The usually stated area theorem of classical general relativity assumes null energy condition or stronger. Thus, if these conditions are violated, it seems that it opens up possibility that black holes can shrink even in classical general relativity.

Is this assessment true, or did we have some progress over years that black hole area can never decrease for more general energy conditions? Or do we simply not know at current understanding whether area theorem holds more generally?

  • $\begingroup$ First thought was they can evaporate due to hawking radiation. Is this about the Riemannian-Penrose inequality ? $\endgroup$
    – JMLCarter
    Commented Sep 30, 2017 at 9:59
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    $\begingroup$ @JMLCarter evaporation is a quantum process. OP is asking whether relaxing one of the conditions for the area theorem can still be used to prove it. $\endgroup$
    – Bruce Lee
    Commented Sep 30, 2017 at 10:03
  • $\begingroup$ @JMLCarter That's why I said "classical" general relativity. Or can we really model Hawking radiations in terms of classical general relativity language? Then violation, of course, is obvious. I've not seen any treatment of such... $\endgroup$ Commented Sep 30, 2017 at 10:04
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    $\begingroup$ The null energy condition is the weakest energy condition we have, so if you want to weaken the assumptions of the theorem, I can't see what you could use as a candidate for a weaker assumption. It certainly isn't true if you eliminate the NEC assumption without replacing it with something else. See, e.g., arxiv.org/abs/astro-ph/0505618 $\endgroup$
    – user4552
    Commented Sep 30, 2017 at 14:06

1 Answer 1


You may wish to consider the following.


Therein is provided a stronger version of the area theorem permitting for violations of the NEC. There is an exponential damping in the precise energy inequality, which, in turn, shows that black hole area increase or decrease is essentially a near-horizon effect.

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    $\begingroup$ Dear Martin Louis-Marie Lesourd. Wecome to Phys.SE. For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself, not in attached links. $\endgroup$
    – Qmechanic
    Commented Apr 28, 2019 at 8:42

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