On Gravitational Energy in Newtonian Theories

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton–Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.     

Weyl-Dirac geometry and dark matter

Weyl proposed a geometry that differed from Riemannian geometry, which underlies general relativity, in that it contained a vector that could be interpreted as describing the electromagnetic field. Dirac modified this geometry to remove certain difficulties and based it on a variational principle which gave satisfactory field equations for gravitation and electromagnetism. However, by changing the value of a parameter appearing in his variational principle one gets, instead of electromagnetism, a field of massive particles of spin 1, which can be assumed to interact with ordinary matter only through gravitation. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe.     

Energy in the Schwarzschild-de Sitter Spacetime

The energy (due to matter and fields including gravitation) of the Schwarzschild-de Sitter spacetime is investigated by using the Møller energy-momentum definition in both general relativity and teleparallel gravity. We found the same energy distribution for a given metric in both of these different gravitation theories. It is also independent of the teleparallel dimensionless coupling constant, which means that it is valid in any teleparallel model. Our results sustain that (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerfifi concept of energy and momentum.     

Electrodynamical origins of Einstein's theory of general relativity

The failure of the Newtonian theory of gravitation to satisfactorily account for the motion of Mercury's perihelion cannot be held to have justified the development of general relativity. This paper shows how the origins of general relativity were firmly embedded in contemporary attempts to introduce the new mechanics of special relativity into gravitational theory. These new theories of gravitation took as their basis the electrodynamical equations as formulated by Minkowski and attempted to represent the gravitational potential first by a vector and then by a scalar (in the four-dimensional sense). That Einstein chose the symmetric fundamental tensorg _ij as his gravitational potential is seen to have been both a natural and necessary development. With this viewpoint the full theory of general relativity can be seen to be remarkably similar to those theories of gravitation that preceded it. The paper also contains a previously unpublished letter written by Einstein to H. A. Lorentz.     

Competition between neutrino and gravitational radiation

This essay discusses the competition between neutrino radiation and gravitational radiation for the dominant method by which forming neutron stars radiate away their gravitational collapse energy. It is shown that neutrinos may, in fact, be the dominant mode; thus a failure to detect gravitation radiation from a supernova does not imply an error in general relativity but rather the existence of a more efficient radiation mechanism.This essay was awarded the third prize for 1976 by the Gravity Research Foundation.     

“Almost” general relativity

We exhibit theories of gravitation leading to the same set of solutions with algebraically special Ricci tensor as Einstein's equations. Their sets of solutions with algebraically general Ricci tensor differ from general relativity. It will be difficult to empirically distinguish these theories from general relativity.     

On Treder-Type Tetrad Theories of Gravitation I. Equivalence Principle and Invariance Properties

The Principle of relativity and the equivalence principle are the most important foundation of any theory of gravitation. We can formulate these principles by the help of the LORENTZ and the EINSTEIN groups. If we start with an action functional, the demand of invariance of this action with respect to these groups makes possible to get detailed conclusions about the general structure of theories of gravitation. EINSTEIN'S idea, to interpret gravitation as deformation of the local inertial systems of the special theory of relativity, leads to bi-tetrad theories, which we call TREDER-type tetrad theories. In this theories a sufficient number of gauge parameters is introduced in order to ensure the invariance of the action functional without limitations for the field variables.     

The Momentum Four-Vector in Brans–Dicke Wormholes

In this work, in order to compute energy and momentum distributions (due to matter plus fields including gravitation) associated with the Brans–Dicke wormhole solutions we consider Møller’s energy-momentum complexes both in general relativity and the teleparallel gravity, and the Einstein energy-momentum formulation in general relativity. We find exactly the same energy and momentum in three of the formulations. The results obtained in teleparallel gravity is also independent of the teleparallel dimensionless coupling parameter, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model. Furthermore, our results also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime and (b) the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept of energy and momentum. (c) The results calculated supports the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of matter and all non-gravitational fields.     

Energy in a highly ordered universe

A new theory of particles proposed in an earlier paper is now applied to explain energy. Having earlier derived the Rydberg formula for atomic spectra without using the Pauli principle, the authors now derive the photoelectric effect, deflection of light by gravitation, and Planck's law for blackbody radiation without using Planck's assumption on energy quanta or Einstein's theory of general relativity.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

Theories of Gravitation

This paper presents a systematic study of the theories of gravitation that have been proposed. We restrict ourselves to an investigation of the linear approximation since new connections with experiment can be expected in this order in χ only. It turns out that all theories that differ from general relativity contain a scalar field and describe gravitation by a mixture of scalar and tensor interactions. The scalar has negative energy in theories with light deflection larger than the Einstein value. As a consequence instabilities of cosmic systems and continuous creation result in this case. Furthermore, the emission of gravitational radiation with negative energy could be the energy source of the quasars. The question of the mass renormalization of the scalar is investigated. No unique answer is possible at present. Finally a new class of gravitational theories is given.     

The Mathematical Basis for Physical Laws

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory.     

On Mø11er's tetrad theory of gravitation cosmology

We use a particular tetrad field to describe homogeneous isotropic cosmologies in the background of Møller's theory of gravitation. We prove that the universe can be closed or open for any possible value of the density of energy. The relation between the apparent magnitudem and the number of galaxies with a magnitude greater thanm is proved to be different from that of general relativity.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

On the most general linear theory of gravitation

The most general field theory of gravitation is analyzed both group theoretically as well as physically. The field equations are solved by means of an algebraic method and it is found that any field theory of gravitation contains only one essential parameter which is correlated to the spin 0 content of the field. Further it turns out that any theory of gravitation must contain a nonvanishing spin 0 part, but general relativity is distinguished by the fact that its spin 0 component cannot be radiated.