# Hawking Radiation

*118*articles on

the Psi Epsilon Wikia

Quantum Field Theory
| ||
---|---|---|

... no spooky action at a distance (Einstein)
| ||

Early Results
| ||

Relativistic Quantum Mechanics
| Klein-Gordon Equation Dirac Equation | |

The Dawn of QFT
| Spinors Spin Feynman Slash Notation Antimatter Klein-Gordon Field Dirac Field Renormalisation Grassman Variable Conformal Field Theory | |

Countdown to the Standard Model
| ||

From a framework to a model
| Yang-Mills Theory Quantum Electrodynamics Quantum Chromodynamics Electroweak Theory Higgs Mechanism Standard Model | |

Semi-Classical Gravity and the Dark Age
| Hawking RadiationChandrashekhar Limit Inflation Problems with the Standard Model | |

Outlook
| ||

Beyond the Standard Model
| Beyond the Standard Model Quantum Gravity Theory of Everything | |

Related
| ||

Related
| De Donder-Weyl Theory | |

**Hawking Radiation** refers to radiation that is emitted from a black hole.

## Black Hole Temperature EquationEdit this section

We start with a standard expression that relates to Black Hole Entropy:

Here, refers to the Gravitational Field at the surface, given by the following expression: \

Substituting the above in:

We know that , and therefore,

**Black Hole Temperature Equation**

## Calculating the Black Hole EntropyEdit this section

From the equation for Black Hole Temperature, we may calculate the Entropy of a Black Hole, as follows.

Integrating both sides,

Here, is the surface area of the black hole, and is obviously equal to , and therefore,

**Entropy of a Black Hole**

Where is the Planck Area.

## Power radiated by a black holeEdit this section

The Stefan-Boltzmann Law states that:

A Black Hole is a perfect black body, so it's radiativity . Therefore,

**Power radiated from a black hole**

## Countdown to Black Hole EvaporationEdit this section

The Power is the rate of **Hawking Radiation**, i.e.

Let us define a constant term so that . Then,

**Time for Black Hole Evaporation**

This is the time taken for the black hole to completely evaporate. However, taking into consideration the cosmic background microwave radiation, the temperature radiated must be greater than 2.7 K, and thus the mass of the black hole must be lesser than , or of the mass of the Earth, or else, it will not evaporate at all.