Energy-momentum Density Research Articles

Teleparallel Energy-Momentum Distribution of Spatially Homogeneous Rotating Spacetimes

The energy-momentum distribution of spatially homogeneous rotating spacetimes in the context of teleparallel theory of gravity is investigated. For this purpose, we use the teleparallel version of Moller prescription. It is found that the components of energy-momentum density are finite and well-defined but are different from General Relativity. However, the energy-momentum density components become the same in both theories under certain assumptions. We also analyse these quantities for some special solutions of the spatially homogeneous rotating spacetimes.

Topological and physical effects of rotation and spin in the general relativistic theory of gravitation

Interrelations of the intrinsic momentum (spin), rotation of material distributions, and intrinsic momentum of the gravitational field are investigated in the context of the general relativistic theory of gravitation involving the general relativity theory (GRT) and the Einstein-Cartan theory. It is demonstrated that the spin density vector of the gravitational field s g i is equal to the rotor of the tetrad reference point ωi=ɛiklm e k (a) e(a)l,m/2 to within the factor 1/κ (s g i =ω/κc). It is demonstrated that the vector s g i is proportional to the spin density vector of the gravitating field si (ω)=jc(Ψγiγ5Ψ)/2 as well as the pseudovector of space-time torsion Qi in the Einstein-Cartan theory, which in both cases induces a cubic nonlinearity of the spinor field. An expression for the energy-momentum density tensor of the eddy gravitational field is derived. It is also demonstrated that the free eddy gravitational field with polarized spin can form “mole holes.” An ideal fast-rotating self-gravitating fluid can cause a similar effect. The corresponding exact solutions of joint systems of the Einstein and rotating ideal fluid equations are presented.

The interaction of three fields in ECE theory: The inverse Faraday effect

The simultaneous interaction of three fundamental fields is illustrated in Einstein Cartan Evans (ECE) theory with reference to the effect of gravitation on the inverse Faraday effect . The three-field interaction in this case is that of the fermionic, electromagnetic and gravitational fields . The interaction of the first two is developed in a well-defined semi-classical approximation of the ECE wave equation and the effect of gravitation incorporated through the index reduced canonical energy momentum density T . The exercise is repeated using the ECE wave equations and a general rule developed for the effect of gravitation on the fermionic, electromagnetic weak and strong fields.

Multiparticle states in deformed special relativity

We investigate the properties of multiparticle states in deformed special relativity (DSR). Starting from the Lagrangian formalism with an energy dependent metric, the conserved Noether current can be derived which is additive in the usual way. The integrated Noether current had previously been discarded as a conserved quantity, because it was correctly realized that it does no longer obey the DSR transformations. We identify the reason for this mismatch in the fact that DSR depends only on the extensive quantity of total four momentum instead of the energy-momentum densities as would be appropriate for a field theory. We argue that the reason for the failure of DSR to reproduce the standard transformation behavior in the well established limits is due to the missing sensitivity to the volume inside which energy is accumulated. We show that the soccer-ball problem is absent if one formulates DSR instead for the field densities. As a consequence, estimates for predicted effects have to be corrected by many orders of magnitude. Further, we derive that the modified quantum field theory implies a locality bound.

ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

Spherically expanding matter in AdS/CFT correspondence

We discuss an exact time dependent O(3) symmetric solution with a horizon of the 5d AdS classical gravity equations searching for a 4d boundary theory which would correspond to expanding gauge theory matter. The boundary energy-momentum tensor and entropy density are computed. The boundary metric is the flat Friedmann one and any time dependence on the boundary is incompatible with the Minkowski metric. At large times when curvature effects are negligible, perfect fluid behavior arises in a natural way.

The Tensors of the Averaged Relative Energy–Momentum and Angular Momentum in General Relativity and Some of Their Applications

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [1-8] giving the {\it canonical superenergy and angular supermomentum tensors}. In this paper we present another averaging of the differences of the energy-momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy-momentum and angular momentum densities. But these averaged relative energy-momentum and angular momentum tensors, closely related to the canonical superenergy and angular supermomentum tensors, {\it depend on some fundamental length $L>0$}. The averaged relative energy-momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to {\it coordinate independent} analysis (local and in special cases also global) of this field. We have applied the averaged relative energy-momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general) universes. The obtained results are very interesting, e.g., the averaged relative energy density is {\it positive definite} for the all Friedman universes.

Publisher’s Note: Energy and angular momentum densities of stationary gravitational fields [Phys. Rev. D75, 024040 (2007)

Publisher’s Note: Energy and angular momentum densities of stationary gravitational fields [Phys. Rev. D<b>75</b>, 024040 (2007)

Violation of the Equivalence Principle in Modified Theories of Gravity

We show that the metric in f(R) theories of gravity in Palatini formalism can be solved as the product of a rank-two tensor times a scalar function which is very sensitive to the local energy-momentum densities. This local dependence of the metric generates new gravitationally-induced microscopic interactions, which eventually would lead to self-accelerated test body trajectories. These facts make very unlikely the viability of Palatini f(R) models designed to change the late-time cosmic evolution.

