Showing papers on "Stress–energy tensor published in 1988"

Notes on a class of homogeneous space‐times

Abstract: The breakdown of causality in homogeneous Godel‐type space‐time manifolds is examined. An extension of Reboucas–Tiomno (RT) and Accioly–Goncalves studies is made. The existence of noncausal curves is also investigated under two different conditions on the energy‐momentum tensor. An integral representation of the infinitesimal generators of isometries is obtained, extending previous works on the RT geometry.

Holonomy groups in general relativity

Abstract: The infinitesimal holonomy group structure of space‐time is discussed and related to the Petrov type of the Weyl tensor and the algebraic (Segre) type of the energy‐momentum tensor. The number of covariant derivatives of the curvature tensor required to determine the infinitesimal holonomy group is determined in each case and the complete classification scheme is tabulated. Some special cases of physical interest are investigated in more detail. A geometrical approach is followed throughout.

Gravitation, torsion, and electromagnetism

Abstract: A term bilinear in the derivative of the torsion is added to the Lagrangian of general relativity to produce torsion that propagates. Using standard variational techniques, field equations are derived with the torsion being interpreted as the electromagnetic potential and the antisymmetric part of the Ricci tensor as the electromagnetic field tensor. The equation of motion is derived from the field equations, and the results are compared to the Einstein-Maxwell formulation.

A new gravitational energy tensor

Abstract: The Bel-Robinson tensor is the most used gravitational energy tensor; however, it has the dimensions of energy squared. How to construct tensors with the dimensions of energy by using Lancoz tensors is shown here. The resulting tensors have a large number of arbitrary parameters, frequently have spacelike currents, and frequently do not reduce to familiar pseudo-energy tensors in the weak field limit. Two particular examples of interest are one with well-behaved currents and one which reduces to an energy pseudo-tensor in the weak field limit.

Stationary axisymmetric perfect fluid solutions in general relativity

Abstract: A new class of exact solutions of Einstein's field equations with the energy-momentum tensor of a perfect fluid is given. The class of solutions is invariantly characterized by means of the following properties: (i) The energy-momentum tensor describes a perfect fluid. (ii) There are two commuting Killing vectors ξ andη which form an abelian groupG2 of motion. (iii) There is a timelike Killing vector parallel to the four-velocity of the fluid (rigid rotation of the fluid). (iv) The four-vector of the angular velocity of the fluid is a gradientΩi=−(1/4c)ɛirklUl (Ur:k−Uk:r)=χ′i. The last assumption is the reason that all solutions of this class can be found by solving an ordinary differential equation of the second order.

Gravitational repulsion in sources of the Reissner–Nordström field

Abstract: A number of aspects of the phenomenon of gravitational repulsion in static sources of the Reissner–Nordstrom field are investigated. It is found that in the case of perfect fluid spheres there exists a close relation between this phenomenon and the Weyl curvature tensor. In fact, it is proved that such a source gives rise to gravitational repulsion only if the pure gravitational field energy inside the sphere is negative. It is also proved that although the gravitational repulsion always takes place in the interior of a perfect fluid charged sphere when its radius r0 is less than the ‘‘classical electron radius’’ re, this is not necessarily so either in the case of anisotropic charged spheres or if the net charge of the body is concentrated at its boundary only. It is shown that the phenomenon can also occur inside charged sources with r0>re. New sources of repulsive gravitation are constructed. They differ from others in the literature, since they neither satisfy the equation of state of ‘‘false vacuum’’...

Renormalized graviton stress-energy tensor in curved vacuum space-times.

Abstract: The graviton contribution to the renormalized one-loop effective stress-energy tensor is calculated in an arbitrary vacuum space-time with a cosmological constant. This is done for (1) the standard definition of the effective action and (2) the reparametrization-invariant effective action of Vilkovisky and DeWitt. The renormalized one-loop effective stress-energy tensor is given in terms of the graviton two-point function, by making use of its symmetric Hadamard representation.

Some new cosmological results of quadratic Lagrangians.

