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I tried to calculate the gravitational binding energy of a black hole, but I suspect that I did not do it correctly.

I used the following formulae:

black hole radius (Swarzschild radius):

[tex]R(m)=\frac{2Gm}{c^{2}}[/tex]

gravitational potential energy for separating two masses from distance r to infinity:

[tex]dU=G\frac{m_{1}m_{2}}{r}[/tex]

and then integrated them:

[tex]U=G\int^{M}_{0}\frac{mdm}{R(m)}=G\int^{M}_{0}\frac{c^2}{2G}dm=\frac{Mc^2}{2}[/tex]

Mass-energy equivalence:

[tex]M_U=\frac{U}{c^2}=\frac{M}{2}[/tex]

The result is that the binding energy is equivalent to half the mass of the black hole.

I think I have erred somewhere for two reasons: (1) the potential energy formula I have might apply only in a Newtonian universe and (2) Wikipedia states the exact same result for neutron stars - "The gravitational binding energy of a neutron star with two solar masses is equivalent to the total conversion of one solar mass to energy." As the radius of a black hole is less than that of a neutron star (of the same mass), then the binding energy should be greater.

Have I erred, and where? What's the right way of doing this?