How Big Can a Black Hole Grow?

Understand

I show that there is a physical limit to the mass of a black hole, above which it cannot grow through luminous accretion of gas, and so cannot appear as a quasar or active galactic nucleus.

• The limit is Mmax \simeq 5x10^{10}M_sun for typical parameters, but can reach Mmax \simeq 2.7x10^{11}M_sun in extreme cases (e.g.
• maximal prograde spin).
• The largest black hole masses so far found are close to but below the limit.