Related papers: Kerr metric from two commuting complex structures
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit…
We analyze a 1-parameter family of heart shape and a 3-parameter family obtained by gluing three footballs, both of which are examples of reducible spherical conical metrics. For these examples we verify the structure theorem given in [15]…
The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…
Plebanski's second heavenly equation reduces the problem of finding a self-dual Einstein metric to solving a non-linear second-order PDE for a single function. Plebanski's original equation is for self-dual metrics obtained as perturbations…
The gravitational field exterior respectively interior to an axially symmetric, metrically stationary, isolated spinning source made of perfect fluid is examined within the quasi-metric framework. (A metrically stationary system is defined…
In this paper, we study double structures supported on rational normal curves. After recalling the general construction of double structures supported on a smooth curve described in \cite{fer}, we specialize it to double structures on…
In this paper, we study the K\"ahlerian nature of Taub-NUT and Kerr spaces which are gravitational instanton and black hole solutions in general relativity. We show that Euclidean Taub-NUT metric is hyper-K\"ahler with respect to the usual…
We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The n-th subgraph of this family is generated by all knots whose fundamental groups surject to a symmetric group with parameter at least n, where…
In this letter, a two-dimensional (2D) gravity-scalar model is studied. This model supports interesting double-kink solutions, and the corresponding metric solutions can be derived analytically. Depending on a tunable parameter $c$, the…
A concise form of the Kinnersley-Chitre five-parameter metric for a spinning mass is obtained by exploiting a remarkable similarity between the metric's factor structure and the analogous structure of the Tomimatsu-Sato solutions with even…
We show that the Killing tensor of the Kerr spacetime has an analogue in the $\sqrt{\rm Kerr}$ gauge theory solution related to it by the classical double copy. This hidden symmetry of $\sqrt{\rm Kerr}$ leads to an additional constant of…
Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which…
We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a…
The Cartan's equations definig simple spinors (renamed pure by C. Chevalley) are interpreted as equations of motion in momentum spaces, in a constructive approach in which at each step the dimesions of spinor space are doubled while those…
We explore various aspects of the self-dual Pleba\'nski-Demia\'nski family in the Euclidean Einstein-Maxwell-$\Lambda$ system. The Killing-Yano tensor which was recently found by Yasui and one of the present authors allows us to prove that…
We present a simple novel derivation, ab initio, of the equations appropriate for stationary axisymmetric spacetimes using the Papapetrou form of the metric (Papapetrou gauge). It is shown that using coordinates which preserve the…