Related papers: A four--dimensional Neumann ovaloid
An alternative formulation of the no-boundary initial state of the universe in the Euclidean quantum theory of gravity is proposed. Unlike the no-boundary Hartle-Hawking wave function, in which time appears together with macroscopic…
We consider the axially symmetric coupled system of gravitation, electromagnetism and a dilaton field. Reducing from four to three dimensions, the system is described by gravity coupled to a non-linear $\sigma$-model. We find the target…
We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but…
In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape invariant superpotentials that are independent of $\hbar$ obey two partial differential equations.…
Four dimensional simplicial gravity has been studied by means of Monte Carlo simulations for some time, the main outcome of the studies being that the model undergoes a discontinuous phase transition between an elongated and a crumpled…
Recently a new four-dimensional non relativistic renormalizable theory of gravity was proposed by Horava. This gravity reduces to Einstein gravity at large distances. In this paper by using the new action for gravity we present different…
A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the…
We derive two-dimensional (2D) solutions of a generic dilaton gravity model coupled with matter, which describe D-dimensional static black holes with pointlike sources. The equality between the mass M of the D-dimensional gravitational…
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…
This paper introduces a natural definition for the volume of the unit ball in $n$-dimensional normed spaces $\mathbb{R}^n$. This definition preserves the Euclidean relation $P(B)/V(B)=n$ between the perimiter and the volume of the unit ball…
A new approach to obtaining open Universes models as exact solutions of gravitational equations is considered. The proposed method is based on an analogy between electrostatics of conductors and open cosmological models which have a…
Circular orbits are examined in static spacetimes belonging to the Weyl class of vacuum solutions which represent (nonlinear) superposition of the gravitational fields generated by certain collinear distributions of matter. In particular,…
We calculate the motion of binary mass systems in gravity up to the fourth post--Newtonian order. We use momentum expansions within an effective field theory approach based on Feynman amplitudes in harmonic coordinates by applying…
Supersymmetric gauge theories in four dimensions can display interesting non-perturbative phenomena. Although the superpotential dynamically generated by these phenomena can be highly nontrivial, it can often be exactly determined. We…
We consider a Weyl-Lorentz-$U(1)$-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly,…
A classical theorem of Alon and Milman states that any $d$ dimensional centrally symmetric convex body has a projection of dimension $m\geq e^{c\sqrt{\ln{d}}}$ which is either close to the $m$-dimensional Euclidean ball or to the…
Large astronomical objects such as stars or planets, produce approximately spherical shapes due to the large gravitational forces, and if the object is rotating rapidly, it becomes an oblate spheroid. In juxtaposition to this, we conduct a…
Soluble model of a relativistic particle describing a bag of matter with fixed radius held together in perfect balance by a self-consistent combination of three forces generated by electromagnetic and massive scalar and vector fields is…
We report on the results of a study of the motion of a four particle non-relativistic one-dimensional self-gravitating system. We show that the system can be visualized in terms of a single particle moving within a potential whose…
The gravitational potential is a key function involved in many astrophysical problems. Its evaluation inside continuous media from Newton's law is known to be challenging because of the diverging kernel 1/|r-r'|. This difficulty is…