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Silent universes are studied using a ``3+1'' decomposition of the field equations in order to make progress in proving a recent conjecture that the only silent universes of Petrov type I are spatially homogeneous Bianchi I models. The…
We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and…
A classical theorem of Riemannian geometry, due in its original form to Cartan, states that the Taylor expansion of the metric in geodesic normal coordinates is a universal formal power series involving only the symmetrizations of the…
We present exact solutions describing rotating, inhomogeneous dust with generic initial data in 2+1 dimensional AdS spacetime and show how they are smoothly matched to the Banados-Teitelboim-Zanelli (BTZ) solution in the exterior. The…
A group theoretical description of basic discrete symmetries (space inversion P, time reversal T and charge conjugation C) is given. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex…
Using the Geroch transformation we obtain the first example of an exact stiff fluid spike solution to the Einstein field equations in a closed form exhibiting a spacelike $G_1$ group of symmetries (i.e., with a single isometry). This new…
We give the definition of a kind of building I for a symmetrizable Kac-Moody group over a field K endowed with a dicrete valuation and with a residue field containing C. Due to some bad properties, we call this I a hovel. Nevertheless I has…
We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…
We construct exact, regular and topologically non-trivial\ configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and circumvents Derrick's theorem…
Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…
Raynaud and Gruson showed that there is a reasonable algebro-geometric notion of family of discrete (infinite-dimensional) vector spaces. The author introduces a notion of family of Tate spaces ("Tate" means "locally linearly compact") and…
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star.…
Let $V$ be a finite-dimensional positively-graded vector space. Let $b \in V \otimes V$ be a homogeneous element whose rank is $\text{dim}(V)$. Let $A=TV/(b)$, the quotient of the tensor algebra $TV$ modulo the 2-sided ideal generated by…
In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those…
Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…
For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy…
This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmueller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of…