相关论文: On the naturalness of Einstein's equation

The present paper continues the work of the authors [arXiv:1306.6887 [gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity presented more concretely, setting that their Lagrangians are \emph{manifestly} generally…

Determinants of the second-rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function $f(D)$ of…

We clarify the relation among canonical, metric and Belinfante's energy-momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field $\til {\bm T}$, in terms of which the Belinfante tensor is…

Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…

The covariant phase space formalism in general relativity is a covariant method for constructing the symplectic two-form, Hamiltonian and other conserved charges on the phase space of solutions to the Einstein equation with classical…

Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no…

We show that the structure of the Lorentz group in four dimensions is such that unimodular (trace-free) gravity can be consistently represented as an algebraic condition on the symmetric product space of 2-forms. This condition states that…

We extend 2n-dim biconformal gauge theory by including Lorentz-scalar matter fields of arbitrary conformal weight. For a massless scalar field of conformal weight zero in a torsion-free biconformal geometry, the solution is determined by…

This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial quantity. The…

The search for the gravitational energy-momentum tensor is often qualified as an attempt of looking for ``the right answer to the wrong question''. This position does not seem convincing to us. We think that we have found the right answer…

In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…

I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…

A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting…

We treat the semiclassical Einstein equation as a quantum-classical hybrid and demonstrate the formal equivalence of its two derivation methods. This approach identifies the left-hand side of the equation as the expectation value of the…

Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications,…

We solve (2+1) noncommutative gravity coupled to point-like sources. We find continuity with Einstein gravity since we recover the classical gravitational field in the $\theta \to 0$ limit or at large distance from the source. It appears a…

In the literature one often finds the claim that there is no such thing as an energy-momentum tensor for the gravitational field, and consequently, that the total energy-momentum conservation can only be defined in terms of a gravitational…

Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy the conditions of being symmetric and divergence-free. Apart…

A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…