Energy Of Gravitational Field Research Articles

Gravitational energy in the framework of embedding and splitting theories

We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge–Teitelboim approach. For the embedding theory, we consider the coordinate translations on the surface as well as the coordinate translations in the flat bulk. In the latter case, the independent definition of gravitational energy–momentum tensor appears as a Noether current corresponding to global inner symmetry. In the field-theoretic form of this approach (splitting theory), we consider Noether procedure and the alternative method of energy–momentum tensor defining by varying the action of the theory with respect to flat bulk metric. As a result, we obtain energy definition in field-theoretic form of embedding theory which, among the other features, gives a nontrivial result for the solutions of embedding theory which are also solutions of Einstein equations. The question of energy localization is also discussed.

Vector theory of gravity: Universe without black holes and solution of dark energy problem

We propose an alternative theory of gravity which assumes that background geometry of the Universe is fixed four dimensional Euclidean space and gravity is a vector field Ak in this space which breaks the Euclidean symmetry. Direction of Ak gives the time coordinate, while perpendicular directions are spatial coordinates. Vector gravitational field is coupled to matter universally and minimally through the equivalent metric fik which is a functional of Ak. We show that such assumptions yield a unique theory of gravity, it is free of black holes and, to the best of our knowledge, passes all available tests. For cosmology our theory predicts the same evolution of the Universe as general relativity with cosmological constant and zero spatial curvature. However, the present theory provides explanation of the dark energy as energy of longitudinal gravitational field induced by the Universe expansion and yields, with no free parameters, the value of which is consistent with the recent Planck result . Such close agreement with cosmological data indicates that gravity has a vector, rather than tensor, origin. We demonstrate that gravitational wave signals measured by LIGO are compatible with vector gravity. They are produced by orbital inspiral of massive neutron stars which can exist in the present theory. We also quantize gravitational field and show that quantum vector gravity is equivalent to QED. Vector gravity can be tested by making more accurate measurement of the time delay of radar signal traveling near the Sun; by improving accuracy of the light deflection experiments; or by measuring propagation direction of gravitational waves relative to laser interferometer arms. Resolving the supermassive object at the center of our Galaxy with VLBA could provide another test of gravity and also shed light on the nature of dark matter.

Buchdahl compactness limit for a pure Lovelock static fluid star

We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential $\Phi(r)$, it means at the surface of the star $r=r_{0}$, $\Phi(r_{0}) < 2N(d-N-1)/(d-1)^2$ where $d$, $N$ respectively indicate spacetime dimensions and Lovelock order. For a given $N$, $\Phi(r_{0})$ is maximum for $d=2N+2$ while it is always $4/9$, Buchdahl's limit, for $d=3N+1$. It is also remarkable that for $N=1$ Einstein gravity, or for pure Lovelock in $d=3N+1$, Buchdahl's limit is equivalent to the criteria that gravitational field energy exterior to the star is less than half its gravitational mass, having no reference to the interior at all.

Regular charged black holes, quasilocal energy and energy conditions

We revisit the relationship of inequality between the gravitational field energy and the Komar charge, both quantities evaluated at the event horizon, for static and spherically symmetric regular black hole solutions obtained with nonlinear electrodynamics. We found a way to characterize these regular black hole solutions by the energy conditions that they satisfy. In particular, we show the relation between the direction of the inequality and the energy condition that satisfies the regular black hole solutions.

Thermal corrections to the Casimir energy in a general weak gravitational field

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.

The envelope of ballistic trajectories and elliptic orbits

Simple geometric derivations are given for the shape of the “safety domain” boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.

Weak Gravitational Field and Casimir Energy

In this paper we consider the effect of a weak gravitation field on the Casimir energy. Under a weak perturbation of a metric, we first obtain the linear energy-momentum tensor of a scalar field in a generic background and then the corrected energy of a scalar filed which satisfies the Dirichlet boundary condition is calculated up to first order of the metric perturbation. We show that our results coincide to the previous related works e.g., the Casimir effect when studied in Fermi coordinates.

