The Structure and Stability of Relativistic, Differentially Rotating Stars

Citation

Seguin, Frederick Hampton (1975) The Structure and Stability of Relativistic, Differentially Rotating Stars. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8frp-cv61. https://resolver.caltech.edu/CaltechTHESIS:09022021-213136915

Abstract

The stability of axisymmetric, differential rotation in non-magnetic stars of uniform chemical composition is studied in the context of general relativity theory. Criteria are found for stability against local, linear, axisymmetric perturbations in conducting, viscous stars and in perfect fluid models. When stated in the proper language, the relativistic stability conditions have the same forms as the non-relativistic conditions. When thermal conduction is much more efficient than viscosity, a star must be barytropic (the level surfaces of the pressure, P, and the total density of mass energy, ∈, must coincide) and the gradient of the geometrical angular momentum (L = - U_Ø/U_o) must never point toward the interior of the quasi-cylindrical level surfaces of L. When viscosity dominates thermal conductivity by a large margin a star must be barytropic and must have an entropy (per baryon, S) gradient which is parallel to the vector (∂∈/∂S)_P ∇P. When conduction and viscosity have comparable efficiencies or are absent the criteria are only slightly more complex. Applications of the stability conditions to models of specific astrophysical objects are discussed.

The equations of hydrodynamics in the post-Newtonian approximation to general relativity are applied to differentially rotating, barytropic stars. In this approximation the equation of hydrodynamic equilibrium can be integrated to yield a simple algebraic equation, and the gravitational field equations can be written in easily handled integral forms; these facts make possible an iterative scheme of the "self-consistent field method" type which can be used to construct numerical models.

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