Showing papers on "Stress–energy tensor published in 1984"

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

Abstract: The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle The gauge symmetries of the theory and the associated conservation laws are investigated Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory

Quantum creation of a universe with nontrivial topology

Abstract: Quantum creation of a universe with flat comoving 3-space is possible in nontrivial topology. For 3-torus topology, the relative probability of quantum birth of a spatially flat, isotropic world having finite 3-volume during the de Sitter (inflationary) stage is calculated, allowing for the vacuum energy-momentum tensor of massless quantum fields that will result from the nontriviality of the topology.

Electromagnetic mass models in general relativity

Abstract: The metric coefficients g/sub 00/ and g/sub 11/ of both the Schwarzschild and Reissner-Nordstroem metrics satisfy the relation g/sub 00/g/sub 11/ = -1. A coordinate-independent statement of this relation using the eigenvalues of the Einstein tensor is given. By considering the relation between the metric coefficients to be valid inside a charged perfect-fluid distribution, it is shown that the mass-energy density and the pressure of the distribution are of electromagnetic origin. In the absence of charge, however, there exists no interior solution. A particular solution which confirms the same and matches smoothly with the exterior Reissner-Nordstroem metric is obtained. This solution represents a charged particle whose mass is entirely of electromagnetic origin.

Vaidya Spacetime as an Evaporating Black Hole

Abstract: On etudie le tenseur energie-impulsion d'un champ scalaire pour un trou noir qui s'evapore modelise par la metrique de Vaidya a 2 dimensions

The gravitational contribution to the stress-energy tensor of a medium in general relativity

Abstract: The macroscopic stress-energy tensor of an astronomical “medium” such as a galaxy of stars is determined by the field equation of general relativity from the small-scale variations in mass and velocity. In the weak-field, slow-motion approximation, in which the gravitational fields of the stars are Newtonian, it is found that the contribution by the small-scale gravitational fields to the macroscopic density and stress are, respectively, the Newtonian gravitational energy density and the Newtonian gravitational stress tensor. This result is based on the general-relativity field equation, not conservation laws, although the general-relativity field equation has the well-known property of being consistent with conservation laws.

Renormalization of the Energy-Momentum Tensor And the Validity of the Equivalence Principle at Finite Temperature

Abstract: Using the techniques of finite-temperature field theory we renormalize the electromagnetic and gravitational couplings of an electron which is immersed in a heat bath with $T\ensuremath{\ll}{m}_{e}$. By taking the nonrelativistic limit, we demonstrate that the inertial and gravitational masses are unequal. The implications for the equivalence principle are discussed.

Exact Brans-Dicke Bianchi type-I solutions with a cosmological constant

Abstract: Exact cosmological solutions of the vacuum Brans-Dicke field equations are derived. The solutions are the anisotropic generalizations of the isotropic de Sitter solutions of the general theory of relativity.

Relativistic theory of gravitation

Abstract: This paper constructs a relativistic theory of gravitation based on the special principle of relativity and the principle of geometrization. The gravitational field is regarded as a physical field in the spirit of Faraday and Maxwell, possessing energy, momentum, and spin 2 and 0. The source of the gravitational field is the total conserved energy momentum tensor of the matter and the gravitational field in Minkowski space. Conservation laws hold rigorously for the energy, momentum, and angular momentum of the matter and the gravitational field. The theory explains all the existing gravitational experiments. By virtue of the geometrization principle, the Riemann space has a field origin in the theory, arising as an effective force space through the action of the gravitational field on the matter.

Dirac field on newtonian space-time

Abstract: Levy-Leblond's Galilei invariant theory of a spin 1/2-wave equation is generalized to a general curved Newtonian space-time. This is achieved by finding the general quadratic Lagrangian that leads to first order homogeneous equations in the four component spinor field and is invariant under the previously introduced general covariance group of Newtonian gravity. In addition to the field equations expressions for the matter current vector and the stress-energy tensor of the Dirac field are derived. It turns out that this derivation is less straightforward than in the relativistic case. The (gauge invariant) local energy density, for example, retains an arbitrary parameter reminiscent of the free constant in the potential in classical mechanics On generalise l'equation d'onde de Levy-Leblond pour une particule de spin 1/2 invariante par le groupe de Galilee au cas d'un espace-temps newtonien courbe. On construit un lagrangien invariant par le groupe de covariance generale de la gravitation newtonienne. Cela conduit a des equations lineaires homogenes d'ordre 1 pour un champ de spineur a 4 composantes. On deduit les expressions du courant de matiere et du tenseur energie-impulsion du champ de Dirac. Le calcul de ces expressions est moins elementaire qu'en relativite generale. La densite d'energie locale fait apparaitre un parametre libre qui rappelle la constante arbitraire figurant dans le potentiel classique

Manifestly positive-energy expression in classical gravity: Simplified derivation from supergravity

Abstract: A simplified derivation of Witten's expression for the total energy-momentum in classical general relativity is given. The starting point is the supersymmetry transformation law of the surface integral giving the supercharge in supergravity.

