Monti, Mirko
(2014)

*Black hole evaporation and stress tensor correlations.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Fisica [LM-DM270]

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## Abstract

General Relativity is one of the greatest scientific achievementes of the 20th century
along with quantum theory.
These two theories are extremely beautiful and they are well verified by experiments, but
they are apparently incompatible.
Hints towards understanding these problems can be derived studying Black Holes, some the
most puzzling solutions of General Relativity.
The main topic of this Master Thesis is the study of Black Holes, in particular the Physics
of Hawking Radiation.
After a short review of General Relativity, I study in detail the Schwarzschild solution with
particular emphasis on the coordinates systems used and the mathematical proof of the
classical laws of Black Hole "Thermodynamics".
Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations
to the Schwinger-De Witt expansion, useful for the renormalization of the stress
energy tensor.
After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon.
Particular emphasis is given to the analysis of the quantum states, from correlations to the
physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics).
Then I introduce the renormalized stress energy tensor.
Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically
in the various quantum states of interest.
Moreover, I study the correlations between these objects. They are interesting because they
are linked to the Hawking radiation experimental search in acoustic Black Hole models. In
particular I find that there is a characteristic peak in correlations between points inside and
outside the Black Hole region, which correpsonds to entangled excitations inside and outside
the Black Hole.
These peaks hopefully will be measurable soon in supersonic BEC.

Abstract

General Relativity is one of the greatest scientific achievementes of the 20th century
along with quantum theory.
These two theories are extremely beautiful and they are well verified by experiments, but
they are apparently incompatible.
Hints towards understanding these problems can be derived studying Black Holes, some the
most puzzling solutions of General Relativity.
The main topic of this Master Thesis is the study of Black Holes, in particular the Physics
of Hawking Radiation.
After a short review of General Relativity, I study in detail the Schwarzschild solution with
particular emphasis on the coordinates systems used and the mathematical proof of the
classical laws of Black Hole "Thermodynamics".
Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations
to the Schwinger-De Witt expansion, useful for the renormalization of the stress
energy tensor.
After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon.
Particular emphasis is given to the analysis of the quantum states, from correlations to the
physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics).
Then I introduce the renormalized stress energy tensor.
Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically
in the various quantum states of interest.
Moreover, I study the correlations between these objects. They are interesting because they
are linked to the Hawking radiation experimental search in acoustic Black Hole models. In
particular I find that there is a characteristic peak in correlations between points inside and
outside the Black Hole region, which correpsonds to entangled excitations inside and outside
the Black Hole.
These peaks hopefully will be measurable soon in supersonic BEC.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Monti, Mirko

Relatore della tesi

Scuola

Corso di studio

Indirizzo

Curriculum A: Teorico generale

Ordinamento Cds

DM270

Parole chiave

Hawking Radiation, Black Holes, Quantum Fields in Curved Spacetime

Data di discussione della Tesi

27 Giugno 2014

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Monti, Mirko

Relatore della tesi

Scuola

Corso di studio

Indirizzo

Curriculum A: Teorico generale

Ordinamento Cds

DM270

Parole chiave

Hawking Radiation, Black Holes, Quantum Fields in Curved Spacetime

Data di discussione della Tesi

27 Giugno 2014

URI

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