arXiv subjects

Joel Smoller

Publications and source records attributed to Joel Smoller.

39 records · Page 3Linked to original sources

arXiv1999

Particle-Like Solutions of the Einstein-Dirac Equations

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well-behaved even for strong coupling.

gr-qc↗

arXiv1998

Cosmology with a shock wave

We construct the simplest solution of the Einstein equations that incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric whose equation of state accounts for the Hubble constant and the microwave background radiation temperature. This produces a new solution of the Einstein equations from which we are able to derive estimates for the shock position at present time. We show that the distance from the shock-wave to the center of the explosion at present time is comparable to the Hubble distance. We are motivated by the idea that the expansion of the universe as measured by the Hubble constant might be accounted for by an event more similar to a classical explosion than by the well-accepted scenario of the Big Bang.

astro-ph↗

arXiv1992

Smooth static solutions of the Einstein-Yang/Mills equation

We consider the Einstein/Yang-Mills equations in $3+1$ space time dimensions with $\SU(2)$ gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymptotically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime.

math.AP↗