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Relativistic velocity - potential hydrodynamics and stellar stability


Schutz, Bernard Frederick (1972) Relativistic velocity - potential hydrodynamics and stellar stability. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/05NX-9C06.


The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation

Uʋ-1 (ø,ʋ + αβ,ʋ + ƟS,ʋ).

Einstein's equations and the velocity-potential hydrodynamical equations follow from a variational principle whose action is

I = (R + 16π p) (-g)1/2 d4x,

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 –T00 (-goo)-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 + i)

(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, 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):
  • Thorne, Kip S.
Group:TAPIR, Astronomy Department
Thesis Committee:
  • Unknown, Unknown
Defense Date:10 August 1971
Funding AgencyGrant Number
Office of Naval ResearchNonr-220(47)
Record Number:CaltechTHESIS:03212016-112353716
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9630
Deposited On:21 Mar 2016 21:59
Last Modified:09 Nov 2022 19:20

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