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## Homework Statement

Suppose that a black hole of mass M accretes mass at a rate ##\dot{M}##. Further suppose that accretion of mass Δm leads to the radiation of energy ##\Delta E= \eta Δmc^2##, for some effeciency of energy conversion, ##\eta##. What is the luminosity of emitted radiation in terms of ##\dot{M}## and ##\eta##?

## Homework Equations

Luminosity equation, sort of?

## The Attempt at a Solution

The only equation I've ever seen for luminosity has been in terms of temperature and radius. So I'm at a loss here where to go with this. I understand that luminosity is the amount of energy an object gives off over time but I'm sure I can't just put that ΔE over a Δt and call it good. This is suppose to be a simple question but I'm just not making the connections I need to solve it.

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