Related papers: A geometric view on the generalized Proudman-Johns…
A new family of spherically symmetric inhomogeneous solutions of Brans-Dicke gravity is generated using the Fonarev solution of general relativity as a seed and a map from the Einstein to the Jordan conformal frame. The Brans-Dicke scalar…
We derive the non-linear semiclassical equation of motion for a general diffeomorphism-invariant theory of gravity by leveraging the thermodynamic properties of closed causal horizons. Our work employs two complementary approaches. The…
New approach to exact solvability of dilaton gravity theories is suggested which appeals directly to structure of field equations. It is shown that black holes regular at the horizon are static and their metric is found explicitly. If a…
In this note we will discuss a potentially interesting extension of some recent results on primitive solutions to completely integrable partial differential equations. We will discuss a family distributions that are holomorphic on the…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
Recollect that Heron's formula for the area of a triangle given its sides has a counterpart given the medians instead, which carries an extra factor of $\frac{4}{3}$. On the one hand, we formulate the pair of these in Linear Algebra terms,…
We study a generalization of the Holst action where we admit nonmetricity and torsion in manifolds with timelike boundaries (both in the metric and tetrad formalism). We prove that its space of solutions is equal to the one of the Palatini…
Using the Penner--Fock parameterization for Teichmuller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit.…
The objective of this paper is to find some inequalities satisfied by periodical solutions of multi-time Hamilton systems, when the Hamiltonian is convex. To our knowledge, this subject of first-order field theory is still open. Section 1…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
This is a short review of the construction of quasi-periodic (algebraic-geometrical) solutions to hierarchies of nonlinear integrable equations. As is well known, the solutions are expressed through Riemann's theta-functions associated with…
We present novel geometric numerical integrators for Hunter--Saxton-like equations by means of new multi-symplectic formulations and known Hamiltonian structures of the problems. We consider the Hunter--Saxton equation, the modified…
Using simple algebraic methods along with an analogy to the BFSS model, we explore the possible (target) spacetime symmetries that may appear in a matrix description of de Sitter gravity. Such symmetry groups could arise in two ways, one…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
We study generalized variants of the Burgers equation and the KdV equation on the circle. The main goal of the paper is to show that both extensions can be recast as geodesic equations on a suitable diffeomorphism group of the circle and…
We introduce a periodic two-dimensional $\mu$-$b$-equation and a periodic two-dimensional two-component $(\mu)$-Camassa-Holm equation which we study as geodesic flows on the diffeomorphism group of the torus and a semidirect product…
In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics…