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Spherically symmetric solutions of theories of gravity built one fundamental class of solutions to describe compact objects like black holes and stars. Moreover, they serve as starting point for the search of more realistic axially…
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide class of 3D…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
Gravitational waves from merging compact objects provides the opportunity to explore the properties of black holes and neutron stars in the strong regime of gravity. It is therefore of interest to explore the theoretical model that…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
In this article we consider the problem to what extent the motion of gauge-charged matter that generates the gravitational field can be arbitrary, as well as what equations are superimposed on the gauge field due to conditions of…
Within the framework of algebraic quantum field theory, we propose a new method of constructing local generators of (global) gauge symmetries in field theoretic models, starting from the existence of unitary operators implementing locally…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
Hidden symmetries provide a powerful tool for finding exact solutions in multifield cosmological models. We review how, using such symmetries, one can find inflationary solutions in two-field models, which lead to the generation of…
Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black…
The paper deals with phantom scalar field cosmology in Einstein gravity. At first using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter…
In the context of $f(R)$ gravity theories, the issue of finding static and spherically symmetric black hole solutions is addressed. Two approaches to study the existence of such solutions are considered: first, constant curvature solutions,…
A spherically symmetric space-time solution for a diffusive two measures theory is studied. An asymmetric wormhole geometry is obtained where the metric coefficients have a linear term for galactic distances and the analysis of Mannheim and…
In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we…
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The…
In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the…
Apart from a few remarks on lattice systems with global or gauge symmetries, most of this talk is devoted to some interesting ancient examples of symmetries and their breakdowns in elasticity theory and hydrodynamics. Since Galois Theory is…