# Equation for the energy of Hawking Radiation

• Uranium235
In summary, the equation for the energy of Hawking radiation, also known as the Hawking temperature, is E = h(c^3)/8πGM where E is the energy, h is the Planck constant, c is the speed of light, G is the gravitational constant, and M is the mass of the black hole. It was derived by Stephen Hawking in 1974 using quantum field theory and general relativity. The equation tells us that black holes emit thermal radiation and eventually evaporate over time, contrary to previous beliefs. It has been used in various theoretical and experimental studies and is widely accepted in the scientific community, although there have been some challenges to its validity.
Uranium235
What is the equation for the energy/frequency of Hawking radiation emitted from a black hole?

EDIT: I found this http://library.thinkquest.org/C007571/english/advance/core5.htm but the website doesn't seem to be a legitimate source and it doesn't give the derivation of the formula.

EDIT: Oh, and I would also like to know how far away from the event horizon is Hawking radiation emitted.

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## 1. What is the Equation for the Energy of Hawking Radiation?

The equation for the energy of Hawking radiation, also known as the Hawking temperature, is given by: E = h(c^3)/8πGM where E is the energy, h is the Planck constant, c is the speed of light, G is the gravitational constant, and M is the mass of the black hole.

## 2. How was the Equation for the Energy of Hawking Radiation derived?

The equation was derived by Stephen Hawking in 1974 using quantum field theory and general relativity. He applied quantum mechanics to the space-time near a black hole and found that black holes emit thermal radiation at a specific temperature, known as the Hawking temperature.

## 3. What does the Equation for the Energy of Hawking Radiation tell us about black holes?

The equation tells us that black holes are not completely black, as was previously thought. They emit radiation and eventually evaporate over time. This also suggests that black holes have a finite lifespan and will eventually disappear.

## 4. Does the Equation for the Energy of Hawking Radiation have any practical applications?

Yes, the equation has been used in various theoretical and experimental studies, such as in the study of black hole thermodynamics and the information paradox. It has also been used to calculate the temperature of cosmic microwave background radiation.

## 5. Is the Equation for the Energy of Hawking Radiation universally accepted?

While the equation has been widely accepted in the scientific community, there have been some debates and challenges to its validity. Some physicists have proposed alternative theories to explain the phenomenon of Hawking radiation. However, the equation remains a fundamental concept in our understanding of black holes and the universe.

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