On charges of massless particles

Abstract: We are concerned with the theorem of Weinberg and Witten stating that a massless particle of helicity ‖h‖> 1/2 cannot be a carrier of a charge of an internal symmetry induced by a Lorentz covariant current and that for a massless field theory of ‖h‖>1 a Lorentz covariant energy momentum tensor cannot be constructed. We complete the proof of the theorem, as that given by Weinberg and Witten it is inconclusive. We suggest how to evade the difficulties which arise as a consequence of this theorem.

On the quantization of the world-line

Abstract: The fully covariant formalism of the quantization of a world-line is presented. It leads naturally to the Dirac equation. We use the Stueckelberg 4-dimensional normalization of the wave function ψ. If ψ is localized in a certain 4-dimensional region, then it represents a particle with indefinite mass. The product ψ* ψ integrated over a 4-volume is the probability of finding a particle (in general with indefinite mass) within this 4-volume. This should be distinguished from the probability that a world-line will penetrate through a certain 3-dimensional spacelike hypersurface. It is demonstrated that the probability density is always positive though the zero component of the currentjμ can be negative. It is also shown that the components of the canonical momentumpμ (which can all be negative) do not represent a particle’s energy-momentum. A particle’s energy (and momentum) is given by the integral of its stress energy tensor over a 3-volume encompassing the particle. The result is always positive energy for positive rest mass. This is the formal expression of the so-called reinterpretation principle.

Questions about gravitational instability of axion density fluctuations in an axion dominated universe

Abstract: It has recently been suggested that the axion with its spontaneous symmetry breaking mass scale of IA""'10 12 GeV would dominate the energy density of the present universe and possibly explain the observed structure of the universe.') However most of previous analyses on this topic seem to rely on a too simplified argument on the development of density fluctuations in an axion dominated universe (e.g. treating axions as a ,usual bosonic fluid). Since in the scenario of our interest, the energy density of the universe is not dominated by an axion fluid but by a coherent energy of the axion field, we must take account of its coherent nature when considering the development of density fluctuations. Keeping this point in mind, we investigate perturbations of the coherent axion fi~ld in this letter. The result strongly indicates that the coherent nature of the axion field restrains the growth of density fluctuations. Although only the case of the axion is considered here explicitly, our result applies to other cosmologically possible coherent fields if they have a chance to dominate the energy density of the universe. When the Peccei-Quinn symmetry breaks down spontaneous1y at cosmic time t = to, the corresponding' U(1)PQ angle 1J (modulo 2ir) would attain some finite expectation value which would be coherent over at least the horizon size of the universe (Hubble radius) to. Although the expectation value of If at this epoch is not quite physical, it will eventually affect the physics at later times and hence should be regarded as a physical quantity. Therefore the axion field, which is defined by ? = fA If, should be considered as being materialized classically and its energy momentum tensor as contributing to the r.h.s. of the Einstein equations directly. This is in' contrast with the case when the field' is highly incoherent and its expectation value is essentially zero; in such a case we know that a fluid picture becomes more adequate. Now, since rp= is realized at least over the horizon scale at t = to, spatial fluctuations of rp on scales l~to are real classical (observable) fluctuations. Hence their Fourier amplitudes rp k (where k is the comoving wavenumber) are classically observable. Although the phases of rp k cannot be predicted a priori, this probabilistic nature of rp k is completely classical and nothing to do with quantum uncertainty. Note that the same is true in the usual case of cosmological density fluctuations where each Fourier component 8p k represents an observable density fluctuation though fluctuations may be quite incoherent as a whole. This is a characteristic feature in cosmology where scales of fluctuations are so large. The energy momentum tensor of the field is expressed as

Theory of gravitation based on Minkowski space and the principle of geometrization

Abstract: The authors construct a theory of graviation on the basis of Minkowski space and the principle of geometrization. In it, the first six equations are Hilbert-Einstein equations, while the remaining four field equations are universal covariant harmonicity conditions. In contrast to the general theory of relativity, there are rigorous conservation laws for the energy, momentum, and angular momentum of a closed system. In the theory, only a ''flat'' universe is possible, and therefore the matter density must be equal to the critical density.

