Abstract

In this thesis, gravitational instability of self-gravitating systems was studied using Jeans analysis, by coupling the collisionless Boltzmann equation with the weak-field, non-relativistic limit of GR and f(R). By studying how a system in equilibrium responds to perturbations in its density, Jeans analysis allows us to determine the conditions under which these disturbances grow exponentially, rendering the system gravitationally unstable and subject to collapse. First, the standard results of the response of self-gravitating and non-self gravitating fluids to perturbations in their densities is reviewed. For non-self gravitating fluids density perturbations oscillate throughout the system, whereas, for self-gravitating fluids in the Newtonian limit of GR, the arising dispersion relation exhibits a critical limit, defined by the Jeans wavenumber kJ, below which the perturbations exponentially grow, and the system becomes unstable. Then, the dispersion relation that arises for stellar systems described by a Maxwell Boltzmann distribution is analysed in the Newtonian limit of GR, in response to small perturbations in their densities. For one-component stellar systems, composed entirely of baryonic matter, the instability limit is defined by the critical Jeans mass MJ, which if exceeded the system is unstable and subject to collapse upon its own gravitation. The work of [42] in two-component stellar systems, composed of dark and baryonic matter is revisited. Particularly, for the mass density and velocity dispersion ratios between dark and baryonic matter given by ρd = 5.5 σ ρb and d = 1.83, first the result of [42] is reproduced, in which the two-component σb system seems to lower the limit of instability in comparison with the a dark matter dominated system such that the new Jeans mass M(db)J ≈ 0.58MJd. Then this re- sult is extended by comparing the two-component system to a system dominated by baryonic matter, in which case, the instability limit appears to be raised such that M(db)J ≈ 1.5MJ . Lastly, the work of [5, 18, 68] in analysing the dispersion relations for one-component stellar systems in f(R) is revisited, and then it is extend to two- components. It is shown that f(R) appears to lower the limit of instability in both cases, lowering the critical mass required to initiate the exponential growth in the perturbations.

Department

Physics Department

Degree Name

MS in Physics

Graduation Date

Fall 1-15-2019

Submission Date

January 2019

First Advisor

Mohammad, AlFiky

Committee Member 1

Mohammad, AlFiky

Committee Member 2

Adel, Awad

Extent

151 p.

Document Type

Master's Thesis

Rights

The author retains all rights with regard to copyright. The author certifies that written permission from the owner(s) of third-party copyrighted matter included in the thesis, dissertation, paper, or record of study has been obtained. The author further certifies that IRB approval has been obtained for this thesis, or that IRB approval is not necessary for this thesis. Insofar as this thesis, dissertation, paper, or record of study is an educational record as defined in the Family Educational Rights and Privacy Act (FERPA) (20 USC 1232g), the author has granted consent to disclosure of it to anyone who requests a copy. The author has granted the American University in Cairo or its agents a non-exclusive license to archive this thesis, dissertation, paper, or record of study, and to make it accessible, in whole or in part, in all forms of media, now or hereafter known.

Institutional Review Board (IRB) Approval

Not necessary for this item

Comments

AUC University fellowship from Fall 2013 until Spring 2015 Al Alfi foundation graduate scholarship Fall 2015 Research Assistantship Award from August 2017 till June 2018 (Project Number 12-21-41-43)

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