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We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.
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I exhibit the conflicting roles of Noethers two great theorems in defining conserved quantities, especially Energy in General Relativity and its extensions: It is the breaking of coordinate invariance through boundary conditions that removes the barrier her second theorem otherwise poses to the applicability of her first. There is nothing new here, except the emphasis that General must be broken down to Special Relativity in a special, but physically natural, way in order for the Poincare or other global groups such as (A)dS to re-emerge.
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to study the spacetime manifold in the context of Einsteins theory. In 1961, Tullio Regge published a work on which he uses the old idea of triangulation of surfaces aiming the description of curvature, and, therefore, gravitation, through the use of discrete calculus. In this paper, we approach Regge Calculus pedagogically, as well as the main results towards a discretized version of Einsteins theory of gravitation.
We discuss the evolution of the universe in the context of the second law of thermodynamics from its early stages to the far future. Cosmological observations suggest that most matter and radiation will be absorbed by the cosmological horizon. On the local scale, the matter that is not ejected from our supercluster will collapse to a supermassive black hole and then slowly evaporate. The history of the universe is that of an approach to the equilibrium state of the gravitational field.
C-theory provides a unified framework to study metric, metric-affine and more general theories of gravity. In the vacuum weak-field limit of these theories, the parameterized post-Newtonian (PPN) parameters $beta$ and $gamma$ can differ from their general relativistic values. However, there are several classes of models featuring long-distance modifications of gravity but nevertheless passing the Solar system tests. Here it is shown how to compute the PPN parameters in C-theories and also in nonminimally coupled curvature theories, correcting previous results in the literature for the latter.
We address the gravitation and inertia in the framework of general gauge principle, which accounts for gravitation gauge group generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear realization of the Lie group of distortion of local internal properties of six-dimensional flat space, which is assumed as a toy model underlying four-dimensional Minkowski space. The agreement between proposed gravitational theory and available observational verifications is satisfactory. We construct relativistic field theory of inertia and derive the relativistic law of inertia. This theory furnishes justification for introduction of the Principle of Equivalence. We address the rearrangement of vacuum state in gravity resulting from these ideas.
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