensor theory of gravitation proposed by Saezand Ballester (1985) are obtained with the aid of (i) Friedmann-type metric (ii) a non static plane symmetric metric and (iii) spatially homogeneous Bianchi type – III metric. Some cosmological models corresponding to perfect fluid and bulk viscous fluid are presented. Physical and kinematical properties of the models are also discussed.

General brane cosmology with (4) R term in (A)dS 5 or Minkowski bulk

Abstract: A general analysis of the induced brane dynamics is performed in an (A)dS5 or Minkowski background, when the intrinsic curvature term is included in the brane action. Such a term is known to cause dramatic changes and is generically induced by quantum corrections coming from the bulk gravity and its coupling with matter living on the brane. The induced brane dynamics is shown to be the usual Einstein dynamics coupled to a well-defined modified energy momentum tensor. Conventional general relativity revives for an initial era whose duration depends on the value of the five-dimensional Planck mass. Violations of energy conditions may be possible, as well as matter inhomogeneities on the brane in the above exact bulks. A new anisotropic solution is given in the above context. This solution, for a fine-tuned AdS5 bulk, exhibits an intermediate accelerating phase which is followed by an era corresponding to a 4D perfect fluid solution with no future horizons.

Energy-momentum Tensors in Matrix Theory and in Noncommutative Gauge Theories

Abstract: The energy-momentum tensor of Matrix Theory is derived by computing disk amplitudes with one closed string and an arbitrary number of open strings and by taking the DKPS limit. We clarify its relation to the energy-momentum tensor of the noncommutative gauge theory derived in our previous paper.

The metric and strong coupling limit of the M5-brane

Abstract: We find the analog of the Boillat metric of Born–Infeld theory for the M5-brane. We show that it provides the propagation cone of all 5-brane degrees. In an arbitrary background field, this cone never lies outside the Einstein cone. An energy momentum tensor for the three-form is defined and shown to satisfy the Dominant Energy Condition. The theory is shown to be well defined for all values of the magnetic field but there is a limiting electric field strength. We consider the strong coupling limit of the M5-brane and show that the corresponding theory is conformally invariant and admits infinitely many conservation laws. On reduction to the Born–Infeld case this agrees with the work of Bialynicki-Birula.

Some Aspects of the de Sitter/CFT Correspondence

Abstract: We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder. Correlation functions are also computed for CFTs on two-dimensional hyperbolic space. We furthermore determine the energy momentum tensor and the Casimir energy of the conformal field theory dual to the Schwarzschild-de Sitter solution in five dimensions. Requiring the pressure to be positive yields an upper bound for the black hole mass, given by the mass of the Nariai solution. Beyond that bound, which is similar to the one found by Strominger requiring the conformal weights of CFT operators to be real, one encounters naked singularities.

From discontinuous models towards a continuum description

Abstract: One of the essential questions of material sciences is how to bridge the gap between microscopic quantities, like contact forces and deformations, in a granular assembly, and macroscopic quantities like stress, strain or the velocity-gradient. A twodimensional shear-cell is examined by means of discrete element simulations. Applying a volume averaging formalism, one obtains volume fractions, coordination numbers, and fabric properties. Furthermore, the stress tensor and the “elastic” (reversible) mean displacement gradient can be derived. From these macroscopic quantities, some material properties can be computed by different combinations of the tensorial invariants. Because an essential ingredient of both simulations and experiments are rotations of the independent grains, we apply a Cosserat type description. Therefore we compute quantities like the couple stress and the curvature tensor as well as a combination of them, the “torque-resistance”.

True energy-momentum tensors are unique. Electrodynamics spin tensor is not zero

Abstract: A true energy-momentum tensor is unique and does not admit an addition of a term. The true electrodynamics' energy-momentum tensor is the Maxwell-Minkowski tensor. It cannot be got with the Lagrange formalism. The canonical energy-momentum and spin tensors are out of all relation to the physical reality. The true electrodynamics' spin tensor is not equal to a zero. So, electrodynamics' ponderomotive action comprises a force from the Maxwell stress tensor and a torque from the spin tensor. A gauge non-invariant expression for the spin tensor is presented and is used for a consideration of a circularly polarized standing wave. A circularly polarized light beam carries a spin angular momentum and an orbital angular momentum. So, we double the beams angular momentum. The Beths experiment is considered.

Counting form factors of twist-two operators

Abstract: We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the vector current and energy-momentum tensor being special examples) is n+1. These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the J{sup PC} rules for quarkonium states arise in the helicity formalism.

