Internal structure of multicomponent static spherical gravitating fluids

Details Internal structure of multicomponent static spherical gravitating fluids Internal structure of multicomponent static spherical gravitating fluids

Nov 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975phrvd..12.3030o&link_type=abstract

Physical Review D - Particles and Fields, 3rd Series, vol. 12, Nov. 15, 1975, p. 3030-3036.

Physics

Fluid Dynamics

13

Charged Particles, Einstein Equations, Fluid Dynamics, Gravitational Effects, Maxwell Equation, Particle Interactions, Degenerate Matter, Equations Of State, Equilibrium Equations, Ideal Fluids, Variational Principles

Scientific paper

The Maxwell-Einstein equations for a fluid comprised of more than one type of particle are not a determinate system even if an equation of state is added. The problem of what the charge distribution is in such fluids is therefore also not determinate. To complete the definition of the problem, more equations are needed. We obtain these for the simple case of a static spherically symmetric multicomponent system by minimizing the energy of the fluid with respect to variations in the number densities of the constituents, with the side conditions that the total number of each constituent is constant during the variations. This procedure results in a determinate set of hydrostatic equilibrium equations, the sum of which is the familiar Tolman-Oppenheimer-Volkoff equation. The necessary and sufficient condition for charge neutrality is that the mass-energy density be some function of some linear combination of the number densities. Thus since it is well known that the electrons in a white dwarf star at absolute zero form a degenerate gas, there must be a charge imbalance throughout such a star.

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