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In nuclear physics we have a mass defect by the binding energy of the nuclides. A similar effect appears in the theory of gravitation induced by the gravitational binding energy, which reduces the mass. But for example at the ISCO of an Kerr black hole we have binding energies about $\sim 0.4 mc^2$ so if a particle would go to $r\to 0$ the binding energy $E_B\to-\infty$ and so the effective mass will be negative (and the mass defect will also be infinite)?

What is the problem about this thoughts?

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  • $\begingroup$ The Penrose process: (en.wikipedia.org/wiki/Penrose_process) relies that the effective energy of a particle near a Kerr black hole can be negative. $\endgroup$
    – John Davis
    Nov 27 '15 at 19:10
  • $\begingroup$ Sure but Penrose associated this negative energy as an extraction of the rotational energy from the black hole. So I think this isn't the same? $\endgroup$
    – Alpha001
    Nov 27 '15 at 19:50
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The 1960 paper by Arnowitt, Deser and Misner addressed the issue of mass defect on the cosmological scale. Basically, both negative and positive energies contribute to the total gravitational field - hence the measured gravity field in systems that have large gravity fields, will be larger than what can be accounted for by the bare mass (i.e., bear mass being defined as the sum of all particles in the system one would obtain by reducing the matter to small pieces and moving them far apart such that there is no significant gravitational interaction). Taking the earth for example, the energy in its gravitational field is insignificant compared to its positive mc^2 energy. If the same earth mass were shrunk to a black hole, there would an additional gravitational energy present (depending upon how one models the black hole). As a shell, the gravitational energy is [(1/2)m^2]/2R and since the black hole radius would be 2mG/c^2, the additional energy would be (mc^2)/4.

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Is negative binding energy negative energy?

No. Positive binding energy is negative energy.

Negative binding energy is negative negative energy.

And negative negative energy is of course positive energy.

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