The Self-Gravity of Pressure in Neutron Stars

Following an earlier analysis which examined the effect of the self-gravity of pressure on big-bang nucleosynthesis (BBN), we explore the effect of pressure's self-gravity on the structure of neutron stars. We construct an ad hoc modification of the Tolman-Oppenheimer-Volkoff equation wherein pressure's self-gravity is parameterized by a constant, $\chi$, with $0 \le \chi \le 1$. The full general relativistic contribution to the gravity of pressure is recovered with $\chi = 1$, and is eliminated when $\chi = 0$. This formulation is not proposed as an alternative theory of gravity, but is merely used to quantify the extent to which the self-gravity of pressure contributes to the structure of dense objects. As can be surmised qualitatively, neutron star masses can be quite sensitive to $\chi$, with higher values of neutron-star mass (by $\sim$20--25%) allowed for smaller values of $\chi$. However, for a given equation of state, neither the range of neutron star radii nor the radii at fixed central density depend sensitively on $\chi$. Over the neutron star mass range measured so far, the presence or absence of pressure's self-gravity yields a nearly immeasurable change in radius -- much smaller than the variations in radius due to the uncertainty in the equation of state. In contrast to the result for BBN, we thus find that neutron stars are not likely to be useful testbeds for examining the self-gravity of pressure.