Related papers: (2+1)-Einstein spacetimes of finite type
We study the canonical description of the axisymmetric vacuum in 2+1 dimensional gravity, treating Einstein's gravity as a Chern Simons gauge theory on a manifold with the restriction that the dreibein is invertible. Our treatment is in the…
We discuss a formalism for solving (2+1) AdS gravity on Riemann surfaces. In the torus case the equations of motion are solved by two functions f and g, solutions of two independent O(2,1) sigma models, which are distinct because their…
We prove that a globally hyperbolic smooth spacetime endowed with a $\smash{\mathrm{C}^1}$-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike…
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its…
The Mann-Marolf surface term is a specific candidate for the "reference background term" that is to be subtracted from the Gibbons-Hawking surface term in order make the total gravitational action of asymptotically flat spacetimes finite.…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant…
For all $k\in]0,1[$, we construct a canonical bijection between the space of ramified coverings of the sphere and the space of complete immersed surfaces in $3$-dimensional hyperbolic space of finite area and of constant extrinsic curvature…
We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge…
Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly…
This is a survey of the author's recent work rather than a broad survey of the literature. The survey is concerned with the global in time solutions of the Cauchy problem for matter waves propagating in the curved spacetimes, which can be,…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
We equip the space of Cauchy hypersurfaces in a globally hyperbolic spacetime with a natural Hausdorff-type metric and study its properties, in particular completeness and local compactness, for Lorentzian manifolds and in more general…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which…
Explicit models for the restricted conformal group of the Einstein static universe of dimension greater than two and for its universal covering group are constructed. Based on these models, as an application we determine all oriented and…
We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes $(\mathrm{M},l)$. It is based on ideas of Kunzinger-S\"amann, but does not require Lipschitz continuity of causal curves. We study geodesics on…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…