相关论文: Global simulations of Minkowski space-time includi…
We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
We investigate a Lie algebra-type $ \kappa$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ \kappa$-Minkowski space. The…
A simple visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean 4-space to yield accurate visualizations as…
This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered…
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…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard…
We analyse various conformal properties of the extremal Reissner-Nordstr\"om spacetime. In particular, we obtain conformal representations of the neighbourhoods of spatial infinity, timelike infinity and the cylindrical end ---the so-called…
Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide…
We prove, for the relativistic Boltzmann equation in the homogeneous case, on the Minkowski space-time, a global in time existence and uniqueness theorem. The method we develop extends to the cases of some curved space-times such as the…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
The asymptotic behaviour of massless spin-0 fields close to spatial and null infinity in Minkowski spacetime is studied by means of Friedrich's cylinder at spatial infinity. The results are applied to a system of equations called the…
We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…
We have investigated some issues relevant for the possibility to construct physical theories on the $\kappa$-Minkowski noncommutative spacetime. The notion of field in $\kappa$-Minkowski has been introduced by generalizing the Weyl…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
A de-Sitter gauge theory of the gravitational field is developed using a spherical symmetric Minkowski space-time as base manifold. The gravitational field is described by gauge potentials and the mathematical structure of the underlying…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…