Related papers: The Petrov type D isolated null surfaces
The Petrov type D equation imposed on the 2-metric tensor and the rotation scalar of a cross-section of an isolated horizon can be used to uniquely distinguish the Kerr - (anti) de Sitter spacetime in the case the topology of the…
We consider isolated horizons (Killing horizons up to the second order) whose null flow has the structure of a U(1) principal fiber bundle over a compact Riemann surface. We impose the vacuum Einstein equations (with the cosmological…
We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov…
Non-extremal isolated horizons embeddable in 4-dimensional spacetimes satisfying the vacuum Einstein equations with cosmological constant are studied. The horizons are assumed to be stationary to the second order. The Weyl tensor at the…
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…
Local condition that imply the no-hair property of black holes are completed. The conditions take the form of constraints on the geometry of the 2-dimensional crossover surface of black hole horizon. They imply also the axial symmetry…
In this paper we consider vacuum Kasner spacetimes, focusing on those that can be parametrized as linear perturbations of the special Petrov type D case. For these quasi-D Kasner models we first investigate the modification to the principal…
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)…
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…
We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from…
The vacuum and electrovacuum Einstein equations for spacetimes with two commuting Killing vectors can be solved by indirect methods of integrable systems. But if, in addition, the spacetime admits an irreducible Killing tensor and the…
We discuss Petrov type D Einstein-Maxwell fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and…
We consider a general class of four-dimensional geometries admitting a null vector field that has no twist and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such Robinson-Trautman (and Kundt)…
We extend our previous work in which we derived the most general form of an induced metric describing the geometry of an axially symmetric extremal isolated horizon (EIH) in asymptotically flat spacetime. Here we generalize it to EIHs in…
We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free and vorticity free solution of Einstein's field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where…
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned…
We show that all static spacetimes in higher dimensions are of Weyl types G, I_i, D or O. This applies also to stationary spacetimes if additional conditions are fulfilled, as for most known black hole/ring solutions. (The conclusions…
We classify all pseudo-supersymmetric near horizon geometries of extremal black holes in five dimensional de-Sitter supergravity coupled to vector multiplets. We find that there are three types of solution. The first type corresponds to the…
We provide a classification of near-horizon geometries of supersymmetric, asymptotically anti-de Sitter, black holes of five-dimensional U(1)^3-gauged supergravity which admit two rotational symmetries. We find three possibilities: a…
We systematically investigate axisymmetric extremal isolated horizons (EIHs) defined by vanishing surface gravity, corresponding to zero temperature. In the first part, using the Newman-Penrose and GHP formalism we derive the most general…