The power output of a black holes hawking radiation is inversely proportional to the square of it's mass. According to here, in it's final second of existence, it'll emit over 2E22 joules of energy, or the equivalent to almost 5 Teratons of TNT. From how far away would we be able to detect such an event?
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I voted to close because this is a homework like question – anna v Jul 21 '23 at 11:09
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@annav how is this homework when How far should be a supernova to not be seen from Earth? isn't? – John Rennie Jul 21 '23 at 15:16
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@JohnRennie a lot of homework like questions go through, imo. – anna v Jul 21 '23 at 16:49
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Calculators like the one referenced in OP are usually based on expressions for the Hawking radiation consisting only of photons. While this would give mostly accurate power and lifetime for black holes heavy enough that they radiate mostly massless particles, for the last stages of black hole evaporation the results would be highly innacurate, because then the number of different particle species radiated by black hole would be quite large. And while the Standard Model calculations can provide answers about known kinds of particles at the energy ranges accessible for observations presently (see e.g. this answer), the final moments of black hole explosion would produce particles of much greater energy and so there is a great deal of speculation here.
Nevertheless, the problem has been studied by many authors under various assumptions. Recent review paper
- Auffinger, J. (2023). Primordial black hole constraints with Hawking radiation—a review. Progress in Particle and Nuclear Physics, 104040, doi:10.1016/j.ppnp.2023.104040, arXiv:2206.02672.
provides an estimate $D\lesssim 10\text{ pc}$ for a range at which the final black hole explosion could be detected if it happened today under reasonable assumptions.
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