On the Energy Density in a Gravitational Field

1950 ◽  
Vol 18 (4) ◽  
pp. 237-237
Author(s):  
Julius Sumner Miller
1951 ◽  
Vol 19 (1) ◽  
pp. 63-64
Author(s):  
John A. Eldridge

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1545-1548 ◽  
Author(s):  
M. D. MAIA ◽  
A. J. S. CAPISTRANO ◽  
E. M. MONTE

General relativity postulates the Minkowski space-time as the standard (flat) geometry against which we compare all curved space-times and also as the gravitational ground state where particles, quantum fields and their vacua are defined. On the other hand, experimental evidences tell that there exists a non-zero cosmological constant, which implies in a deSitter ground state, which not compatible with the assumed Minkowski structure. Such inconsistency is an evidence of the missing standard of curvature in Riemann's geometry, which in general relativity manifests itself in the form of the cosmological constant problem. We show how the lack of a curvature standard in Riemann's geometry can be fixed by Nash's theorem on metric perturbations. The resulting higher dimensional gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity represents a gravitational term which is not confined. In this case, the comparison between the vacuum energy and the cosmological constant in general relativity does not make sense. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.


1988 ◽  
Vol 03 (15) ◽  
pp. 1425-1429 ◽  
Author(s):  
VARUN SAHNI

The creation of particles by a nonstationary gravitational field during the formation of a straight, static cosmic string has been investigated and the contribution to the number density of created particles from modes with the lowest angular quantum number assessed. It is found that for GUT scale strings the energy density of created particles is many orders of magnitude smaller than the corresponding energy density of radiation at GUT times.


1995 ◽  
Vol 10 (12) ◽  
pp. 1821-1844
Author(s):  
CHRISTOPHE M. MASSACAND

We compute the energy density and pressures due to the quantum production of particles of a scalar field. This scalar field propagates in the external gravitational field of a (3+1)-dimensional, spherically symmetric, static geometry with flat spatial sections. We assume that the gravitational potential is weak, and we work to the first order in the strength of this potential. We consider only the l=0 sector of the scalar field. Our method for computing the energy density is based on the gauge-invariant definition of particles and normal ordering with respect to the energy measurable on a hypersurface with no extrinsic curvature. The initial state of the quantum field is the gauge-invariant vacuum on one of these hypersurfaces. Our computations are finite step by step. For the pressures we use the covariant conservation of Tμν and its four-dimensional trace. We apply our results to the gravitational potential of a homogeneous spherical body. At late times, i.e. when all switch-on effects are far away from the body, the result is that a static, gravitational vacuum polarization cloud of energy and pressure is formed inside and outside the body.


This paper concerns itself with the possibility of thermal equilibrium between a black hole and a heat bath implied by Hawking’s discovery of black hole emission. We argue that in an isolated box of radiation, for sufficiently high energy density a black hole will condense out. We introduce thermal Green functions to discuss this equilibrium and are able to extend the original arguments, that the equilibrium is possible based on fields interacting solely with the external gravitational field, to the case when mutual and self interactions are included.


Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Abraão Capistrano ◽  
Pedro Odon

AbstractThe cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.


2021 ◽  
Author(s):  
Wim Vegt

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.


2019 ◽  
Vol 17 (1) ◽  
pp. 13-16
Author(s):  
Vo Van On

We show that, in the framework of the vector model of gravitational field, the total mass density and the mass of the Universe are quite the same as of experimental observed ones \(\rho_{\text{total}} \simeq 1.0 \times 10^{−29}\) g/cm\(^3\) and \(M_{\text{universe}}\simeq 1053\) kg.


2016 ◽  
Vol 25 (09) ◽  
pp. 1641017
Author(s):  
C. H. G. Bessa ◽  
V. B. Bezerra ◽  
J. C. J. Silva

In this work, we study the influence of the gravitational field induced by the presence of a cosmological constant [Formula: see text] on the Casimir energy density. We consider two metrics with the presence of the [Formula: see text]-term, namely de Sitter and Schwarzschild-de Sitter (SdS). In the former case, we consider a conformal de Sitter spacetime and in the last one, a weak gravitational SdS spacetime.


1979 ◽  
Vol 32 (4) ◽  
pp. 405 ◽  
Author(s):  
HA Buchdahl

The first-order perturbation induced by the first-order perturbation of a given Lagrangian in its associated characteristic function V is given by a simple integral along the unperturbed extremals. This result is applied to the world characteristic of the linearized gravitational field. Various specialized situations are considered. For example, to obtain V(1) in the quasi-Newtonian approximation one merely needs to evaluate a three-dimensional volume integral over the product of the energy density and a type of two-point Green's function.


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