Calculation of the TOV Limit Based on Neutron Degeneracy Pressure

Abstract

Original theory on the mass limit beyond which a cold, non-rotating neutron star cannot be formed, instead only stellar black holes will be created, was stipulated by J.R. Oppenheimer and G.M. Volkoff based on R.C. Tolman’s work in 1939. The limit calculated from the equation established by them is known as the TOV limit which is analogous to the Chandrasekhar limit for White Dwarfs. But the results obtained using the formula was found to be not valid today. Subsequent theoretical works place the limit in the range 1.5 to 3 solar masses. There are several basic theories and related formulae for calculating the TOV limit. In this article a different and novel approach has been adopted to calculate the TOV limit using the theory on neutron degeneracy pressure. As per present calculations, the TOV limit is around 2.928 times the solar mass. These calculations also highlight two aspects which are conceptually new; first, a black hole having mass higher than the TOV limit can also become a neutron star and both can coexist concurrently up to a certain limit; and second, that upper limit of star mass beyond which a black hole will explode in supernova before becoming a neutron star is 7.15 times the solar mass as at that stage the gravitational energy of the black hole will be equal or exceed to its nuclear binding energy.