Abstract: We present the field equations derived from a gravitational Lagrangian which includes a general combination of terms quadratic in the curvature tensor, assuming a space-time with one timelike dimension and two maximally symmetric spacelike subspaces, with arbitrary dimensions d and D. We then restrict ourselves to the case d = 3, and find a general solution for the case of a radiation-dominated universe with a static pressureless internal space. Conditions for the existence of Friedmann-type solutions are derived and discussed. Finally we study the equations, again with a static internal space, for pressureless matter in both subspaces.

Energy momentum tensor of fields in the standard cosmology

Abstract: With the use of the equations of motion of massless fields moving in a curved Friedmann-Robertson-Walker universe, we show, in some simple cases, that the energy-momentum tensor of a maximally 3-space symmetric distribution of the fields (i.e., an incoherent averaging over a complete set of modes of the field propagating in a Robertson-Walker background) has the standard perfect fluid form. As far as we know such an explicit demonstration, as well as the establishment of the compatibility of the equations of motion of the gravitational field with such an incoherently averaged source in the standard cosmology, has not previously been presented in the literature. Our results are found to hold for any value of the spatial curvature of the universe.

An attempt to explain the smallness of the cosmological constant

Abstract: Fields which couple directly to the cosmological constant (Λ) may provide a scenario for explaining the smallness of Λ at the present epoch. In this paper we postulate the existence of a scalar field which couples universally to the trace of energy—momentum tensor of matter. Various possibilities for the explicit form of the coupling function are considered. The field equations in such a theory are derived, and the cosmological models with such a scalar field are analyzed. The proposed coupling makes the effective cosmological constant a dynamically evolving quantity, which can be driven to zero by allowing the scalar field to grow to sufficiently large values. For the case of linear coupling, however, it does not seem to be possible to attain sufficient growth during the age of the universe (~1017s). A quadratic coupling to the trace can evolve Λ to a value consistent with today’s observations, but the universe is dominated by the scalar field, rather than by radiation, at late times. The evolution is singular for couplings through a higher power law, in that the scalar field blows up at a finite time. The model is not very sensitive to initial conditions and the problems encountered can be avoided only by a severe fine-tuning of the parameters in the basic theory.

On a parametrization method for the semiclassical vacuum problem. I

Abstract: A formalism to study the semiclassical vacuum problem is introduced. Using this formalism we try to satisfy two competitive natural hypotheses: H1, the vacuum definition must assure the absorption of the infinities, coming from the vacuum expectation value of the energy‐momentum tensor of the matter fields, in the bare constants of the gravitational classic action; H2, the vacuum must be the ground state. It is proved that the system of equations yielded by these two hypotheses is, in general, incompatible. With this formalism, the vacuum problem in curved space‐time is stated. It is hoped that this formalism could eventually be used to solve the problem.

Hauser–Malhiot spaces admitting a perfect fluid energy‐momentum tensor

Abstract: In this paper a special case of Hauser–Malliot (HM) space‐times is examined in the presence of a perfect fluid source The obtained solutions are all known except for a generalization of a stationary axisymmetric solution found by Kramer [Class Quantum Gravit 1, L3 (1984)]

Stiff magnetofluid cosmological model

Abstract: We intestigate the behavior of the magnetic field in a cosmological model filled with a stiff perfect fluid in general relativity The magnetic field is due to an electric current along thex axis The behavior of the model when a magnetic field is absent is also discussed

Minimally relativistic Newtonian gravity

Abstract: Special relativity is introduced into the theory of Newtonian gravity in a systematic manner. The modifications of Newtonian gravity that are made can be seen to be minimal for special relativistic covariance. Space is assumed to be flat. Particle trajectories are determined from a Hamiltonian formulation with a tensor potential hμν. The tensor nature of the potential is justified by requiring Lorentz covariance alone. Nongeneral relativistic field equations for the hμν are obtained. The static, spherically symmetric solutions of these equations are shown to produce the correct values for the precession of the orbit of Mercury and the bending of light near the Sun.

On the trace anomaly of the energy-momentum tensor from the one-loop effective Lagrangian in QED

Abstract: Using the results on one-loop corrections to the effective Lagrangian in QED for constant prescribed electromagnetic fields, the authors demonstrate a new way to derive the trace anomaly in spinor and scalar QED.

