arXiv research

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally…

Classifies a specific type of Lie groups related to Einstein geometry.

New conformally Einstein metrics on Heisenberg group found.

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.

Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.

Paper generalizes results from nilpotent Lie algebras to broader types.

Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.

3D Lorentzian manifolds can't be closed Einstein with positive constant.

We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with $Λ>0$ and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.

In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie gr…

Study of Riemann solitons and $η$-hyperbolic Ricci solitons on Bochner-flat Lorentzian Kähler spacetime manifolds.

We find all three-dimensional Einstein--Weyl spaces with the vanishing scalar curvature

This survey introduces synthetic timelike Ricci curvature bounds in Lorentzian spaces.

The invariant metric affine connections on Berger spheres which are Einstein with skew torsion are determined in both Riemannian and Lorentzian signature. Expressions of such connections are explicitly given. In particular, every Berger sphere with Lorentzian signature admits invariant metric affine connections Einstei…

We introduce the notion of $\varepsilonη\,$-Einstein $\varepsilon\,$-contact metric three-manifold, which includes as particular cases $η\,$-Einstein Riemannian and Lorentzian (para) contact metric three-manifolds, but which in addition allows for the Reeb vector field to be null. We prove that the product of an $\vare…

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected holonomy groups is obtained. As the applications, the Einstein equation, Lorentzian man…

Einstein-Kropina metrics extend Einstein condition to all signatures and classify Finsler gravity solutions.

New decomposable solutions found in 11D supergravity.

We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.

In this note, we construct new examples of Lorentzian Sasaki-Einstein (LSE) metrics on Smale manifolds $M.$ It has already been established in \cite{Gmz2} that such metrics exist on the so-called torsion free Smale manifolds, i.e. the $k$-fold connected sum of $S^{2}\times S^{3}.$ Now, we show that LSE metrics exist on…

Study on Einstein metrics on SU(3) Lie group, including new Lorentzian example.

The study examines curvature tensors and solitons in Lorentzian trans-Sasakian space forms.

We characterize Lorentzian three-dimensional hyper-CR Einstein-Weyl structures in terms of invariants of the associated third order ordinary differential equations.

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.

This paper explores Lorentzian manifolds with specific connections and their symmetries.

Geometric derivation of Einstein equations from causal fermion systems.

The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.

Stability of timelike Ricci bounds in low-regularity spacetimes.

We call a metric $m$-quasi-Einstein if $Ric_X^m$, which replaces a gradient of a smooth function $f$ by a vector field $X$ in $m$-Bakry-Emery Ricci tensor, is a constant multiple of the metric tensor. It is a generalization of Einstein metrics which contains Ricci solitons. In this paper, we focus on left-invariant met…

An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. For indefinite metrics this is no longer true, not even for simple Lie groups. We study the question of whether a semi-Riemannian bi-invariant metric is conformal to an Einstein metric. We obtain results for all three c…

Study generalised Einstein metrics on Lie groups, classifying various types.

The study explores Lorentzian manifolds with specific null vector fields and their geometric properties.

We investigate the local structure of four-dimensional Lorentzian quasi-Einstein manifolds under conditions on the Weyl tensor. We show that if the Weyl tensor is harmonic and the potential function preserves this harmonicity then, in the isotropic case, the manifold is necessarily a $pp$-wave. Using the quasi-Einstein…

We show that conformally compact, globally hyperbolic, Lorentzian Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a holomorphic-disk analog of Hitchin's mini-twistor correspondence.

The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector fields of the obtained metrics are found.

The holonomy algebras of Einstein not Ricci-flat pseudo-Riemannian manifolds of arbitrary signature are classified. As illustrating examples, the cases of Lorentzian manifolds, pseudo-Riemannian manifolds of signature $(2,n)$ and the para-quaternionic-Kählerian manifolds with non-zero scalar curvature are considered. E…

New metrics constructed dual to specific wave-like geometries.

We investigate geometric properties of indecomposable but non-irreducible Lorentzian manifolds, which are total spaces of circle bundles. We investigate under which conditions these manifolds are complete and give examples which fulfill the obtained conditions. In particular we investigate the Einstein equation for the…

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature $(2,n-2)$. Derived geometries include Brinkmann spaces, Lorentzian Einstein-Sasaki spaces and cer…

We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use techniques developed for the classification of supersymmetric solutions to superg…

The study finds Ricci solitons on a specific type of 3D Lorentzian Walker manifold.

The paper investigates $(m,ρ)$-quasi-Einstein structures on almost co-Kähler manifolds.

Researchers classify harmful structures on unimodular Lie groups.

Negative Sasakian manifolds, where the first Chern class of the contact subbundle is a torsion class, can be viewed as Seifert-$S^1$ bundles where the base orbifold has an ample orbifold canonical class. We use this framework to settle completely an open problem formulated by C.Boyer and K.Galicki which asks whether or…

The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is $C^0$-inextendible. For…

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of $η$-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a …

Constructs perturbed Fefferman spaces on almost CR manifolds.