相关论文: Curvature invariants in algebraically special spac…
We have investigated the behavior of three curvature invariants for Schwarzschild, Reissner-Nordstr{\o}m, Kerr, and Kerr-Newman black holes. We have also studied these invariants for a Schwarzschild-de Sitter space-time, the $\gamma$…
We investigate several integer invariants of curves in 3-space. We demonstrate relationships of these invariants to crossing number and to total curvature.
We give a complete description of all order 1 invariants of spherical curves. We also identify the subspaces of all J-invariants and S-invariants, and present two equalities satisfied by any spherical curve.
In the first part of this paper we consider expanding vacuum cosmological spacetimes with a free $T^N$-action. Among them, we give evidence that Gowdy spacetimes have AVTD (asymptotically velocity term dominated) behavior for their initial…
We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background…
We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein's equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some…
We construct an associative differential algebra on a two-parameter quantum plane associated with a nilpotent endomorphism $d$ in the two cases $d^{2}=0$ and $d^3=0$ $(d^2\neq 0).$ The correspondent curvature is derived and the related non…
We give a complete description of all order 1 invariants of planar curves.
We consider static spacetimes whose spatial part admits foliations with the extrinsic curvature tensor K_{ab}=0. There are two complementary cases when the gradient of the lapse function points 1) to the direction of foliation or 2)…
It has recently been suggested that vacuum black holes of General Relativity (GR) can become spontaneously scalarised when appropriate non-minimal couplings to curvature invariants are considered. These models circumvent the standard black…
We consider the integrals of $r$-mean curvatures $S_r$ of a complete hypersurface $M$ in space forms $\mathcal{Q}_c^{n+1}$ which generalize volume $(r=0)$, total mean curvature $(r=1)$, total scalar curvature $(r=2)$ and total curvature…
A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,....…
Curvature collineations of Bianchi type IV space-times are investigated using the rank of the 6X6 Riemann matrix and direct integration technique. From the above study it follows that the Bianchi type IV space-times possesses only one case…
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…
It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string…
We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci…
We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations - the connection operator based `A' quantization and the extrinsic curvature based `K' quantization. We…
We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
Under the quadratic-decay-conditions of the radial curvatures of an end, we shall derive growth estimates of solutions to the eigenvalue equation and show the absence of eigenvalues.