Citation
Bardeen, James Maxwell (1965) Stability and dynamics of spherically symmetric masses in general relativity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HQ2N0J27. https://resolver.caltech.edu/CaltechETD:etd04152003164152
Abstract
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The Einstein equations for a spherically symmetric distribution of matter are recast in comoving (Lagrangian) coordinates in a form similar to that of the classical hydrodynamic equations, thus facilitating the physical interpretation of the equations. The jump conditions for a shock wave in an ideal fluid are found in these coordinates. The equation of radiative transfer in general relativity is derived, and analyzed with respect to the nongravitational interaction of the radiation and the matter as reflected in the equations arising from the zero covariant divergence of the energymomentum tensor. The radiative transfer equation is solved assuming the radiation is in local thermodynamic equilibrium with the matter.
We present some examples of numerical calculations of the equilibrium, stability, and dynamics near equilibrium of spherically symmetric masses for a simple, although physically reasonable, type of equation of state, in which the thermal energy density is given solely in terms of the pressure and an adiabatic index [...] that is independent of density and. pressure. One numerical method follows the growth of instabilities to all orders in the fractional change in radius away from equilibrium. Our formulation of the Einstein equations is applied to the analytical study of the stability, and we prove that, regardless of the equation of state, a maximum. or minimum of the binding energy as a function of central density along a sequence of masses in hydrostatic and convective equilibrium with constant number of baryons and constant rest mass per baryon implies some mode of radial oscillation has zero frequency there. As a result of this theorem, the stability properties of models in convective equilibrium can be read off a plot of fractional binding energy against the ratio of gravitational radius to radius. One example is presented of a numerical difference equation calculation of the collapse of a large mass inside the gravitational radius.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  6 May 1965 
Record Number:  CaltechETD:etd04152003164152 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd04152003164152 
DOI:  10.7907/HQ2N0J27 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1392 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  18 Apr 2003 
Last Modified:  20 Dec 2019 19:47 
Thesis Files

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