Related papers: An example of algebraically general para-K\"ahler …
Spaces equipped with two complementary (distinct) congruences of self-dual null strings and at least one congruence of anti-self-dual null strings are considered. It is shown that if such spaces are Einsteinian then the vacuum Einstein…
Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with…
We describe natural K\"ahler or para-K\"ahler structures of the spaces of geodesics of pseudo-Riemannian space forms and relate the local geometry of hypersurfaces of space forms to that of their normal congruences, or Gauss maps, which are…
Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized K\"ahler geometry. We investigate the reduction from (2,2) to…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein's Field…
A para-K\"ahler manifold can be defined as a pseudo-Riemannian manifold $(M,g)$ with a parallel skew-symmetric para-complex structures $K$, i.e. a parallel field of skew-symmetric endomorphisms with $ K^2 = \mathrm{Id} $ or, equivalently,…
4-dimensional spaces equipped with congruences of null strings are considered. It is assumed that a space admits a congruence of expanding self-dual null strings and its self-dual part of the Weyl tensor is algebraically degenerate.…
We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…
Spaces equipped with congruences of null strings are considered. A special attention is paid to the spaces which belong to the two-sided Walker class and para-K\"ahler class. Properties of an intersection of self-dual and anti-self-dual…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
Five-dimensional relativity as an extension of general relativity has field equations that simplify considerably given the adoption of a new gauge. The result is a scalar field governed by the Klein-Gordon equation, in an empty spacetime…