相关论文: An invariant measure of deviation from Petrov type…

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set…

A geometrical invariant for regular asymptotically Euclidean data for the vacuum Einstein field equations is constructed. This invariant vanishes if and only if the data correspond to a slice of the Kerr black hole spacetime --thus, it…

We describe the construction of a geometric invariant characterising initial data for the Kerr-Newman spacetime. This geometric invariant vanishes if and only if the initial data set corresponds to exact Kerr-Newman initial data, and so…

A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to…

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are {\em Kerr initial} data. Our scalar quantity only depends on the quantities…

For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for…

In this paper the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. This is not done in a coordinate sense, but through quantification of the deviation from a specific symmetry.…

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…

For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data giving rise to an initial data set for the Friedrich vacuum conformal equations. When…

We provide a characterisation of the Kerr spacetime close to future null infinity using the asymptotic characteristic initial value problem in a conformally compactified spacetime. Stewart's gauge is used to set up the past-oriented…

In this paper we develop a new framework for non-linear perturbations of the Kerr spacetime. This is based on a characterization of the Kerr spacetime in terms of a Killing spinor. On the perturbed spacetime, one can construct an…

In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at…

We employ an isometry group invariants approach to study Killing tensors of valence three defined in the Euclidean plane. The corresponding invariants are found to be homogeneous polynomials of the parameters of the vector space of the…

We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and…

In this article we construct a geometric invariant for initial data sets for the vacuum Einstein field equations $(\mathcal{S},h_{ab},K_{ab})$, such that $\mathcal{S}$ is a 3-dimensional manifold with an asymptotically Euclidean end and an…

We show that a spacetime satisfying the linearized vacuum Einstein equations around a type D background is generically of type I, and that the splittings of the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the Weyl…

We present a new approach to the intrinsic properties of the type D vacuum solutions based on the invariant symmetries that these spacetimes admit. By using tensorial formalism and without explicitly integrating the field equations, we…

We formulate conditions on the geometry of a non-expanding horizon $\Delta$ which are sufficient for the space-time metric to coincide on $\Delta$ with the Kerr metric. We introduce an invariant which can be used as a measure of how…

The general line element corresponding to the family of algebraically general, gravito-electric, expanding, rotating dust models with one functionally independent zero-order Riemann invariant is constructed. The isometry group is at most…

Exploiting a 3+1 analysis of the Mars-Simon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of…