Covariant field theory and surface terms

Abstract: We develop a formalism for field theory in which all the directions of the space-time are treated in an equivalent way. Consequently four velocities and four momenta are defined for each component of the fields. The role of the Hamiltonian is played by the energy-momentum tensor modified by an (unique) identically conserved tensor. This gives the covariant version of Hamilton equations, Poisson brackets and of the Jacobi identity. The surface terms of the canonical field theory, appearing for the energy, for the linear and angular momentum, found a natural explanation within this formalism.

Four‐momentum and angular momentum in classical electrodynamics

Abstract: The total four‐momentum Pμ and the total angular momentum tensor Mλμ for a classical point charged particle and its field are considered. The standard definition of Pμ and Mλμ is used as the integrals of their respective densities over a spacelike hyperplane orthogonal to the four‐velocity of the particle. It is shown that the integral defining Pμ exists and is a conserved quantity, but that the integral defining Mλμ does not exist. The last result is due to the asymptotic behavior of the Coulomb field at spatial infinity.

Radiating fluid distribution interacting with scalar field

Abstract: Taking the combined energy-momentum tensor for a perfect fluid, radially expanding the radiation and zero-mass scalar field, we investigate their interaction and obtain five new analytic solutions in a spherically symmetric Einstein universe. For the corresponding models various physical and geometrical properties are discussed. In one case an interesting equation of state is derived.

Quantization of the rotations of axially symmetric systems in the Skyrme model

Abstract: In the Skyrme model of baryons as topological solitons, we consider the quantization of the rotations of states possessing axial symmetry and described in terms of two functions of two variables. Expressions are obtained for the moments of inertia and the rotational energy, starting from the energy-momentum tensor of the system for arbitrary mapping index. In general the behavior of the system is described in terms of four different moments of inertia. We study the limiting case of two skyrmions separated by a distance which is large in comparison with the size of the skyrmions.

Central charge, trace and gravitational anomalies in two dimensions.

Abstract: The origin of the trace anomaly and of the central charge in the Virasoro algebra associated with the energy-momentum tensor of a bosonic two-dimensional model is considered. It is shown that both these quantities represent different aspects of the same gravitational anomaly.

On the gravitational field of superconducting cosmic strings.

Abstract: A Comment on the Letter by E. Copeland, H. Hindmarsh, and N. Turok, Phys. Rev. Lett. 58, 1910 (1987).

On spinor field equations of BUCHDAHL and WÜNSGH

Abstract: Les equations du champ de Buchdahl et Wunsch pour la description de champs de particules avec des masses au repos non nulles et des spins arbitraires dans des espaces-temps courbes sont considerees. Le lagrangien, les equations du champ et le tenseur impulsion-energie pour des champs de spin entier sont formules au moyen des champs tensoriels reels

The Vaidya–Patel solution with Robertson–Walker metric as a rotating inflationary scenario

Abstract: The Vaidya–Patel solution of a rotating homogeneous fluid in the presence of a Maxwellian source‐free electromagnetic field is interpretated as an inflationary scenario with a gauge field with local U(1) symmetry, a vacuum energy, and a rotating perfect fluid. An explicit solution is found to be expressible in terms of known solutions representing the radiation filled Robertson–Walker universe with a cosmological term. In the case that the rotating fluid is radiation, the discussion of the model is considerably simplified. How the time scale of transition into a pseudo‐de Sitter stage, as observed by an observer following the rotating fluid, is affected by vorticity is also studied.

Cold dense fermionic matter in the electroweak theory: anisotropic w-boson condensate at b≠l

Abstract: The one loop effective potential of cold dense fermionic matter is calculated in the standard electroweak theory. It is shown that the anisotropic W-boson condensate is formed at sufficiently high density and B≠L. The anisotropic part of the energy-momentum tensor is calculated for this state. It is shown that this state is metastable, the instability being due to the electroweak baryon number violating transitions.

The d=2 conformally invariant SU(2) σ-model with wess-zumino term and related critical theories +)

Abstract: The structure of the four point correlation functions of the conformally invariant SU(2) a-model is presented. Relations of the SU(2) model to other critical theories are pointed out.