Pressure profile bounds from relaxing the TOV equation

Abstract

We develop several new and quite general bounds on the internal pressure profiles of general relativistic perfect fluid spheres --- based on various ways of relaxing the TOV system of ODEs to obtain several distinct differential inequalities. There is, as usual, a trade-off between strength of the bound, weakness of the input assumptions, and tractability of the analysis. Specifically we shall develop several straightforward but nontrivial bounds that variously depend only on the positivity of density, the boundedness of density, the monotonicity of density, or the monotonicity of the average density. We shall carefully place these new bounds within the historical framework of previous efforts in this regard, and explore the ways in which they are inter-related.