useful bounds can be set on the pressure at the center of star without detailed stellar structure calculations 4. a. show that in hydrostatic equilibrium the function gm(r)2 8rr4 decreases with r. hence, show that the central pressure satisfies the inequality p. go4/3m2/3 c613 where m* is the mass of the whole star. b. if you assume that the density ρ(r) decreases with r, it is possible to derive a tighter lower bound and, in addition, a useful upper bound for the central pressure. show that gō4/3m2/3 in addition, show that 1/3 nd誾 gp: /3m 4/3 42/3 where pc is the central density