# Black hole expiration dates [closed]

Very "light" black holes have a life expectancy in the range of $10^{18}$ years while very "heavy" black holes have a life expectancy between $10^{12}$ or so years.

• Stephen Hawkings book Black Holes and Baby Universes.

How heavy would a black hole have to be to have a life expectancy, so that it could have ended life within the time frame of our universe?

What is the relationship between life expectancy of a black hole and its mass?

## closed as off-topic by Emilio Pisanty, Kyle Kanos, Gert, ACuriousMind♦, HDE 226868Feb 14 '16 at 18:59

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• 1. "According to a comment on this site" is a pretty useless reference. Give the link! 2. Is this comment meant to hold in classical GR or in the semi-classical picture where black holes radiate Hawking radiation? – ACuriousMind Feb 13 '16 at 14:56
• There is no way that is correct - the evaporation time increases with the cube of the mass, cf. e.g. the (crude) analysis in Wikipedia. Moreover, for black holes bigger than the mass of the Moon, the Hawking radiation temperature is cooler than the CMB, so any evaporation is cancelled out by CMB photons going in. – Emilio Pisanty Feb 13 '16 at 15:07
• 0. It was just a mistake – user46925 Feb 13 '16 at 15:08
• This is basically an exercise in doing some math from the equations Wikipedia gives (see the link in Emilio's post). – Kyle Kanos Feb 13 '16 at 15:29
• @ACuriousMind I've added a link to the question. – frodeborli Feb 15 '16 at 16:36