Explaining Hawking Radiation in Detail

[Moore1879]

Could someone explain to me, in excrusiating detail, Hawking Radiation, to include Hawking math and steps leading to the formation of the equations used to define and descibe it. It would be much appreciated.

THANK YOU!

 

[ZapperZ]

Could someone explain to me, in excrusiating detail, Hawking Radiation, to include Hawking math and steps leading to the formation of the equations used to define and descibe it. It would be much appreciated.

THANK YOU!

You might do better byt reading a few papers on this:

http://xxx.lanl.gov/abs/gr-qc/9912119
http://xxx.lanl.gov/abs/astro-ph/0202032
http://arxiv.org/abs/gr-qc/0304042

Zz.

 

[R0man]

Sure, I'd be happy to provide a detailed explanation of Hawking Radiation. To understand Hawking Radiation, we first need to understand the concept of black holes.

A black hole is a region in space where the gravitational pull is so strong that nothing, not even light, can escape from it. This phenomenon is caused by the extreme curvature of space and time near the center of the black hole, known as the singularity. The boundary of the black hole, beyond which nothing can escape, is called the event horizon.

Now, according to classical physics, nothing can escape from a black hole. However, in the 1970s, physicist Stephen Hawking proposed that black holes are not completely black and can emit radiation. This radiation is now known as Hawking Radiation.

Hawking Radiation is a type of thermal radiation that is emitted by black holes. It is named after Stephen Hawking, who first described the phenomenon in 1974. Hawking Radiation is a result of quantum effects near the event horizon of a black hole.

To understand the formation of Hawking Radiation, we need to consider the concept of virtual particles. These are particles that pop in and out of existence in the vacuum of space. According to quantum mechanics, these particles can appear and disappear in pairs, with one particle having positive energy and the other having negative energy. Normally, these pairs of particles annihilate each other and disappear back into the vacuum.

However, near the event horizon of a black hole, one of the particles in the pair can be pulled into the black hole while the other escapes. This escaping particle is known as Hawking Radiation. The black hole loses energy in this process, causing it to shrink in size. This is known as black hole evaporation.

Now, let's dive into the math behind Hawking Radiation. The equation that describes Hawking Radiation is known as the Hawking-Bekenstein equation. It is a combination of two equations - the Bekenstein-Hawking entropy equation and the Stefan-Boltzmann law.

The Bekenstein-Hawking entropy equation states that the entropy (a measure of disorder) of a black hole is proportional to its surface area. This means that as a black hole loses energy through Hawking Radiation and shrinks in size, its entropy decreases.

The Stefan-Boltzmann law, on the other hand, relates the energy radiated by a black body (such as a black hole) to its temperature. This means that