Applying Fractional Calculus in Gravitational Collapse
PT-CERN Call 2022/2
Universidade da Beira Interior
CMA-UBI – Centro de Matemática e Aplicações
The research that will eventually be conducted to write a PhD thesis within this proposal involves using a seldom used mathematical technique in high energy physics, but only because the HEP community has not been aware. Otherwise, it has been employed in many domains of physics: e.g. including fractional calculus in atomic or solid-state physics. The possibilities are pretty interesting as far as gravitational settings are concerned. In this proposal, we will investigate (analytically, whenever possible, and numerically) fractional differential calculus and subsequent equations that generalize well-known ones in gravitational physics. We aim to consider the equations governing gravitational collapse either classically or from a quantum (semi-classically) perspective with several fractional derivatives. This may allow making predictions and contrast them to establish which limits or ranges for the fractional derivatives are permitted, given known gravitational data. Fractional quantum gravity is very much in its infancy, and many cases need to be investigated.