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ+E+x2)u(x1,x2)=0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.

The Schrödinger–Newton system with self-field coupling

We study the Schrödinger–Newton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like general relativity (GR)), and its appearance in this simplified scalar setting (one of Einstein's precursors to GR) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between SN and the self-coupled scalar case.

Accelerated universe with inflation and a divergence-free Big Bang

We consider a two-component universe consisting of ordinary matter and vacuum energy quantitatively described by the cosmological term L c = (l/a)ρ c , where l is a quantity having the dimension of length, ρ c is the density of ordinary matter, and a is the scale factor. To justify the form of L c , we use the Maxwell-like approach to gravitation in which it is supposed that the gravitational field energy gravitates. The total energy conservation law for both cosmic components determines the mass density and the vacuum energy density as a function of the scale factor. Applying this two-component cosmic model to the present universe, the important cosmic parameters get values consistent with observations. The ratio of density parameters of ordinary matter and vacuum mass-energy, Ω m /Ω l , in today’s universe is 1/2. Interesting features of our model are (i) the existence of an inflationary phase just at the earliest era of the universe follows directly from the modified Friedmann equations, and (ii) the beginning of cosmic expansion, the Big-Bang, is singularity-free, i.e., both the mass and vacuum energy contents assume finite values at the very origin of the universe.

The role of observers in the measurement of teleparallel gravitoelectromagnetic fields in Schwarzschild spacetime

In the context of the teleparallel equivalent of general relativity (TEGR) we investigate the role of local observers, associated with tetrad fields, in the description of the gravitational interaction through the concepts of the gravitoelectric (GE) and gravitomagnetic (GM) fields. We start by analyzing the gravitoelectromagnetic (GEM) fields obtained from an observer freely falling in Schwarzschild space-time. Then, we investigate whether it is possible to distinguish between this situation and that of an observer at rest in Minkowski space-time. We conclude that, although there are non-zero components of the fields obtained in the case of a free fall, its dynamical effect, measured by the gravitational Lorentz force, is zero. Moreover, the gravitational field energy obtained from the GEM fields for an observer freely falling in Schwarzschild spacetime, is zero. These results are in complete agreement with the equivalence principle.

The Light during Gravitational Super-Compressibility

The interaction of electromagnetic and gravitational fields and gravitational super-compressibility were investigated experimentally. Dynamic emitter provides conditions for the generation of eigenfunctions with eigenvalues for the various fields, including: acoustic, gravitational and electromagnetic. We observe the gravitational waves in gas flowing from the dynamic emitter and their interaction with electromagnetic waves. The gravitational field energy was decreasing when electromagnetic field was emitted through the excitation of condensed medium. The direction of maximum change of the emitted energy of excited medium was strongly opposed to gravity vector at that point. The frequency of radiation against the gravity vector in given point of space exceeded radiation frequency of same source in opposite direction.

The Planck mass plasma roton solution of the cosmological constant problem

The failure of the Large Hadron Collider to detect supersymmetry and the Higgs particle suggests that one should replace supersymmetry with another fundamental symmetry, for example the symmetry of the Planck mass plasma where the vacuum is made up of an equal number of positive and negative Planck mass particles. The Planck mass plasma has for each mass component a phonon–roton spectrum and explains the small positive cosmological constant observed. The masses of the elementary particles are here explained by the gravitational field energy of pole–dipole particles, which explain the Dirac spinors as composed of gravitationally interacting positive and negative masses.

Another look at Helmholtz's model for the gravitational contraction of the Sun

We take another look at the Helmholtz model for the gravitational contraction of the Sun. We show that there are two other pedagogically useful ways of rederiving Helmholtz's main results that make use of Gauss's law, the concept of gravitational field energy and the work–kinetic energy theorem. An account of the energy balance involved in the gravitational contraction process is also discussed.

