Recent simulations of coalescing neutron stars conducted by Wilson, Mathews, and Marronetti show a rising central density as the orbital separation shrinks. Mathews and Wilson (MW) claim this ``star crushing'' is partially due to a nonlinear, first post-Newtonian order (1PN) enhancement of the self-gravity of each star caused by the other star. Here we show (contrary to the MW claim), within general relativity, 1PN interactions with the other star leave the central baryon density unchanged as the orbital radius shrinks. Alternative gravitational theories (e.g., Brans-Dicke) can exhibit a crushing of the stars as they near coalescence.
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Alan Wiseman (1997) studied this question.
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