相关论文: On the naturalness of Einstein's equation
Motivated by the apparent dependence of string $\sigma$--models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show that all such "geometrical"…
The solution to the linearized Einstein equation in de Sitter (dS) spacetime and the corresponding two-point function are explicitly written down in a gauge with two parameters `$a$' and `$b$'. The quantization procedure, independent of the…
On a smooth metric measure spacetime $(M,g,e^{-f} dvol_g)$, we define a weighted Einstein tensor. It is given in terms of the Bakry-\'Emery Ricci tensor as a tensor which is symmetric, divergence-free, concomitant of the metric and the…
By embedding Einstein's original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor $T^G$ is constructed from a…
It is proven that the usual quadratic general-covariant Lagrangian for the Dirac field leads to a symmetric, divergence-free energy-momentum tensor in the standard Riemannian framework of space-time without torsion, provided the tetrad…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
We give a complete proof of the result stated in an earlier article, that the general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and nonzero scalar curvature is determined by a solution of the $SU(\infty)$-Toda field…
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein- Langevin…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization…
The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the…
Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
The two-jet of the curvature tensor at some point of a pseudo-Riemannian manifold is called Einstein if the Ricci tensor is a multiple of the metric tensor at the given point and additionally its first two covariant derivatives vanish…
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including…
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin…
The generalized noncommutative Heisenberg algebra, which is based on the generalized uncertainty principle, imposes a minimal length uncertainty on quantum mechanics (QM), on one hand. On the other hand, the quantum-induced spacetime which…
In the context of the teleparallel equivalent of general relativity, we show that the energy-momentum density for the gravitational field can be described by a true spacetime tensor. It is also invariant under local (gauge) translations of…
Based on the gauge invariant variables proposed in [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], general framework of the second order gauge invariant perturbation theory on arbitrary background spacetime is considered. We derived…