Hawking Radiation - Temperature of a black body (or a black hole)

Description

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black hole is a region of spacetime from which nothing escapes. Around a black hole there is a mathematically defined surface called an event horizon that marks the point of no return. It is called “black” because it absorbs all the light that hits the horizon, reflecting nothing, making it almost an ideal black body. black holes have a non-zero temperature and emit radiation with a nearly perfect black-body spectrum, ultimately evaporating.The mechanism for this emission is related to vacuum fluctuations in which a virtual pair of particles is separated by the gravity of the hole, one member being sucked into the hole, and the other being emitted. The energy distribution of emission is described by Planck’s law with a temperature T, related to the mass of the black hole.

Stephen Hawking

Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his death.

His scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics.

Hawking achieved commercial success with several works of popular science in which he discusses his own theories and cosmology in general. His book A Brief History of Time appeared on the British Sunday Times best-seller list for a record-breaking 237 weeks. Hawking was a Fellow of the Royal Society (FRS), a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC’s poll of the 100 Greatest Britons.

In 1963, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease (MND; also known as amyotrophic lateral sclerosis “ALS” or Lou Gehrig’s disease) that gradually paralysed him over the decades. Even after the loss of his speech, he was still able to communicate through a speech-generating device, initially through use of a hand-held switch, and eventually by using a single cheek muscle. He died on 14 March 2018 at the age of 76, after living with the disease for more than 50 years.

Hawking died at his home in Cambridge, England, on 14 March 2018, at the age of 76.
Inscribed on his memorial stone are the words “Here lies what was mortal of Stephen Hawking 1942 – 2018” and his most famed equation. He directed, at least fifteen years before his death, that the Bekenstein–Hawking entropy equation be his epitaph. In June 2018, it was announced that Hawking’s words, set to music by Greek composer Vangelis, would be beamed into space from a European space agency satellite dish in Spain with the aim of reaching the nearest black hole, 1A 0620-00.

Related formulas

Variables

TThe temperature (K)
hPlanck constant
cSpeed of light
πpi
GNewtonian constant of gravitation
MThe mass of the black hole (kg)
kBBoltzmann constant