On Parametrized General Relativity

A physical framework has been proposed which describes manifestly covariant relativistic evolution using a scalar time . Studies in electromagnetism, measurement, and the nature of time have demonstrated that in this framework, electromagnetism must be formulated in terms of -dependent fields. Such an electromagnetic theory has been developed. Gravitation must also use of -dependent fields, but many references do not take the metric's dependence on fully into account. Others differ markedly from general relativity in their formulation. In contrast, this paper outlines steps towards a -dependent classical intrinsic formulation of gravitation, patterned after general relativity, which we call parametrized general relativity (PGR). Given the existence of a preferred foliation, the Hamiltonian constraint is removed. We find that some nonmetricity in the connection is allowed, unlike in general relativity. Conditions on the allowable nonmetricity are found. Consideration of the initial value problem confirms that the metric signature should normally be O(3, 2) rather than O(4, 1). Following the lead of earlier works, we argue that concatenation (integration over ) is unnecessary for relating parametrized physics to experience, and propose an alternative to it. Finally, we compare and contrast PGR with other relevant gravitational theories.     

Thermal Equilibrium of Static and Spherical Structures in General Relativity

The condition of thermal equilibrium of static and spherically symmetric structures on the basis of General Relativity Theory is obtained. Their general behaviour under isentropic and non-isentropic conditions is discussed. It is seen that under thermal equilibrium a perfect gas sphere can not have a terminating solution and the perfect gas equation of state (EOS) is equivalent to the equation, P=KE (where P and E represent pressure and energy-density and K is a constant). The structure with γ-law EOS have a vanishing surface density only when the system is isentropic, and in that case the three adiabatic indices are not equal to each other, and Γ₁ does not represent the ratio of specific heats. Structures with γ-law EOS and non-vanishing surface density can have Γ₁=Γ₂=Γ₃=γ. One such case, corresponding to homogeneous density is discussed and it is seen that for u(≡M/a; mass to size ratio in geometrized units) < (1/3) the homogeneous spheres with constant γ are bound and the speed of sound is less than that of light throughout the structure. There are number of other spherically symmetric and static solutions of Einstein’s field equations available in the literature and a detailed discussion in light of this paper can be given for each of them.     

On quadratic lagrangians in General Relativity

Theories of gravitation similar to General Relativity but with an additionalR ² term in the Lagrangian are explored. The Schwarzschild metric is not the exterior solution that can be continued to the interior of the body to give a positive definite mass distribution. The experimental consequences ofR ² terms are investigated. Furthermore, it is shown that a theory with anR ² term only possesses an interesting singular dependence on the coupling constant.     

On Caustics and Singularities in General Relativity

Comparing gravitational converging effects with self-focussing and lense effects in ordinary optics, we consider some physical properties of caustics in General Relativity. The resulting relations between geometrical and physical features of caustics are used to discuss the power asymptotes of homogeneous cosmological models in more detail.     

On the Geodesic Hypothesis in General Relativity

In this paper, we give a rigorous derivation of Einstein’s geodesic hypothesis in general relativity. We use small material bodies ${\phi^\epsilon}$ governed by the nonlinear Klein–Gordon equations to approximate the test particle. Given a vacuum spacetime ${([0, T]\times\mathbb{R}^3, h)}$ , we consider the initial value problem for the Einstein-scalar field system. For all sufficiently small ε and δ ≤ ε ^q , q > 1, where δ, ε are the amplitude and size of the particle, we show the existence of the solution ${([0, T]\times\mathbb{R}^3, g, \phi^\epsilon)}$ to the Einstein-scalar field system with the property that the energy of the particle ${\phi^\epsilon}$ is concentrated along a timelike geodesic. Moreover, the gravitational field produced by ${\phi^\epsilon}$ is negligibly small in C ¹, that is, the spacetime metric g is C ¹ close to the given vacuum metric h. These results generalize those obtained by Stuart in (Ann Sci École Norm Sup (4) 37(2):312–362, 2004, J Math Pures Appl (9) 83(5):541–587, 2004).     

