相关论文: On the Chermnykh-Like Problems: II. The Equilibriu…

In the paper we find new inequalities involving the intersections $A\cap (A-x)$ of shifts of some subset $A$ from an abelian group. We apply the inequalities to obtain new upper bounds for the additive energy of multiplicative subgroups and…

The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…

We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians…

In this note we examine the relationship between two-dimensional Coulomb systems and the thermal equilibrium measure, such as defined in the lecture notes [arXiv:2407.21194v1], pointing out some of its discrepancies with respect to the…

Chern-Simons modified gravity is an effective extension of general relativity that captures leading-order, gravitational parity violation. Such an effective theory is motivated by anomaly cancelation in particle physics and string theory.…

Quasi-polar spaces are sets of points having the same intersection numbers with respect to hyperplanes as classical polar spaces. Non-classical examples of quasi-quadrics have been constructed using a technique called pivoting [5]. We…

After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to…

We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one…

The abundance of clusters is a classical cosmological probe sensitive to both the geometrical aspects and the growth rate of structures. The abundance of clusters of galaxies measured by Planck has been found to be in tension with the…

When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat space kinks,…

We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity. The solving method is a multi-domain spectral method which we have recently developed. An improvement is introduced here for…

The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…

Using equations of motion accurate to the third post-Newtonian (3PN) order (O(v/c)^6 beyond Newtonian gravity), we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or…

We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is…

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…

In this article we consider $SU(2)$ Chern-Simons/Higgs theory coupled to gravity in three-dimensions. It is shown that for a cylindrically symmetric vortex both the Einstein equations and the field equations can be reduced to a set of…

We found new class of solutions to the Einstein-Maxwell system of equations for charged quark matter within the framework of MIT Bag Model considering a gravitational potential Z(x) proposed by Thirukkanesh and Ragel (2013), which depends…

We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then…

This paper is concerned with the Hamiltonian elliptic system in dimension two\begin{equation*}\aligned \left\{ \begin{array}{lll} -\epsilon^2\Delta u+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\\ -\epsilon^2\Delta v+V(x)v=f(u)\ &…

Weighted Fekete points are defined as those that maximize the weighted version of the Vandermonde determinant over a fixed set. They can also be viewed as the equilibrium distribution of the unit discrete charges in an external…