## Black hole lifespan

how long do black holes last before they vaporize?
 Recognitions: Gold Member Science Advisor Staff Emeritus That depends on a number of factors: The size of the black hole and how fast other stuff is falling into the black hole etc. If you ignore incoming mass, you can use the formula $$T_{evap} = 5120 \pi \sqrt{\frac{\hbar G}{c^5}}$$ For example, a black hole the mass of the Sun would take ~2e67 years to evaporate.
 Recognitions: Science Advisor Janus: That is the result for a black hole of the Planck mass. The generic result for a black hole of mass M is, $$T_{\rm evap} = 5120 \pi \frac{ G^2 M^3}{\hbar c^4}$$

## Black hole lifespan

Are the formula for the time that it takes for a BH to evaporate and for an object of same mass to gravitationally collapse alike , or would the latter give rise to BH that is expressed by aforementioned ^ formula ?
 Recognitions: Gold Member Science Advisor It takes a very long time. In fact, it will take way longer than the age of the universe before any black hole of a solar mass or more can actually radiate more energy than it absorbs from the environment.

Recognitions:
Gold Member
 Are the formula for the time that it takes for a BH to evaporate and for an object of same mass to gravitationally collapse alike ,
The evaporation time of a black hole and the time of 'collapse' of mass are not related. Most mass is not dense enough to 'collapse'....but before the end of the universe most mass may be consumed by black holes. In other words, a lot of mass may is likely to be consumed by existing black holes rather than form new black holes.

 Quote by Chronos It takes a very long time. In fact, it will take way longer than the age of the universe before any black hole of a solar mass or more can actually radiate more energy than it absorbs from the environment.
 Quote by Naty1 The evaporation time of a black hole and the time of 'collapse' of mass are not related. Most mass is not dense enough to 'collapse'....but before the end of the universe most mass may be consumed by black holes. In other words, a lot of mass may is likely to be consumed by existing black holes rather than form new black holes.
Thanks for the clarification.
 Mentor Blog Entries: 1 If you can't be bothered (or just can't) to do the math here's a black hole calculator http://xaonon.dyndns.org/hawking/
 This is something I learned today; I always thought that a black hole was actually an extremely large nuclear explosion in progress…. And due to the time dilation of a black hole, it would never come to a conclusion.

Mentor
Blog Entries: 1
 Quote by rcttsoul2 This is something I learned today; I always thought that a black hole was actually an extremely large nuclear explosion in progress…. And due to the time dilation of a black hole, it would never come to a conclusion.
That is not the case. A black hole is an object whose escape velocity exceeds the speed of light.