An Algebraic Approach to Quantum Field Theory and Commutation Relations for Energy Momentum in the Framework of General Relativity

Abstract: We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg ik (x) andg 00(x) with coordinate gaugeg i0=0. The Hamiltonian of the system is found to be a linear function of [−g 00(x)]1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc 2)[H σ(x) ,H σ′(x) ]=P σ∇σ′−σ′∇σ , whereH σ(x) is the Hamiltonian of the system, which is a linear functional of σ(x)≡[−g 00(x)]1/2 andP s(x) represents the momentum-density operator [averaged with the classical functions(x)].

Incoherent radiation in an n-dimensional space

Abstract: The standard freshman kinetic theory of pressure would indicate the equation of state p=μ/n for incoherent radiation in an n‐dimensional space. The validity of this can be demonstrated by two different methods—one using Maxwell’s equations to show the vanishing of the averaged trace of the stress energy tensor, the other following a statistical mechanical derivation. One use of the result is in the study of cosmological solutions to Einstein’s equations in n dimensions.

Einstein-Weyl field equations in a Bianchi type-IX space-time

Abstract: It is proved that there exists no solution of the combined gravitational-neutrino field equations in general relativity if the space-time metric admits a group of isometries of Bianchi type IX and the neutrino field has geodesic and shearfree rays.

The role of spin in cosmological models

Abstract: On etudie le role du spin, tel qu'il apparait dans le tenseur impulsion-energie de Ray-Smalley, dans les modeles cosmologiques

Invariance under conformal coordinate and point transformations

Abstract: Coordinate and point transformations are studied in the context of conformal symmetry. When invariance requirements on arbitrary rank tensors are involved in both contexts, the similitudes and differences in transformation laws and invariance conditions are analysed in connection with those on tensor densities of weight W . Physically interesting tensors like the metric tensor, the electromagnetic field and the energy-momentum tensor are specifically examined. Some remarks on scalar fields and densities are added.

Scaling behavior of semiclassical gravity

Abstract: Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.

Comment on Einstein-massless-scalar field equations and conformally flat solutions

Abstract: An (infinite) family of comformally flat solutions of the Einstein-massless-scalar field equations is derived when the space-time dependence of the conformal factor and of the scalar field is of the type u = kxx, k being a constant and uniform lightlike four-vector. This includes the Penney solution and completes Guerses discussion on the subject. Parallel developments are discussed when the space-time dependence is given by the variable ..nu.. = x/sup 2/: they lead to the unique Guerses's solution.

On invariant electromagnetic and energy-momentum tensors under Weyl transformations

Abstract: Invariant electromagnetic and energy-momentum tensors are studied under the Weyl symmetry. Theirkinematical groups are discussed and related to the corresponding study in the Poincare context. Their physical interest is pointed out in connection with zero-mass particle descriptions.

Bianchi type-I models with conformally invariant scalar field with trace-free energy-momentum tensor

Abstract: A new exact solution of the Einstein equations corresponding to a conformally invariant scalar field with trace-free energy-momentum tensor is obtained for the Bianchi type-I metric. The solution represents an anisotropic homogeneous cosmological model which admits anisotropic expansions. The Kasner universe is found in a systematic way. Some properties of the model have been discussed.

Use of the irreducible tensor expansion for the multipole interaction

Abstract: An irreducible tensor expansion for the multipole interaction written in the product basis for the interacting atoms is used to derive an analogous expression in a coupled-angular-momentum basis. The result may be applied directly to a recent theory (Phys. Rev. A 22, 1848 (1980)) of coherences produced by radiatively assisted inelastic collisions.

Quantum effects in inhomogeneous cosmological models

Abstract: The modification of the inhomogeneous metric due to trace anomaly has been analysed. The behaviour of the perturbed energy density seems to suggest the homogenisation effect of the original spacetime.

Gauge invariance of the observables in the general relativistic theory of the locally anisotropic space-time

Abstract: The equations of motion of test bodies have been obtained within the framework of the general relativisticc theory of the locally anisotropic space-time and gravity. These equations, as well as observable quantities of the proper time and 3-space distances, have been found to be invariant under the gauge transformations of the fields. The conserved gauge-invariant pseudo-tenso for the total energy-momentum of mattger and the fields that determine the Finslerian metric function for the locally anisotropic space of events has been constructed.

Hydrodynamic flow structures in quantum field theory

Abstract: The transport of matter is examined in the context of relativistic quantum transport theory for the case of neutral scalar fields The goal is to formulate a theory valid off mass shell and out of equilibrium We construct a conserved moment tensor which coincides with the ensemble average of the Noether tensor, or the improved energy‐momentum tensor with the ensemble average of the Noether tensor, or the improved energy‐momentum tensor within an additive constant of the ‘‘improvement’’ term Conditions for closure of the conservation equation are given for the φ4 coupling