Gravitational Collapse and Black Holes

07/17/2020

A collapsing star can be studied, to first approximation, by using a distribution of dust with similar initial conditions. More recently, developments in junction conditions allowed the same models to be applied with lesser mathematical complexity. They also allowed thin shells to be used for the same purpose as well, albeit with gained simplicity. While dust stars and thin shells approximate reality, the general features of gravitational collapse are preserved in both models. In this work, we apply the junction conditions to study marginally bound, unbound and bound, non rotating and spherically symmetric, collapsing stars and thin shells of dust. For all cases we find the trajectory of the surface and thus describe the evolution of the collapse. Following that, we obtain the causal structure of the interior and exterior spacetimes and uncover how the collapse and eventual formation of the black hole unfolds. We extend the study, of the marginally bound thin shell, to various coordinate systems representing the exterior Schwarzschild spacetime to bring out different features of the sequence of events. Additionally, we also give particular attention to the trajectories of the unbound and bound collapsing thin shells and their dependency on the energy parameter M. We find the limiting cases with the ratio between the mass of the shell, m, and the energy, M. Thus we obtain the set of possible solutions for collapsing, spherically symmetric, non rotating, stars and thin shells made of dust.

Authors in the community:

• 

  D

  Diogo Luís Farinha Gomes da Silva

  ist156845

Supervisors of this institution:

• 

  J

  José Pizarro de Sande e Lemos

  ist13673

physical-sciences - Physical sciences

eng - English

Instituto Superior Técnico