USAAAO — 2017 First Round
Question 8
In 1974, Stephen Hawking proved that black holes emit blackbody radiation according to the Stefan-Boltzmann law (due to quantum effects near the event horizon). This radiation is called Hawking radiation and through this process, black holes slowly evaporate their mass away in the absence of new material to accrete. Assume that the Hawking temperature of a black hole is inversely proportional to its mass (i.e. Tₕ = const. / M) and that our initial black hole of mass M gets split into N smaller black holes, each with a mass M / N. Using the results found in problems 6 and 7, what is the relation between the final combined luminosity of the smaller black holes (L) and the luminosity of the initial black hole (L₀)?
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