8 papers
Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates
B. G. Konopelchenko, W. K. Schief, A. Szereszewski
Eigenfunctions are shown to constitute privileged coordinates of self-dual Einstein spaces with the underlying governing equation being revealed as the general heavenly equation. T…
Lie point symmetries of near-horizon geometry equation
Eryk Buk, Jerzy Lewandowski, Adam Szereszewski
All the Lie point symmetries of the near extremal horizon geometry equation, in the case of 4-dimensional Einstein vacuum spacetime with cosmological constant, are the diffeomorphi…
Spacetimes foliated by non-expanding null surfaces in the presence of a cosmological constant
Jerzy Lewandowski, Adam Szereszewski
We prove that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single non-expand…
The Near Horizon Geometry Equation on Compact 2-Manifolds Including the General Solution for g > 0
Denis Dobkowski-Ryłko, Wojciech Kamiński, Jerzy Lewandowski +1
The Near Horizon Geometry (NHG) equation with a cosmological constant Λ is considered on compact 2-dimensional manifolds. It is shown that every solution satisfies the Type D equat…
The Petrov type D equation on genus sections of isolated horizons
Denis Dobkowski-Ryłko, Wojciech Kamiński, Jerzy Lewandowski +1
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…
The axial symmetry of Kerr without the rigidity theorem
Jerzy Lewandowski, Adam Szereszewski
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…