Citation
Schutz, Bernard Frederick (1972) Relativistic velocity  potential hydrodynamics and stellar stability. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:03212016112353716
Abstract
The equations of relativistic, perfectfluid hydrodynamics are cast in Eulerian form using six scalar "velocitypotential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation
U_{ʋ}=µ^{1} (ø,_{ʋ} + αβ,_{ʋ} + ƟS,_{ʋ}).
Einstein's equations and the velocitypotential hydrodynamical equations follow from a variational principle whose action is
I = (R + 16π p) (g)^{1/2} d^{4}x,
where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T_{0}^{0} (g^{oo})^{1/2}.
The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.
By introducing three scalar fields defined by
ρ ᵴ = ∇λ + ∇x(xi + ∇xɣi)
(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the massdensity, and i, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Physics  
Degree Grantor:  California Institute of Technology  
Division:  Physics, Mathematics and Astronomy  
Major Option:  Physics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Group:  TAPIR  
Thesis Committee: 
 
Defense Date:  10 August 1971  
Funders: 
 
Record Number:  CaltechTHESIS:03212016112353716  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:03212016112353716  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9630  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  21 Mar 2016 21:59  
Last Modified:  18 Aug 2017 21:56 
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