Let X be a smooth manifold of dimension 1 + n endowed with a Lorentzian metric g. The energy tensor of a 2-form F is locally defined as Tab := − ( Fa Fbi − 1 4 F Fijgab ) . In this paper we characterize this tensor as the only 2-covariant natural tensor associated to a Lorentzian metric and a 2-form that is independent of the unit of scale and satisfies certain condition on its divergence. This...

Once the action for Einstein’s equations is rewritten as a functional of an SO(3, C) connection and a conformal factor of the metric, it admits a family of “neighbours” having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in ...

We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than −2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the ...

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks...

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energymomentum density should be proportional to the Bel-Robinson tensor Bαβμν . However, we propose a...

A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of auxiliary fields. As a by-product we present a consistent non-linear coupling of a spin-2 tensor to gravitation. It is shown that non-vanishing (Cμναβ) 2 terms...

Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian f (R) where R is the scalar curvature and f is an arbitrary function. It may happen that a singularity in the Einstein frame corresponds to a regular surfac...

The electromagnetic interaction in the Einstein-Infeld-Hoffmann (EIH) equations of motion for charged particles in Einstein’s Unified Field Theory is found to be automatically precluded by the conventional identification of the skew part of the fundamental tensor with the Faraday tensor. It is shown that an alternative identification, suggested by observations of Einstein, Bergmann and Papapetr...

A closed Riemannian manifold (Mn, g) is called Einstein if the Ricci tensor of g is a multiple of itself; that is, ric(g) = λ · g. This equation, called the Einstein equation, is a complicated system of second order partial differential equations, and at the present time no general existence results for Einstein metrics are known. However, there are results for many interesting classes of Einst...

A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential V [φ] is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no essential singularity at the origin of coordinates. The weak energy condition ρφ > 0 fails to be satisfied for r . 1.3rS (where rS is the Schwarzschild radius) but th...