On the maximization of the central gravitational red-shift of a Schwarzschild sphere with a given surface gravitational red-shift.

Details On the maximization of the central gravitational red-shift of a Schwarzschild sphere with a given surface gravitational red-shift. On the maximization of the central gravitational red-shift of a Schwarzschild sphere with a given surface gravitational red-shift.

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976gregr...7..769n&link_type=abstract

General Relativity and Gravitation, Volume 7, Issue 10, pp.769-780

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Following Bondi static, spherically symmetric equilibrium configurations with a core and an envelope have been considered. It has been shown that for any configurations with nonnegative pressure and density and with a surface red-shiftz s ⩽ 4.77 arbitrarily large central red-shiftsz c are possible in the limiting case of arbitrarily large radius. The effects of imposition of further constraints in the form of a real speed of sound not exceeding the speed of light are also examined. It is seen that for a given limiting sound-to-light-speed ratio √λ. (i) There exists a limiting surface red-shiftz s(λ) ⩽ 1.71. (ii) A configuration withz s >z s(λ) is not possible, (iii) A configuration withz s=z s(λ) has a unique and finitez c=z c(λ). (iv) Forz s

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