Related papers: On Asymptotically Locally Hyperbolic Metrics with …
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under…
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of…
Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…
All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is…
We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy…
Motivated by the relative differential geometry, where the Euclidean normal vector of hypersurfaces is generalized by a relative normalization, we introduce anisotropic area measures of convex bodies, constructed with respect to a gauge…
We construct several new families of vacuum solutions that describe black holes in uniformly accelerated motion. They generalize the C-metric to the case where the energy density and tension of the strings that pull (or push) on the black…
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This…
We study the existence of conformal metrics on non-compact Riemannian manifolds with non-compact boundary, which are complete as metric spaces and have negative constant scalar curvature in the interior and negative constant mean curvature…
This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…
We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more…
In this paper we produce families of complete non compact Riemannian metrics with positive constant $\sigma_k$-curvature by performing the connected sum of a finite number of given $n$-dimensional Delaunay type solutions, provided $2 \leq…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in $\mathbb{H}^{3}$ is proved under the assumption that there exists a strictly locally convex…
A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be…
We report that a class of three-dimensional bimetric theories contain asymptotically flat solutions. These spacetimes can be cast in a set of asymptotic conditions at null infinity which are preserved under the infinite dimensional BMS…
We give a family of monotone quantities along smooth solutions to the inverse curvature flows in Euclidean spaces. We also derive a related geometric inequality for closed hypersurfaces with positive k-th mean curvature.
We show that in D=2n+1 dimensions, when mass is negative and all angular momenta are non-vanishing, Kerr and Kerr-AdS metrics describe smooth time machines, with no curvature singularity. Turning off the angular momenta appropriately can…
We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics…