Sebastianutti, Marco
(2019)
Geodesic motion and Raychaudhuri equations.
[Laurea], Università di Bologna, Corso di Studio in
Fisica [LDM270]
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Abstract
The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given spacetime, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given spacetime must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given spacetime. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given spacetime, like expansion, shear and twist parameters govern the focusing or defocusing of geodesic congruences. Physical requirements on matter stressenergy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the HawkingPenrose singularity theorems.
Abstract
The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given spacetime, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given spacetime must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given spacetime. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given spacetime, like expansion, shear and twist parameters govern the focusing or defocusing of geodesic congruences. Physical requirements on matter stressenergy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the HawkingPenrose singularity theorems.
Tipologia del documento
Tesi di laurea
(Laurea)
Autore della tesi
Sebastianutti, Marco
Relatore della tesi
Scuola
Corso di studio
Ordinamento Cds
DM270
Parole chiave
geodesic motion,congruence,test particle,geodesic equation,General Relativity,spacetime,Raychaudhuri,Raychaudhuri equations,gravity,cosmology,geometric parameters,expansion,shear,twist,focusing,stressenergy tensor,FLRW metric,initial singularity,big bang,geodesic focusing theorem,energy conditions,HawkingPenrose theorems,geodesic deviation,Einstein's Equations,covariant derivative,WEC,NEC,SEC
Data di discussione della Tesi
20 Settembre 2019
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Sebastianutti, Marco
Relatore della tesi
Scuola
Corso di studio
Ordinamento Cds
DM270
Parole chiave
geodesic motion,congruence,test particle,geodesic equation,General Relativity,spacetime,Raychaudhuri,Raychaudhuri equations,gravity,cosmology,geometric parameters,expansion,shear,twist,focusing,stressenergy tensor,FLRW metric,initial singularity,big bang,geodesic focusing theorem,energy conditions,HawkingPenrose theorems,geodesic deviation,Einstein's Equations,covariant derivative,WEC,NEC,SEC
Data di discussione della Tesi
20 Settembre 2019
URI
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