ISSN:
1572-946X
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = Kρ g , ε = ρ g c 2.Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (ξ, ψ), (ξ,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density ρ g to the central density ρ gc , ρ g /ρ gc ; pressureP to the ρ gc ,P/ρ gc ; and the metric componente −λ, for three representative general relativistic (GR) isothermal configurations σ=0.1, 0.2, and 0.3. Figure 4 shows the solution curve (ξ, ψ) for σ=0.1, 0.2, and 0.3 (σ=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4πr 2 P *(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of ξ=0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c 2 to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00639981
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