Energy and angular momentum densities of stationary gravitational fields

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary spacetimes. These expressions involve nonlocally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.

Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence

The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction term. The characterization of tetrad fields as reference frames is addressed in the context of the Kerr space–time. It is also pointed out that Einstein’s version of the principle of equivalence does not preclude the existence of a definition for the gravitational energy-momentum density.

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein's simplest staticgeometrical model for an isotropic and homogeneous universe areevaluated. For this purpose, Einstein, Bergmann–Thomson,Landau–Lifshitz (LL), Møller and Papapetrou energy-momentumcomplexes are used in general relativity. While Einstein andBergmann–Thomson complexes give exactly the same results, LL andPapapetrou energy-momentum complexes do not provide the same energydensities. The Møller energy-momentum density is found to be zeroeverywhere in Einstein's universe. Also, several spacetimes are thelimiting cases considered here.

To the substantiation of the radiation damping force

The differential law of conservation of energy-momentum density for an arbitrary moving relativistic charge is formulated in the most general form. Based on it, the radiation damping force is derived for two neighboring moments of proper time by integration over the closed hypersurface surrounding the world line of the point charge. The calculations performed elucidate the origin of the dynamic and static electromagnetic masses.

Energy Distribution Associated with Static Axisymmetric Solutions

This paper has been addressed to a very old but burning problem of energy in General Relativity. We evaluate energy and momentum densities for the static and axisymmetric solutions. This specializes to two metrics, i.e., Erez-Rosen and the gamma metrics, belonging to the Weyl class. We apply four well-known prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller to compute energy-momentum density components. We obtain that these prescriptions do not provide similar energy density, however momentum becomes constant in each case. The results can be matched under particular boundary conditions.

(e,2e)study on distorted-wave and relativistic effects in the inner-shell ionization processes of xenon4d5∕2and4d3∕2

Inner-shell ionization of xenon $4d$ electrons have been studied by the binary $(e,2e)$ spectroscopy at the impact energies of 1200, 1600, and $2400\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Experimental energy-momentum densities and the impact-energy dependence of momentum distributions of $4{d}_{5∕2}$ and $4{d}_{3∕2}$ are reported, the results are compared with the distorted-wave impulse approximation and the distorted-wave Born approximation. Moreover, the cross-section ratios of $4{d}_{5∕2}$ to $4{d}_{3∕2}$ are further provided at these different impact energies, which clearly manifest the relativistic effects. Some similarities and dissimilarities are observed on the impact-energy dependence of momentum distributions of $4{d}_{5∕2}$ and $4{d}_{3∕2}$ states and their cross-section ratios.

ENERGY–MOMENTUM OF A REGULAR MMaS–CLASS BLACK HOLE

We compute the energy and momentum of a regular black hole of type defined by Mars, Martín-Prats, and Senovilla by using the Einstein and Papapetrou definitions for energy–momentum density. Some other definitions of energy–momentum density are shown to give mutually contradictory and less reasonable results. In addition, the resuts support the Cooperstock hypothesis.

ENERGY–MOMENTUM DISTRIBUTION: A CRUCIAL PROBLEM IN GENERAL RELATIVITY

This paper is aimed to elaborate the problem of energy–momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under consideration are the nonnull Einstein–Maxwell solutions and the singularity-free cosmological model. The electromagnetic generalization of the Gödel solution and the Gödel metric become special cases of the nonnull Einstein–Maxwell solutions. It turns out that these prescriptions do not provide consistent results for any of these space–times. These inconsistent results verify the well-known proposal that the idea of localization does not follow the lines of pseudotensorial construction but instead follows from the energy–momentum tensor itself. These differences can also be understood with the help of the Hamiltonian approach.

SPACE-TIME DEFECTS AS A SOURCE OF CURVATURE AND TORSION

Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal "stress" is originated by the presence of defects. The defects are described according to the typical Volterra process. The case of a point defect in an otherwise isotropic four-dimensional medium is discussed showing that the resulting metric tensor corresponds to an expanding (or contracting) universe filled up with a non-zero energy-momentum density.

Classification of Subsystems for Graded-Local Nets with Trivial Superselection Structure

We classify Haag-dual Poincaré covariant subsystems of a graded-local net on 4D Minkowski spacetime which satisfies standard assumptions and has trivial superselection structure. The result applies to the canonical field net of a net of local observables satisfying natural assumptions. As a consequence, provided that it has no nontrivial internal symmetries, such an observable net is generated by (the abstract versions of) the local energy-momentum tensor density and the observable local gauge currents which appear in the algebraic formulation of the quantum Noether theorem. Moreover, for a net of local observables as above, we also classify the Poincaré covariant local extensions which preserve the dynamics.

ENERGY AND MOMENTUM IN SPACETIME HOMOGENEOUS GÖDEL-TYPE METRICS

Using Einstein and Papapetrou energy–momentum complexes, we explicitly calculate the energy and momentum distribution associated with spacetime homogeneous Gödel-type metrics. We obtain that the two definitions of energy-momentum complexes do not provide the same result for these type of metrics. However, it is shown that the results obtained are reduced to the energy–momentum densities of Gödel metric already available in the literature.