How Does Hawking Radiation Affect Black Hole Temperature?

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Discussion Overview

The discussion revolves around the formula for black hole temperature, specifically the equation T = \frac{\hbar c^3}{8 \pi GK_BM}, and its implications for understanding Hawking radiation. Participants explore the nature of this radiation, its statistical properties, and the challenges in quantifying the mass of a black hole.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents the formula for black hole temperature and questions whether it describes the temperature of the radiation emitted by a black hole.
  • Another participant explains that the formula relates to the statistics of radiation emitted near the event horizon, suggesting that the radiation follows a blackbody spectrum characterized by the temperature given in the equation.
  • A further inquiry is made regarding how to quantify the mass of a black hole, specifically questioning whether it refers to the mass of the singularity.
  • A participant emphasizes the importance of careful terminology when discussing concepts from relativity and quantum mechanics, indicating the complexity of the topic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and inquiry regarding the implications of the formula and the nature of black hole mass, indicating that the discussion remains unresolved with multiple viewpoints presented.

Contextual Notes

There is an emphasis on the need for precision in definitions and terminology, particularly when discussing concepts that intertwine relativity and quantum mechanics. The discussion does not resolve the complexities surrounding the mass of a black hole.

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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