Abstract
SIXTY years ago, Schwarzschild1 developed what he, and others through the years, regarded as the general relativistic solution for a static, spherically symmetric, incompressible fluid sphere with equation of state ρ = ρ0 = constant. Others have rejected the incompressibility interpretation of this solution including Eddington2 who regarded ρ−3p = constant as the incompressible equation of state. We present here a new definition of incompressibility, consistent with basic principles of relativity. We then consider the natural generalisation of the Schwarzschild equation of state to general relativity, namely the constancy of proper density, and find that this approximates a truly incompressible fluid more closely than that presented by both Schwarzschild and Eddington. This could have interesting consequences in astrophysics since the maximum value of gravitational redshift, as well as the upper limit to the mass of a neutron star, are larger for this model than for the Schwarzschild model, which is traditionally considered.
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COOPERSTOCK, F., SARRACINO, R. General relativistic incompressibility. Nature 264, 529–531 (1976). https://doi.org/10.1038/264529a0
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DOI: https://doi.org/10.1038/264529a0
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General relativistic incompressibility
Nature (1977)
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