Self-Similar Collapse in Spherically Symmetric Elasticity

Perfect fluids have been widely used in the simulation of realistic astrophysical phenomena, such as collapse and binary coalescence. Nevertheless, these fluid models are very simple and their use to describe the full extension of a compact object, from core to envelope, may not be adequate and leave out more complex aspects of stellar dynamics. Elastic matter models generalize perfect fluids by also taking into account deviations from a relaxed state and, furthermore, allow for a smooth matching at separation surfaces. Thus, elasticity can be used to model compact objects with complex compositions.

Despite showing promise, there are few results using elasticity. To this end we studied this matter model in the context of self-similar spherically symmetric gravitational collapse. Self-similarity pertains to systems displaying invariance with regards to scale changes. In the context of collapse it provides two advantages. On the one hand, the description of the system depends only on the scale variable, removing the need to solve PDEs, while still retaining many properties of collapse. On the other hand, self-similarity is closely linked with critical collapse, the study and understanding of collapse at the threshold of black hole formation and associated processes.

In this talk I will go over the results obtained for self-similar collapse. I will show how elasticity compares with perfect fluid models, and how the tuning of the material parameters affects the spacetime through the material's response to the collapse, specifically in the generalization of the well known Evans-Coleman solution, as well as in the case of other modes of collapse. I will also show how the material's characteristics affect the regularity of the spacetime, and how they may forbid the existence of self-similarity altogether.