How Does Hawking Radiation Affect Black Hole Temperature?

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SUMMARY

The discussion centers on the formula T = \frac{\hbar c^3}{8 \pi GK_BM}, which defines the temperature of radiation emitted by black holes, known as Hawking radiation. This temperature is derived from the statistics of radiation near the event horizon, where the gravitational gradient is significant. The radiation follows a blackbody spectrum, and the temperature is a crucial characteristic of this emission. Additionally, the conversation touches on the complexities of quantifying the mass (M) of a black hole, emphasizing the need for precision in terminology when discussing concepts from relativity and quantum mechanics.

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AbsoluteZer0
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Hi,

I recently came across this formula:

T = \frac{\hbar c^3}{8 \pi GK_BM}

As I understand it deals with the radiation that is believed to be emitted by a black hole.
Does it describe the temperature of the radiation?

Thanks
 
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It describes the statistics of the radiation coming from close to the event horizon of a black-hole due to the large gravity gradient there.
"Temperature" is a common way of describing such statistics - the model says that the radiation coming from the black hole follows a blackbody spectrum with a characteristic temperature given by that equation.
 
Thanks.

One more question I have regarding this equation is: how can we quantify the mass of a black hole (M)? Is it the mass of the singularity?
 
Last edited:
No worries.

In relativity or QM it helps to be carefully pedantic about what things are saying - and that goes squared for when when both of them are used together :)
 

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