On the Possibility of Supertasks in General Relativity

Malament-Hogarth spacetimes are the sort of models within general relativity that seem to allow for the possibility of supertasks. There are various ways in which these spacetimes might be considered physically problematic. Here, we examine these criticisms and investigate the prospect of escaping them.     

On the Motion of Shells in General Relativity

We use Lanczos equations to analyze the motionof shells in the gravitational field of a sphericallysymmetric central body. A first integral of Israel'smatching conditions is used to show that the motion of the shell depends on the equation of stateof the shell matter. In particular, the case of abarotropic equation of state is analyzed. The questionof how the type of motion determines the equation of state for the matter of the shell is alsoinvestigated.     

On the Philosophical Foundations of Measurements in General Relativity

In this paper, first, the question of what a measurement is in General Relativity is tackled; then, some foundational problems it involves are analysed. In particular, by recalling what a measurement is in general, we will try to precisely define what it is in General Relativity. Then, we will analyse, by means of a suitable example, some foundational problems it involves. It will be stressed that such foundational problems do not arise owing to the gauge invariance or the correlation among the measuring observers but owing to the principle of equivalence.     

On the Domain of Applicability of General Relativity

We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue that, as it stands, GR is deficient whether it is treated as a microscopic or a macroscopic theory of gravity. We briefly discuss some recent attempts at removing this shortcoming through the construction of a macroscopic theory of gravity. We point out that such macroscopic extensions of GR are likely to be nonunique and involve non-Riemannian geometrical frameworks.     

General Covariance in General Relativity?

The mathematical approach to General Relativity insists that all coordinate systems are equal. However physicists and astrophysicists in fact almost always use preferred coordinate systems not merely to simplify the calculations but also to help define quantities of physical interest. This suggests we should reconsider and perhaps refine the dogma of General Covariance.     

Massive photons in General Relativity

In order to avoid a speed-of-light catastrophe in General Relativity with an electromagnetic source, gauge invariance with respect to the electric charge is broken with the photon acquiring mass. The general equations for the Einstein-Maxwell system are derived for the case with massive photons. Nonminimal couplings which might compete with the small minimal photon mass term are included.     

Curvature Diffusions in General Relativity

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.     

Electrical Conductivity in General Relativity

The general relativistic kinetic theory including the effect of a stationary gravitational field is applied to the electromagnetic transport processes in conductors. Then it is applied to derive the general relativistic Ohm's law where the gravitomagnetic terms are incorporated. The total electric charge quantity and charge distribution inside conductors carrying conduction current in some relativistic cases are considered. The general relativistic Ohm's law is applied to predict new gravitomagnetic and gyroscopic effects which can, in principle, be used to detect the Lense-Thirring and rotational fields.     

Quantum CTC's in General Relativity

We review different spacetimes that contain nonchronal regions separated from the causal regions by chronology horizons and investigate their connection with some important aspects one would expect to be present in a final theory of quantum gravity, including: stability to classical and quantum metric fluctuations, boundary conditions of the universe and gravitational topological defects corresponding to spacetime kinks.     

Fermat's principle in General Relativity

We derive Fermat's principle from the causal structure of spacetime, as well as from an appropriate variational principle. We show that the latter leads to a particular Hamilton-Jacobi formalism.     

Electromagnetic Duality in General Relativity

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to those in electromagnetic theory. It turns out that the duality transformation implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts, giving rise to the same vacuum solutions but with the opposite sign for the gravitational constant. Further, by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spacetimes.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Geometrization of Mass in General Relativity

In this paper we will extend the notion of tangent bundle to a Z ₂ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-Riemannian metrics, Levi-Civita connection, and curvature, on it. In case of space-times manifolds, even part of the tangent bundle is related to space and time structures (gravity) and odd part is related to mass distribution in space-time. In this structure, mass becomes part of the geometry, and Einstein field equation can be reconstructed in a new simpler form. The new field equation is purely geometric.