Energy Of Gravitational Field Research Articles

Gravitational field energy density for spheres and black holes

We show by physical arguments that static spherical systems have a coordinate-independent field energy density. For Schwarzschild's spacetime it is +(g2/8πG) where |$g=\lbrace GM/[(1+m/2\bar r)^3\bar r^2]\rbrace$| and |$\bar r$| is the isotropic coordinate. The total field energy outside |$\bar r$| is |$GM^2/2\bar r$|⁠. Schwarzschild's r=2m corresponds to |$\bar r$|=½GM/c2 so the field energy outside a Schwarzschild black hole totals Mc2. In this sense all the energy remains outside the hole.

LOCALISATION OF ENERGY IN GENERAL RELATIVITY

The main statements of paper [1] are critically reviewed and the blunders in the deduction are indicated. It is showend that the total energy-momentum complex proposed in paper [1] and the energy of gravitational field in a finite part of space are not unique under pure spatial transformation and, therefore, are not possessed of a definite physical meaning.

Shear-free gravitational collapse

Spherically symmetric perfect fluids are studied under the restriction of shear-free motion. All solutions of the field equations are found by solving a single second order nonlinear equation containing an arbitrary function. It is shown that this arbitrary function is a geometric invariant, E, which measures the gravitational field energy, and it is shown that E=const generates all the homogeneous density solutions. An improved proof is given for the nonexistence of any one-parameter equation of state. A number of exact solutions are presented and discussed.

The localisation of energy in general relativity

The logic of gravitational field energy localisation for static or quasi-static fields is discussed. A particular form of localisation in the case of spherical symmetry is justified by physical considerations. This form coincides with that general form presented by Moller (1952) for the case of the Schwarzschild constant-matter-density fluid but differs when one considers other equations of state.

Conformal changes of metrics and the initial-value problem of general relativity

Conformal techniques are reviewed with respect to applications to the initial-value problem of general relativity. Invariant transverse traceless decompositions of tensors, one of its main tools, are related to representations of the group of “conformeomorphisms” acting on the space of all Riemannian metrics onM. Conformal vector fields, a kernel in the decomposition, are analyzed on compact manifolds with constant scalar curvature. The realization of arbitrary functions as scalar curvature of conformally equivalent metrics, a generalization of Yamabe's conjecture, is applied to the Hamiltonian constraint and to the issue of positive energy of gravitational fields. Various approaches to the solution of the initial-value equations produced by altering the scaling behavior of the second fundamental form are compared.

The possibility of negative gravitational energy

The status and physical importance of the question “Can the energy of gravitational fields be negative?” is discussed. To study this question further a particular model of a gravitational shock wave has been developed. The energy corresponding to this model is a scalar functional of the two-geometry of the shock front. Values of the energy for special choices of the shock front have been calculated. These cases all give rise to positive energy, the energy becoming more positive as the shock front becomes more curved. However, no general proof is known to show that the energy is positive for all choices of two-geometries.

Gravitational Radiation Damping of Slowly Moving Systems Calculated Using Matched Asymptotic Expansions

This paper treats the slow-motion approximation for radiating systems as a problem in singular perturbations. By using the method of matched asymptotic expansions, we can construct approximations valid both in the near zone and the wave zone. The outgoing-wave boundary condition applied to the wave-zone expansion leads, by matching, to a unique and easily calculable radiation resistance in the near zone. The method is developed and illustrated with model problems from mechanics and electromagnetism; these should form a useful and accessible introduction to the method of matched asymptotic expansions. The method is then applied to the general relativistic problem of gravitational radiation from gravitationally bound systems, where a significant part of the radiation can be attributed to nonlinear terms in the expansion of the metric. This analysis shows that the formulas derived from the standard linear approximation remain valid for gravitationally bound systems. In particular, it shows that, according to general relativity, bodies in free-fall motion do indeed radiate. These results do not depend upon any definition of gravitational field energy.

Can the Energy of a Weak Gravitational Field Become Negative?

The energy-momentum linkages for asymptotically flat solutions of Einstein's equations are considered as functionals of the metric field variables. When the metric components are varied, it is found that the extrema of the rest mass occur only when its value is zero. By considering the weak-field limit, flat space-time is shown to be a local minimum. The implications of this result for the sign of the weak-field energy are discussed, and the effects of nongravitational sources are investigated.

Positive Definiteness of Gravitational Field Energy

The total gravitational field energy functional is shown to have only one extremum under variation of the metric field variables. At the extremum the energy vanishes and space is flat; second variation shows that the vacuum state is also a local minimum.

On the energy of a static gravitational field

On the energy of a static gravitational field

New Formulation of the General Theory of Relativity

The principle of equivalence is partly abandoned as a basis for general relativity, and cosmic time is introduced as a new field variable. Field equations are obtained which take account of the self-energy of the gravitational field. The central symmetrical solution of the new field equations shows a significant deviation from the well-known Schwarzschild solution. It is free from singularities and gives a slightly smaller value for the perihelion motion of planetary orbits. Other consequences of the new formalism are: (a) A rigorous definition can be given to the concept of ether.(b) The energy-stress tensor of gravitational fields can be defined in a satisfactory manner.(c) The gravitational field energy of a particle is distributed continuously over the space and its integral is equal to the gravitational mass of the particle.(d) There are proper gravitational waves, generated by oscillating matter and propagating with the velocity of light.(e) There is a noticable ether drift which tends to increase the gravitational mass of a body of given intertial mass.(f) The ratio of gravitational and inertial mass of radiating energy is twice the corresponding ratio for neutral static matter.(g) Hubble's recession constant is equal to the reciprocal of the age of the universe.An outstanding problem is to determine the coupling constant between the gravitational field and the cosmic time field. The value $\ensuremath{\beta}=1$ is strongly suggested by cosmological considerations. An experimental determination is possible if the rate of advance of the perihelion of the Mercury orbit is known more accurately.