N-body model of black holes with quantum dust cores

Gravitational collapses are natural laboratories where observable signatures of a quantum theory of gravity may be produced and may be hidden in detectable astrophysical phenomena. A rooted theoretical description of a spherically symmetric gravitational collapse in General Relativity is given by the Oppenheimer-Snyder model. However, General Relativity is expected to break down at the very late stages of the collapse, and the classical dynamics to be affected by quantum gravitational effects. An effective quantum description of the Oppenheimer-Snyder model is provided by means of a bound-state quantisation procedure, where the areal radius of a single layer of dust is quantised in analogy to the position of the electron in the hydrogen atom [1]. In this work, the same procedure has been extended to an isotropic distribution of dust, which is discretised into an arbitrary number N of nested layers, each containing νi dust particles. The final state of the collapsed matter is represented by the global ground state of a core of quantum dust of average areal radius Rs ≈ 3/2GNM, where M is the total ADM mass, which naturally reproduces the area quantisation of a black hole. Then, macroscopic properties of the core have been investigated assuming that a fraction of dust particles is in an arbitrary excited state. Furthermore, a more accurate description of the ground state dust distribution has been explicitly determined. Near the centre, the mass function is shown to grow linearly with the areal radius, and the central singularity is replaced by an integrable singularity. The core surface is instead described by a non-linear fifth-order polynomial in the transitional shell 16/9 RH ≲ r ≲ 3/4 RH and matches smoothly the outer Schwarzschild solution and the inner bulk matter. Finally, observational signatures of quantum gravitational effects provided by this model has been addressed.