scholarly journals Kerr Metric, de Donder Condition and Gravitational Energy Density

1987 ◽  
Vol 78 (5) ◽  
pp. 1186-1201 ◽  
Author(s):  
M. Abe ◽  
S. Ichinose ◽  
N. Nakanishi
Keyword(s):  
Energy Density ◽  
Gravitational Energy ◽  
Kerr Metric

Is the Gravitational Energy Density Observable?

2002 ◽  
Vol 15 (2) ◽  
pp. 176-182
Author(s):  
Jean Chevalier
Keyword(s):  
Energy Density ◽  
Gravitational Energy

scholarly journals The Fundamental Discussion between Newton and Einstein

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gravitational Field ◽  
Energy Density ◽  
Speed Of Sound ◽  
Gravitational Energy ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Speed Of Light ◽  
Light Theory

Isaac Newton and Albert Einstein lived in fundamentally different time frames. An interesting question would be: “Who would win the fundamental discussion about the interaction between gravity and light”? Einstein or Newton? Einstein with the fundamental concept of a “curved space-time continuum” within a gravitational field. Or Newton with the fundamental “3rd law of equilibrium between the forces (force-densities)”. It is still the question who was right? Einstein or Newton? Einstein assumes a deformation of the space-time continuum because of a gravitational field. But in general a deformation of any medium will be caused by the change of the energy density within the medium. Like the speed of sound will increase/ decrease when we change the air pressure. However, the speed of sound (which became higher or lower) will still be the same in any direction. The change of the speed of sound will be omni-directional.A gravitational field contains a gravitational energy-density. For that reason the change in the speed of light will be omni-directional within a gravitational field (with a omni-directional gravitational energy density). Einstein however assumes a one-directional change in the speed of light, (only in the direction of the gravitational field). When the change of the speed of light was omni-directional, a beam of light would never be deflected by a gravitational field which is in contradiction with what we measure. Only the absolute value of the speed of light would change omni-directional.The theory of Newton however results in the theory of a 2-directional inertia of photons. The inertia of photons equals zero only in the direction of propagation. Perpendicular to the direction of propagation the mass density of photons is according Einstein’s E = m c^2).The inertia of photons in the direction of propagation will not change within a gravitational field. Gravity can only interact with mass (inertia). Because the mass of the photons in the direction of propagation equals zero, there will ne no interaction with the gravitational field and the photon in the direction of propagation. The speed of light in the direction of propagation will remain unaltered. But according Newton, the photon will have inertia (mass) in the directions perpendicular to the direction of propagation and for that reason the photon will interact with the gravitational field and the photon will be deflected, only in the direction of the gravitational field.And that leads to the consequence that photons will be deflected within a gravitational field when the direction of the gravitational field is perpendicular to the direction of propagation of the photons.To find fundamental mathematical evidence for this concept, we have to make use of Quantum Light Theory. Quantum Light Theory (QLT) is the development in Quantum Field Theory (QFT). In Quantum Field Theory, the fundamental interaction fields are replacing the concept of elementary particles in Classical Quantum Mechanics. In Quantum Light Theory the fundamental interaction fields are being replaced by One Single Field. The Electromagnetic Field, generally well known as Light. To realize this theoretical concept, the fundamental theory has to go back in time 300 years, the time of Isaac Newton to follow a different path in development. Nowadays experiments question more and more the fundamental concepts in Quantum Field Theory and Classical Quantum Mechanics. The publication “Operational Resource Theory of Imaginarity“ in “Physical Review Letters” in 2021 (Ref. [2]) presenting the first experimental evidence for the measurability of “Quantum Mechanical Imaginarity” directly leads to the fundamental question in this experiment: How is it possible to measure the imaginary part of “Quantum Physical Probability Waves”? This publication provides an unambiguously answer to this fundamental question in Physics, based on the fundamental “Gravitational Electromagnetic Interaction” force densities. The “Quantum Light Theory” presents a new “Gravitational-Electromagnetic Equation” describing Electromagnetic Field Configurations which are simultaneously the Mathematical Solutions for the Quantum Mechanical “Schrodinger Wave Equation” and more exactly the Mathematical Solutions for the “Relativistic Quantum Mechanical Dirac Equation”. The Mathematical Solutions for the “Gravitational-Electromagnetic Equation” carry Mass, Electric Charge and Magnetic Spin at discrete values.

