Speaker: Gerardo García-Moreno

Title: Dissecting Buchdahl’s limit: A surgeon’s guide to compact objects

Abstract:
One of the theoretical motivations behind the belief that black holes as described by general relativity exist in nature is that it is hard to find solutions that mimic their properties, especially their compactness. One of the classic results that goes in this direction is the so-called Buchdahl limit: a bound for the maximum compactness that, under a few assumptions, static fluid spheres in hydrostatic equilibrium can possibly have. In this talk, I will highlight two of the main assumptions that could be violated in realistic physical situations: isotropy and outward decreasing monotonicity of the density profile, which, as I will discuss in detail, can be understood as a form of energy condition. I will illustrate separately how this limit can be overcome as long as any of these two assumptions are relaxed. For that purpose, I will present two toy models exemplifying that violations of any of these two assumptions can yield objects that are more compact than the Buchdahl limit. I will also discuss how these toy models represent some of the main features of realistic systems, and how they could be extended to find more realistic models.