Related papers: Vacuum initial data on $\mathbb{S}^3$ from Killing…

We revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which…

This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein's equations…

We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…

Very recently Harada proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is…

This work follows earlier investigations in which the existence of canonical Killing tensor forms and the application of general null tetrad transformations led to a variety of solutions, Petrov types D, III, N, in vacuum with a…

We consider four-dimensional, Riemannian, Ricci-flat metrics for which one or other of the self-dual or anti-self-dual Weyl tensors is type-D. Such metrics always have a valence-2 Killing spinor, and therefore a Hermitian structure and at…

Given an initial-boundary value problem for an anti-de Sitter-like spacetime, we analyse conditions on the conformal boundary ensuring the existence of Killing vectors in the spacetime arising from this problem. This analysis makes use of a…

In this paper we present a collection of general identities relating the deformation tensor $\mathcal{K}=\mathcal{L}_{\eta}g$ of an arbitrary vector field $\eta$ with the tensor $\Sigma=\mathcal{L}_{\eta}\nabla$ on an abstract hypersurface…

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at…

We consider the possibility of the scenario in which the $P$, $T$ and Lorentz symmetry of the relativistic quantum vacuum are all the combined symmetries. These symmetries emerge as a result of the symmetry breaking of the more fundamental…

A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of…

The existence of the initial value constraints means that specifying initial data for the Einstein equations is non-trivial. The standard method of constructing initial data in the asymptotically flat case is to choose an asymptotically…

This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…

We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…

We construct exact, regular and topologically non-trivial\ configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and circumvents Derrick's theorem…

In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…

There are described hierarchies of equations coupling a metric with a trace-free tensor having prescribed symmetries and in the kernel of certain generalized gradients. These specialize, when the tensor vanishes identically, to the usual…

We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after…

A rank $m$ symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the first integral of the geodesic flow which is a degree $m$…

Axially symmetric spacetimes are the only models for isolated systems with continuous symmetries that also include dynamics. For such systems, we review the reduction of the vacuum Einstein field equations to their most concise form by…