Related papers: From Geometry to Numerics: interdisciplinary aspec…
Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to…
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts of an international community in many variants and with the…
Previously, it was noticed that in some space-times with Killing horizons some curvature components, responsible for tidal forces, small or even zero in the static frame, become enhanced from the viewpoint of a falling observer. This leads…
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses…
This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler…
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case…
Numerical Relativity has been using orbifolds for a long time, although they appear under different names in the literature. We review orbifolds previously used in simulations also discuss some that have not been used yet but are likely to…
We study geometry and topology as complementary and dual aspects of the mathematical space. The same is used to get a better understanding of the Cosmological Constant. Having failed so far to include gravity in a proper unified framework…
I examine the results obtained so far in exploring the recent proposal of theories of the relativistic transformations between inertial observers that involve both an observer-independent velocity scale and an observer-independent…
The paper is based on the recently proposed 4-dimensional optical space theory and draws some of its consequences for gravitation. Starting with the discussion of central movement, the paper proceeds to establish the a metric compatible…
Equilibrium states of black holes can be modelled by isolated horizons. If the intrinsic geometry is spherical, they are called type I while if it is axi-symmetric, they are called type II. The detailed theory of geometry of quantum type I…
The prediction of spacetime singularities, regions of infinite curvature where classical physics breaks down, is one of the most profound challenges in General Relativity (GR). In particular, black hole solutions such as the Schwarzschild…
The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…