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Violations of spacetime symmetries have recently been identified as promising signatures for physics underlying the Standard Model. The present talk gives an overview over various topics in this field: The motivations for spacetime-symmetry…
In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$, and through which the existence of spacelike admissible graphic…
This paper claims that local space-time curvature can non-trivially contribute to the properties of orbital angular momentum in quantum mechanics. Of key importance is the demonstration that an extended orbital angular momentum operator due…
The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…
The internal symmetry of composite relativistic systems is discussed. It is demonstrated that Lorentz-Poincar\'e symmetry implies the existence of internal moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL)…
We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…
Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also…
We consider a bounded Lipschitz domain $\Omega\subseteq\mathbb{R}^3$ with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regular curl and divergence, but may be discontinuous across…
We prove a low-regularity version of Hawking's singularity theorem for Lorentzian metrics in $W^{1,p}$ with Riemann curvature in $L^p$, where $p>2n$ and $n$ the dimension of spacetime. This extends previous results beyond the Lipschitz…
It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type $\eta_\mn = {\rm diag} (1,-1,-1,-1)$ this is usually presented as an independent axiom of the theory, which…
We prove a local well-posedness theorem for the (n+1)-dimensional Einstein equations in Lorentzian signature, with initial data $(\tilde g, K)$ whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space, and…
Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…
We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature symmetry…
We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the…
Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface.…
In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development…
A curved static de Sitter-like metric is analyzed. The source of curvature is rooted from a constant stress tensor with positive energy density and negative pressures. All the curvature invariants are constant everywhere and the geometry is…
We derive a generic identity which holds for the metric (i.e. variational) energy-momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under…
We describe in parallel the Lorentzian homogeneous spaces $G=\mathrm{PSL}(2,\mathbb{R})$ and $\mathfrak{g}=\mathfrak{psl}(2,\mathbb{R})$, and review some recent results relating the geometry of their quotients by discrete groups.
Consider a manifold with boundary, and such that the interior is equipped with a pseudo-Riemannian metric. We prove that, under mild asymptotic non-vanishing conditions on the scalar curvature, if the Levi-Civita connection of the interior…