相关论文: Curvature invariants in algebraically special spac…

The class of Petrov type I curvature tensors is further divided into those for which the span of the set of distinct principal null directions has dimension four (maximally spanning type I) or dimension three (nonmaximally spanning type I).…

We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on…

One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to…

We study the existence of a non-spacelike isometry, \zeta, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of…

We obtain new solutions of topologically massive gravity. We find the general Kundt solutions, which in three dimensions are spacetimes admitting an expansion-free null geodesic congruence. The solutions are generically of algebraic type…

For many purposes, a three-dimensional foliation of spacetime is more advantageous to understanding its light cone structure. We derive the equations describing such foliations for the Kerr geometry with non-zero cosmological constant, and…

Let T be the standard torus of revolution in R^3 with radii b and 1, 0<b<1. Let \alpha be a (p,q) torus curve on T. We show that there are points of zero curvature on \alpha for only one value of the variable radius of T, b=p^2/(p^2+q^2).…

We consider extension of some established techniques of study of tensor fields on Lorentzian manifolds of arbitrary dimension to non-Abelian gauge covariant fields. These are then applied to study of gauge fields with vanishing scalar…

A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum spacetimes are zero.…

We find the most general algebraic type N solution with non-vanishing scalar curvature, which comprises all type N solutions of new massive gravity in three dimensions. We also give the special forms of this solution, which correspond to…

In this paper we show that a particular extrinsic pointwise hypersurface invariant is always non-positive on minimal hypersurfaces of constant curvature spaces and vanishes identically if and only if the hypersurface is rotational. We show…

We study the curvature-dimension inequality in regular graphs. We develop techniques for calculating the curvature of such graphs, and we give characterizations of classes of graphs with positive, zero, and negative curvature. Our main…

We consider vacuum spacetimes with a crushing singularity. Under some scale-invariant curvature bounds, we relate the existence of Kasner-like regions to the asymptotics of spatial volume densities.

All non-twisting Petrov-type N solutions of vacuum Einstein field equations with cosmological constant Lambda are summarized. They are shown to belong either to the non-expanding Kundt class or to the expanding Robinson-Trautman class.…

The gravitational collapse in fourth order theories of gravity defined by an arbitrary action of the scalar curvature shows significant deviations with General Relativity. The presence of a new scalar mode produces a higher initial…

We classify all finite order invariants of immersions of a closed orientable surface into R^3, with values in any Abelian group. We show that they are all functions of order one invariants.

We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…

We present a cyclic symmetric space-time, admitting closed time-like curves (CTCs) which appear after a certain instant of time, i. e., a time-machine space-time. These closed time-like curves evolve from an initial spacelike hypersurface…

We determine the class of $p$-forms $F$ which possess vanishing scalar invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we prove that $F$ is VSI if and only if it is of type N, its multiple null direction $l$ is…

Using the momentum constraint, the standard evolution system is written in a fully first order form. The class of first order invariant algebraic slicing conditions is considered. The full set of characteristic fields is explicitly given.…