# At the TOV limit (almost black hole), how much of a neutron star's primordial mass has been converted to energy?

The following rough approximation seems to show a neutron star at its Tolman–Oppenheimer–Volkoff limit of 2.17 solar masses and 12km radius, has gravitational binding energy on the same order as its relativistic mass-energy:

$$\frac{3}{5} \frac{(2.17*1.989*10^{30}kg)^2G}{12km}=6.2*10^{48}J$$ $$2.17∗1.989∗10^{30}kg *c^2=3.88*10^{48}J$$

While numbers and formula I've used are very rough -- which would explain the apparent 60% excess -- it does seem as though once a TOV star has settled down through radiation, just about all of its mass has been effectively converted to energy. Is this correct? If not, how much of its primordial (H, He, etc.) mass has been converted to energy?

• The relativistic binding energy of a neutron star is well discussed in the book "Compact Stars" by Glendenning. Related: physics.stackexchange.com/q/2902/226902 Nov 1, 2023 at 6:45
• That is a Newtonian form of the gravitational potential energy (which is negative) for a uniform body. The gravitational binding energy is the sum of that and the internal energy of the star, which is also negative for a bound star, but smaller in magnitude. Are you asking what fraction of $M$ is in the form of rest mass? The gravitational mass $M$ includes all contributions. See physics.stackexchange.com/questions/133625/… Nov 1, 2023 at 8:10
• I invoked "primordial" rather than "rest" mass because, for example, iron-56 has a rest mass that is lower than its primordial mass that arose during nucleosynthesis era in lambdaCDM. I'm trying to get rid of any residual loss of energy to mass for the most extreme conditions. Nov 1, 2023 at 11:47
• What does "residual loss of energy to mass" mean? Nov 1, 2023 at 12:10
• Stellar synthesis of iron-56 is via exothermic fusion results in lower mass than its reactants. Nov 1, 2023 at 20:20