arXiv research

Classifies Lie algebras and related spacetimes for a specific type of symmetry.

Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdička-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes possess higher rank Stäckel-Killing tensors and that in the case of the pp-wave spacetimes the symmetry group of the Stäckel-Killing ten…

In the framework of Galilei classical mechanics (i.e., general relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplec…

We prove several global existence theorems for spacetimes with toroidal or hyperbolic symmetry with respect to a geometrically defined time. More specifically, we prove that generically, the maximal Cauchy development of $T^2$-symmetric initial data with positive cosmological constant $Λ>0$, in the vacuum or with Vlaso…

It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime is described by the Vlasov equation (collisionless matter) or the wave equation…

Study shows instability of certain MOTSs with continuous symmetry.

Stability of a special spacetime solution is proven under certain symmetries.

Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.

Proves stability of spacetime Penrose inequality for spherical symmetric initial data.

Researchers compute differential invariants for Carrollian spacetimes.

Proves existence of solutions with concentrated energy in 2+1 spacetime.

Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.

Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to expon…

The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.

We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularitie…

Paper constructs non-symmetric collapsing spacetimes without symmetries.

Study shows no hidden symmetries in specific spacetime metrics.

It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered by a foliation of compact constant mean curvature hypersurfaces. Moreover, the …

Higher-dimensional spacetimes have well-behaved boundaries.

Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.

Study of Ricci flow equations in topological quantum gravity.

The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence, namely whether the static black hole uniqueness theorems extend to static spacetim…

Study of spacetimes in cosmology without symmetry assumptions.

The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic…

New exact spherically symmetric vacuum solutions found in Finsler gravity.

The study explores properties of a specific type of spacetime.

We have obtained Finslerian Ressiner-Nordstrom solution where it is asymptotic to a Finsler spacetime with constant flag curvature while $r\rightarrow\infty$. The covariant derivative of modified Einstein tensor in Finslerian gravitational field equation for this solution is conserved. The symmetry of the special Finsl…

Study classifies metrics on anti-de Sitter spacetime with specific symmetries.

The thesis explores kinematical symmetries beyond Lorentzian spacetime.

Warped-product black hole spacetimes are $C^0$-inextendible.

The rigidity statement of the positive mass theorem asserts that an asymptotically flat initial data set for the Einstein equations with zero ADM mass, and satisfying the dominant energy condition, must arise from an embedding into Minkowski space. In this paper we address the question of what happens when the mass is …

We explain the meaning of local symmetries in physics.

Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is assumed that the gauge field inherits the symmetries of the background and is aligned …

The purpose of the present article is to study and characterize sev- eral types of symmetries of generalized Robertson-Walker space-times. Con- formal vector fields, curvature and Ricci collineations are studied. Many im- plications for existence of these symmetries on generalied Robertson-Walker spacetimes are obtaine…

Researchers generalize cosmological models using Finsler geometry.

The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. I…

Proves symmetries of extremal horizons in spacetimes.

In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. hep-th/0501217. Such Einstein-Dirac spacetimes are parametrized by gene…

New mass definition for negative cosmological constant spacetimes.

We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we find several new classes of geometries, some of which exist only for $D=1,2$. Th…

New proof of past stability for Kasner solutions in $(3+1)$-dimensional Einstein vacuum spacetime.

We establish that equally-spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally-symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal struc…

We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the values of differential invariants arising from the compatibility conditions of the…

Study shows nonextendibility of warped spacelike singularities in specific spacetimes.

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate the global causal structure of the constructed spacetimes. Our weak regularity ass…

We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in such quot…

Small deformations of marginally (outer) trapped surfaces are considered by using their stability operator. In the case of spherical symmetry, one can use these deformations on any marginally trapped round sphere to prove several interesting results. The concept of 'core' of a black hole is introduced: it is a minimal …

A common approach to metric-affine, local Poincaré, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to altern…