An improved theory of gravitation. Part I

1968 ◽  
Vol 46 (19) ◽  
pp. 2155-2179 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Field Equation ◽  
Energy Density ◽  
Special Relativity ◽  
Gravitational Potential ◽  
Functional Dependence ◽  
Gravitational Interaction ◽  
Gravitational Energy ◽  
Additive Constant ◽  
Newtonian Theory ◽  
Theory Of Gravitation

A theory of gravitation is developed from assumptions that differ as little as possible from those of special relativity and the Newtonian theory of gravitation. As in special relativity, one assumes the existence of preferred coordinate systems (Newtonian charts) in which the nondiagonal components of the metric vanish, and in which the spatial, diagonal components are equal. The metric is determined by a single real function, the gravitational potential, which is assumed, as in the Newtonian theory, to be arbitrary to the extent of an additive constant. A uniqueness theorem is proved for Newtonian charts, and the functional dependence of the metric on the gravitational potential is determined (apart from two constants, which are later fixed by requiring that the equations of motion of a particle have the correct, nonrelativistic limit, and that the potential due to a fixed particle have the Newtonian form at great distances). By a simple change in the units of space and time, the geometry is made Minkowskian. A similar change in the units of mass makes the theory formally similar to special relativity. Particle dynamics is developed. The red shift and the deflection of light by a star are calculated, and agree with the Einstein results. The combination of the assumptions that the potentials due to particles are additive and that the potential due to a fixed particle is not proportional to 1/r, is shown to lead to difficulties. The weight of a simple system is found to be proportional to its total energy, including its gravitational interaction energy. Continuous, static mass distributions are considered. A field equation is derived for the static gravitational potential, and an expression for the energy density of the static gravitational field. The field equation is modified by assuming that the gravitational energy density is itself a source of the gravitational potential. The potential due to a static, spherically symmetric body is calculated, and the perihelion advance of a planet is found to be 11/12 of the Einstein value, in good agreement with the results of Dicke.

Note on gravitational energy

1982 ◽  
Vol 381 (1780) ◽  
pp. 215-224 ◽  
Keyword(s):  
Energy Density ◽  
Gravitational Energy ◽  
Energy Integral ◽  
Leading Order ◽  
Order Contribution ◽  
Time Component ◽  
Limiting Behaviour

We compute the limiting behaviour of an energy integral proposed by Hawking. In the presence of matter, we find that the leading-order contribution to this integral is just the energy density of the matter. In the absence of matter, the leading-order contribution is the (time component of the) Bel-Robinson tensor.

The gravitational energy density of the Universe

2021 ◽  
pp. 2150125
Author(s):  
J. B. Formiga ◽  
V. R. Gonçalves
Keyword(s):  
Heat Flux ◽  
Energy Density ◽  
Momentum Tensor ◽  
Gravitational Energy ◽  
Field Equations ◽  
Antisymmetric Part ◽  
Total Energy Density ◽  
Magnetic Components ◽  
Isotropic Pressure ◽  
The Universe

The teleparallel gravitational energy–momentum tensor density of the Friedmann–Lemaître–Robertson–Walker spacetime is calculated and analyzed: it is decomposed into density, isotropic pressure, non-isotropic pressures, and the heat-flux 4-vector; the antisymmetric part is decomposed into “electric” and “magnetic” components. It is found that the gravitational field obeys a radiation-like equation of state, the antisymmetric part does not contribute to the gravitational energy–momentum; and the total energy density, the non-isotropic pressures and the heat-flux 4-vector vanish for spatially flat universes. Finally, it is verified that the field equations have a well-defined vacuum.

scholarly journals Towards Energy Discretization in Quantum Cosmology

2018 ◽  
Author(s):  
Sergio Ulhoa ◽  
R.G.G. Amorim ◽  
Abraão Capistrano ◽  
Alexandre Fernandes
Keyword(s):  
Energy Density ◽  
Cosmological Model ◽  
Early Universe ◽  
Quantum Cosmology ◽  
Vacuum Solution ◽  
Empty Space ◽  
Teleparallel Gravity ◽  
Gravitational Energy

In this article we presented an application of the quantum cosmological model in teleparallel gravity. Working with a vacuum solution, the gravitational energy density is quantized with the Weyl procedure and we obtain a discrete expression for the gravitational energy. As an immediate consequence the empty space exhibits an expansion for an early universe.