On the enigmatic Λ – A true constant of spacetime

Had Einstein followed the Bianchi differential identity for the derivation of his equation of motion for gravitation, $\Lambda$ would have emerged as a true new constant of spacetime on the same footing as the velocity of light? It is then conceivable that he could have perhaps made the most profound prediction that the Universe may suffer accelerated expansion some time in the future! Further we argue that its identification with the quantum vacuum energy is not valid as it should have to be accounted for like the gravitational field energy by enlarging the basic framework of spacetime and not through a stress tensor. The acceleration of the expansion of the Universe may indeed be measuring its value for the first time observationally.

중첩중력에너지가 방사선 조사된 밀과 대두의 판별특성에 미치는 영향

The aim of this study was to investigate the changes in identification markers of irradiated foods after treatment of the full-overlapped gravitational field energy (FGFE). Wheat and soybean samples were irradiated at 0-5 kGy of Co-60 gamma energy, and analyzed for photostimulated and thermo luminescence characteristics (PSL and TL) and sprouting rate at 0 and 6th month after FGFE treatment. As a screening method for irradiated samples, PSL photon counts (PCs) for the non-irradiated samples appeared negative (5,000 PCs). But FGFE-treated irradiated samples appeared intermediate (700-5,000 PCs), showing decreased PCs during storage. The TL analysis on irradiated samples exhibited glow curve peaks in range of and TL ratio () was also >0.1. Therefore, identification of irradiated samples was possible using thermoluminescence. But the glow curve range of FGFE-treated irradiated samples shifted from to and TL intensity was decreased 37-60% resulting from FGFE treatment. After 6 months of storage, all the samples showed a decrease in TL intensity, but identification was still possible. The sprouting rate of irradiated samples decreased by about 72%, whereas that of FGFE-treated irradiated samples showed by about 85%, as compared to non-irradiated samples. More detailed study is required to investigate sprouting phenomena for FGFE-treated samples.

Einstein energy associated with the Friedmann–Robertson–Walker metric

Following Einstein’s definition of Lagrangian density and gravitational field energy density (Einstein in Ann Phys Lpz 49:806, 1916, Einstein in Phys Z 19:115, 1918, Pauli in Theory of Relativity, B.I. Publications, Mumbai, 1963), Tolman derived a general formula for the total matter plus gravitational field energy (P 0) of an arbitrary system (Tolman in Phys Rev 35:875, 1930, Tolman in Relativity, Thermodynamics & Cosmology, Clarendon Press, Oxford, 1962, Xulu in hep-th/0308070, 2003). For a static isolated system, in quasi-Cartesian coordinates, this formula leads to the well known result $${P_0 = \int \sqrt{-g} (T_0^0 - T_1^1 - T_2^2 - T_3^3) d^3 x,}$$ where g is the determinant of the metric tensor and $${T^a_b}$$ is the energy momentum tensor of the matter. Though in the literature, this is known as “Tolman Mass”, it must be realized that this is essentially “Einstein Mass” because the underlying pseudo-tensor here is due to Einstein. In fact, Landau–Lifshitz obtained the same expression for the “inertial mass” of a static isolated system without using any pseudo-tensor at all and which points to physical significance and correctness of Einstein Mass (Landau, Lifshitz in The Classical Theory of Fields, Pergamon Press, Oxford, 1962)! For the first time we apply this general formula to find an expression for P 0 for the Friedmann–Robertson–Walker (FRW) metric by using the same quasi-Cartesian basis. As we analyze this new result, it transpires that, physically, a spatially flat model having no cosmological constant is preferred. Eventually, it is seen that conservation of P 0 is honoured only in the static limit.

Mass, Momentum and Energy of Gravitational Field

The energy of the gravitational field and the mass related to it are calculated. The momentum of the gravitational field of a moving body and the appropriate mass of the field are determined. Comparison of the given masses shows their difference. The reasons of violation of relativity and equivalence principles are discussed.

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)

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.