Bambagiotti, Tommaso
(2023)

*N-body model of black holes with quantum dust cores.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Physics [LM-DM270]

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## Abstract

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.

Abstract

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.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Bambagiotti, Tommaso

Relatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

black holes,quantum gravity,gravitational collapse,Oppenheimer-Snyder,Corpuscolar gravity

Data di discussione della Tesi

27 Ottobre 2023

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Bambagiotti, Tommaso

Relatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

black holes,quantum gravity,gravitational collapse,Oppenheimer-Snyder,Corpuscolar gravity

Data di discussione della Tesi

27 Ottobre 2023

URI

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