scholarly journals ANISOTROPIC FLUID INSIDE A RELATIVISTIC STAR

2011 ◽  
Vol 03 ◽  
pp. 455-463 ◽  
Author(s):  
HRISTU CULETU
Keyword(s):  
Gravitational Field ◽  
Energy Density ◽  
Negative Pressure ◽  
Free Space ◽  
Gravitational Energy ◽  
Negative Sign ◽  
Anisotropic Fluid ◽  
Local Mass ◽  
Rindler Space ◽  
Variable Energy

An anisotropic fluid with variable energy density and negative pressure is proposed, both outside and inside stars. The gravitational field is constant everywhere in free space (if we neglect the local contributions) and its value is of the order of g = 10 -8cm/s2, in accordance with MOND model. With ρ, p ∝ 1/r, the acceleration is also constant inside stars but the value is different from one star to another and depends on their mass M and radius R. In spite of the fact that the spacetime is of Rindler type and curved even far from a local mass, the active gravitational energy on the horizon is -1/4g, as for the flat Rindler space, excepting the negative sign.

scholarly journals GENERAL RELATIVITY, GRAVITATIONAL ENERGY AND SPIN–TWO FIELD

2007 ◽  
Vol 04 (01) ◽  
pp. 147-169
Author(s):  
LESZEK M. SOKOŁOWSKI
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Energy Density ◽  
Stress Tensor ◽  
Equations Of Motion ◽  
General Theorem ◽  
Gravitational Energy ◽  
Theory Approach ◽  
Gauge Invariant ◽  
Gravity Theories

In my lectures I will deal with three seemingly unrelated problems: i) to what extent is general relativity exceptional among metric gravity theories? ii) is it possible to define gravitational energy density applying field–theory approach to gravity? and iii) can a consistent theory of a gravitationally interacting spin–two field be developed at all? The connecting link to them is the concept of a fundamental classical spin–2 field. A linear spin–2 field introduced as a small perturbation of a Ricci–flat spacetime metric, is gauge invariant while its energy–momentum is gauge dependent. Furthermore, when coupled to gravity, the field reveals insurmountable inconsistencies in the resulting equations of motion. After discussing the inconsistencies of any coupling of the linear spin–2 field to gravity, I exhibit the origin of the fact that a gauge invariant field has the variational metric stress tensor which is gauge dependent. I give a general theorem explaining under what conditions a symmetry of a field Lagrangian becomes also the symmetry of the variational stress tensor. It is a conclusion of the theorem that any attempt to define gravitational energy density in the framework of a field theory of gravity must fail. Finally I make a very brief introduction to basic concepts of how a certain kind of a necessarily nonlinear spin–2 field arises in a natural way from vacuum nonlinear metric gravity theories (Lagrangian being any scalar function of Ricci tensor). This specific spin–2 field consistently interacts gravitationally and the theory of the field is promising.

Fine-scale taxonomic and temporal variability in the energy density of invertebrate prey of juvenile Chinook salmon Oncorhynchus tshawytscha

2020 ◽  
Vol 655 ◽  
pp. 185-198
Author(s):  
J Weil ◽  
WDP Duguid ◽  
F Juanes
Keyword(s):  
Energy Density ◽  
Chinook Salmon ◽  
Temporal Variability ◽  
Energy Content ◽  
Single Point ◽  
Single Species ◽  
Fine Scale ◽  
Temporal Differences ◽  
Juvenile Chinook Salmon ◽  
Juvenile Chinook

Variation in the energy content of prey can drive the diet choice, growth and ultimate survival of consumers. In Pacific salmon species, obtaining sufficient energy for rapid growth during early marine residence is hypothesized to reduce the risk of size-selective mortality. In order to determine the energetic benefit of feeding choices for individuals, accurate estimates of energy density (ED) across prey groups are required. Frequently, a single species is assumed to be representative of a larger taxonomic group or related species. Further, single-point estimates are often assumed to be representative of a group across seasons, despite temporal variability. To test the validity of these practices, we sampled zooplankton prey of juvenile Chinook salmon to investigate fine-scale taxonomic and temporal differences in ED. Using a recently developed model to estimate the ED of organisms using percent ash-free dry weight, we compared energy content of several groups that are typically grouped together in growth studies. Decapod megalopae were more energy rich than zoeae and showed family-level variability in ED. Amphipods showed significant species-level variability in ED. Temporal differences were observed, but patterns were not consistent among groups. Bioenergetic model simulations showed that growth rate of juvenile Chinook salmon was almost identical when prey ED values were calculated on a fine scale or on a taxon-averaged coarse scale. However, single-species representative calculations of prey ED yielded highly variable output in growth depending on the representative species used. These results suggest that the latter approach may yield significantly biased results.

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