Related papers: (Pseudo-)K\"ahler-Einstein geometries
We construct exact black hole solutions to Einstein gravity with nonlinear electrodynamic field. In these solutions, there are in general four parameters. They are physical mass, electric charge, cosmological constant and the coupling…
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…
Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves of $I$-invariant projective vector fields. The sub-algebra of the $C$-projective vector fields, leaving…
In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even…
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only Riemann tensor rather than its derivative enters the equations of motion. The…
Setting an ansats that the metric is expressible by a power series of the inverse radius and taking a particular gauge choice, we construct a "general solution" of (2+1)-dimensional Einstein's equations with a negative cosmological constant…
We explore how far one can go in constructing $d$-dimensional static black holes coupled to $p$-form and scalar fields before actually specifying the gravity and electrodynamics theory one wants to solve. At the same time, we study to what…
We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…
We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on K\"ahler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to…
New geometric and analytic methods for generating exact and parametric solutions in generalized Einstein-Finsler like gravity theories and nonholonomic Ricci soliton models are reviewed and developed. We show how generalizations of the…
The main purpose of the present paper is to investigate the symmetry properties of a K\"ahler manifold involving the Ricci tensor. In this context, the most symmetric manifolds are K\"ahler-Einstein spaces, and their natural generalizations…
Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
We complete the visible, hidden, sectorial, and discrete symmetries of Ernst-like potential spaces in stationary, axisymmetric Einstein-Maxwell-Scalar Field (EMSF) and Einstein-ModMax-Scalar Field (EMMSF) theories. In the real potential…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We describe a simple gauge-fixing that leads to a construction of a quantum Hilbert space for quantum gravity in an asymptotically Anti de Sitter spacetime, valid to all orders of perturbation theory. The construction is motivated by a…