相关论文: The Einstein equation should be divided by two

The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified…

On an oriented 4-manifold, we study pairs of Riemannian metrics $(g, h)$ for which the curvature tensor of $g$ preserves the Hodge splitting determined by $h$. This extends the Einstein condition in dimension four, which is recovered when…

We classify weakly Einstein algebraic curvature tensors in an oriented Euclidean 4-space, defined by requiring that the three-index contraction of the curvature tensor against itself be a multiple of the inner product. This algebraic…

Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…

On a given closed connected manifold of dimension two, or greater, we consider the squared $L^2$-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant…

We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…

Einstein's theory of general relativity describes gravity as the interaction of particles with space-time geometry, as opposed to interacting with a physical fluid, as in the old gravitational aether theories. Moreover, any theoretical…

We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…

In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…

Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…

The double tetrahedron is the triangulation of the three-sphere gotten by gluing together two congruent tetrahedra along their boundaries. As a piecewise flat manifold, its geometry is determined by its six edge lengths, giving a notion of…

We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3+1 decomposition with arbitrary lapse and…

The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…

It is shown that the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein-Hilbert action to be a total divergence, if the general covariance is to be preserved, that is, a…

In previous works, we suggested considering a (3+1)D quantum gravitational field as an evolution of a (2+1)D renormalized quantum gravitational field along the direction of the gravitational force. The starting point of the suggestion is a…

A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…

Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast to the…

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 reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in…

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…