Current theory suggests that black holes evaporate by the emission of Hawking radiation in a time t that depends on the mass M of the black hole according to the following relation:

(a) Explain without calculating anything why the formula implies that high-mass black holes have longer lifetimes than low-mass ones and why the rate of evaporation accelerates as the black hole loses mass. 

(b) Compute the lifetime of a black hole whose mass equals 1 M_Θ. Compare this time with the current age of the universe. 

(c) According to some theories, the largest black hole that could conceivably form would have a mass 10¹² M_Θ, of the order of the mass of an entire galaxy. What would be the lifetime of a black hole that large?

Transcribed Image Text:

t = (1.024 x 10¹m² m³/s²) G²M²/hc^