Some remarks on the Bel-Robinson tensor

Abstract: In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

5-D actions for 6-D selfdual tensor field theory

Abstract: We present two equivalent five-dimensional actions for six-dimensional (N,0) N=1,2 supersymmetric theories of self-dual tensor whose one spatial dimension is compactified on a circle. The Kaluza-Klein tower consists of a massless vector and infinite number of massive self-dual tensor multiplets living in five-dimensions. The self-duality follows from the equation of motion. Both actions are quadratic in field variables without any auxiliary field. When lifted back to six-dimensions, one of them gives a supersymmetric extension of the bosonic formulation for the chiral two-form tensor by Perry and Schwarz.

Symmetry properties of the metric energy-momentum tensor in classical field theories and gravity

Abstract: We derive a generic identity which holds for the metric (i.e. variational) energy-momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under which a symmetry of the Lagrangian is also a symmetry of the energy-momentum tensor. It turns out that the stress tensor acquires the symmetry if the Lagrangian has the symmetry in a generic curved spacetime. In this sense a field theory in flat spacetime is not self-contained. When the identity is applied to the gauge invariant spin-two field in Minkowski space, we obtain an alternative and direct derivation of a known no-go theorem: a linear gauge invariant spin-2 field, which is dynamically equivalent to linearized General Relativity, cannot have a gauge invariant metric energy-momentum tensor. This implies that attempts to define the notion of gravitational energy density in terms of the metric energy--momentum tensor in a field-theoretical formulation of gravity must fail.

Conserved currents for general teleparallel models

Abstract: The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. In this article a general 3-parameter class of teleparallel models is considered. The field equation turns out to have a form completely similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure, the source 3-form $\T^a$ is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source of the coframe field is interpreted as the total conserved energy-momentum current of the system. A reduction of the conserved current to the Noether current and the Noether charge for the coframe field is provided. An energy-momentum tensor for the coframe field is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in GR. The energy-momentum tensor is calculated for various teleparallel models: the pure Yang-Mills type model, the anti-Yang-Mills type model and the generalized teleparallel equivalent of GR. The latter case can serve as a very close alternative to the GR description of gravity.

Can one generalize the concept of energy-momentum tensor?

Abstract: The answer to the question is yes! Considering here the very simple case of a real Klein-Gordon field in Minkowski space-time, we find a class of rank 4 superenergy tensors generalizing the usual energy-momentum tensor. Then, we construct explicitely an infinite tower of rank 2(n +1) tensors that we call weak n-superenergy tensors and we determine the corresponding quantum operators.

Form factors of SU(N) invariant Thirring model

Abstract: We obtain a new integral formula for solutions of the rational quantum Knizhnik-Zamolodchikov equation associated with Lie algebra sl_{N} at level zero. Our formula contains the integral representation of form factors of SU(N) invariant Thirring model constructed by F. Smirnov. We write down recurrence relations arising from the construction of the form factors. We check that the recurrence relations hold for the form factors of the energy momentum tensor.

Incompatibility of Bianchi type III space time in scale invariant theory

Abstract: It is shown here that the development of scale invariant theory of gravitation is not possible when (a) the space time is governed by diagonal Bianchi type III metric (b) the gauge function β depends on the time coordinate only (Dirac gauge) and (c) the energy momentum tensor is that of a perfect fluid.

Current Algebra Associated with Logarithmic Conformal Field Theories

Abstract: We propose a general framework for deriving the OPEs within a logarithmic conformal field theory (LCFT). This naturally leads to the emergence of a logarithmetic partner of the energy momentum tensor within an LCFT and implies that the current algebra associated with an LCFT is expanded. We derive this algebra for a generic LCFT and discuss some of its implications. We observe that two constants arise in the OPE of the energy-momentum tensor with itself. One of these is the usual central charge.

Variational Formulation of a Material Ageing Model

Abstract: A material ageing parameter, i.e. an additional internal variable, is introduced as the conjugate to the Canonical Energy Momentum Tensor. Ageing is manifested in variation of basic material characteristics such as density, moduli of elasticity, yeald stress, strength and toughness.

Low temperature relation for the trace of the energy-momentum tensor in QCD with light quarks

Abstract: It is shown that the temperature derivatives of the anomalous and normal (quark massive term) contributions to the trace of the energy-momentum tensor in QCD are equal to each other in the low-temperature region. The physical consequences of this relation are discussed.