# Calculational details of Hawking radiation

• mritunjay
In summary, Hawking radiation is a phenomenon that occurs near the event horizon of a black hole, where particles and anti-particles are created from the vacuum. This results in a loss of mass and energy for the black hole, causing it to slowly evaporate. The calculation of this radiation involves complex quantum field theory equations and takes into account the curvature of spacetime near the black hole. The temperature and emission rate of Hawking radiation depend on the mass and size of the black hole, with smaller black holes emitting more radiation at a higher temperature. However, the overall process of Hawking radiation is still not fully understood and remains a topic of ongoing research in theoretical physics.
mritunjay
Can anybody help me with the original calculations of hawking radiation. I am working out the details of Hawking's original paper on black hole radiation. I am getting stuck at many places. Does anyone know about some place where the detailed calculations can be found.

I'm not sure what kind of detail you are looking for, but the topic is for example covered in Townsend's lectures: http://arxiv.org/PS_cache/gr-qc/pdf/9707/9707012v1.pdf . Chapter 7 deals with Hawking radiation, but depending on your level of knowledge I'd recommend reading the previous sections as well.

Polyrhythmic said:
I'm not sure what kind of detail you are looking for

Also, are you looking specifically for the details of the calculations in Hawking's papers, or exposition of Hawking radiation in general? Depending on what you're looking for, another possibility is the first reference that I give in
George Jones said:

Introduction to Quantum Effects in Gravity by Mukhanov and and Winitzki (2009)
https://www.amazon.com/dp/0521868343/?tag=pfamazon01-20

Quantum Field Theory in Curved Spacetime by Parker and Toms.
https://www.amazon.com/dp/0521877873/?tag=pfamazon01-20

Mukhanov and Winitzki is meant as an "easy", pedagogical, and short introduction.

George Jones said:
Also, are you looking specifically for the details of the calculations in Hawking's papers, or exposition of Hawking radiation in general? Depending on what you're looking for, another possibility is the first reference that I give in

Thank you Polyrhythmic and George Jones for the reply and references,

I am looking for detailed calculations. I have some specific questions.

1. when we solve Klein-Gorden equation in Schwarzschild geometry, near scri+ and scri- we get both solutions outgoing and ingoing. how is it that only outgoing forms a complete set of solution near scri+ and ingoing near scri-. What I think is both ingoing as well as outgoing modes should together form a complete set.

2. Can you suggest some place where the complex algebra calculation used in Hawking's paper is done. I want to clearly understand where to put branch cut and how to do the integration.

## 1) What is Hawking radiation?

Hawking radiation is a theoretical phenomenon proposed by physicist Stephen Hawking, where black holes emit particles and energy due to quantum effects near the event horizon.

## 2) How is Hawking radiation calculated?

Hawking radiation is calculated using quantum field theory and the principles of general relativity. Specifically, it involves the Hawking effect, where virtual particle pairs near the event horizon can become separated, with one particle falling into the black hole and the other escaping as radiation.

## 3) What is the significance of Hawking radiation?

Hawking radiation has major implications for our understanding of black holes and the laws of physics. It suggests that black holes are not truly black, as they were previously thought to be, and that they have a finite lifespan due to the continuous emission of radiation. This also has implications for the information paradox and the fate of information that falls into a black hole.

## 4) How is the rate of Hawking radiation calculated?

The rate of Hawking radiation is calculated using the Stefan-Boltzmann law, which relates the temperature of a black hole to its surface area. The smaller the black hole, the higher the temperature and the faster it emits radiation. This rate also depends on the mass and spin of the black hole.

## 5) Can Hawking radiation be observed?

Currently, Hawking radiation has not been directly observed due to its very small amount and the difficulty in detecting it. However, scientists are continuously researching and developing new technologies to try to detect this radiation, which would provide further evidence for the existence of black holes and the laws of quantum mechanics.

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