Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

Self-Gravitating Stellar Collapse: Explicit Geodesics and Path Integration

We extend the work of Oppenheimer and Synder to model the gravitational collapse of a star to a black hole by including quantum mechanical effects. We first derive closed-form solutions for classical paths followed by a particle on the surface of the collapsing star in Schwarzschild and Kruskal coordinates for space-like, time-like, and light-like geodesics. We next present an application of th...

Stellar Collapse and Gravitational Waves

The new generation of gravitational wave (GW) detectors have the potential to open a novel window onto the violent dynamics of core collapse. Although it is certain that core collapse events generate gravitational radiation, understanding the characteristics of the radiation — whether it can be measured with these detectors, and the best way to go about doing so — is a challenging problem. In t...

On chaotic behavior of gravitating stellar shells.

Motion of two gravitating spherical stellar shells around a massive central body is considered. Each shell consists of point particles with the same specific angular momenta and energies. In the case when one can neglect the influence of gravitation of one ("light") shell onto another ("heavy") shell ("restricted problem") the structure of the phase space is described. The scaling laws for the ...

Self-Adaptive Quadrature and Numerical Path Integration

Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions.

We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. This is a basic model of stochastic particles in interaction. The equilibrium states correspond to polytropic configurations similar to stellar polytropes and polytropic stars. The index n of the polytrope is related to the expon...