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In the time-reversal-breaking centrosymmetric systems, the appearance of Weyl points can be guaranteed by an odd number of all the even/odd parity occupied bands at eight inversion-symmetry-invariant momenta. Here, based on symmetry…
First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian…
It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a congruence of freely falling observers.
In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for…
We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions.…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…
A metric space $\mathrm{M}=(M;\de)$ is {\em homogeneous} if for every isometry $\alpha$ of a finite subspace of $\mathrm{M}$ to a subspace of $\mathrm{M}$ there exists an isometry of $\mathrm{M}$ onto $\mathrm{M}$ extending $\alpha$. The…
In this short note, we verify explicitly in static coordinates that the non trivial asymptotic Killing vectors at spatial infinity for anti-de Sitter space-times correspond one to one to the conformal Killing vectors of the conformally flat…
The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms…
A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin $s \geq 1/2$ is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral…
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the…
We investigate static, axially symmetric spacetimes without naked singularities that are constructed by patching Weyl class spacetimes with the flat spacetimes. Once the exterior geometry is specified, the junction conditions determine the…
In this paper, we find all the Conformal Killing Vectors (CKVs) and their Lie Algebra for the recently reported [cqg1] spherically symmetric, shear-free separable metric spacetimes with non-vanishing energy or heat flux. We also solve the…
In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time,, denoted by $L^4_1(f,c)$, having positive relative nullity. First, we give the necessary and sufficient conditions for such space-like and…
We construct a set of conserved charges for asymptotically deSitter spacetimes that correspond to asymptotic conformal isometries. The charges are given by boundary integrals at spatial infinity in the flat cosmological slicing of deSitter.…
In this paper, close surfaces are considered in 3-dimensional harmonic conformally flat space in point of the variation. It is shown that if the conformal vector field be tangent to surface and the sign of the mean curvature does not change…
Killing-Yano one forms (duals of Killing vector fields) of a class of spherically symmetric space-times characterized by four functions are derived in a unified and exhaustive way. For well-known space-times such as those of Minkowski,…
We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid…
We consider the problem of finding all space-time metrics for which all plane-wave Penrose limits are diagonalisable plane waves. This requirement leads to a conformally invariant differential condition on the Weyl spinor which we analyse…
Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of…