Extremal black hole

# Extremal black hole

Overview
In theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, an extremal black hole is a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

with the minimal possible mass that can be compatible with a given charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

and angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed.
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Encyclopedia
In theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

, an extremal black hole is a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

with the minimal possible mass that can be compatible with a given charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

and angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

. In other words, this is the smallest possible black hole that can exist while rotating at a given fixed constant speed.

The concept of an extremal black hole is theoretical and none have thus far been observed in nature. However, many theories are based on their existence.

In supersymmetric theories, extremal black holes are often supersymmetric: they are invariant under several supercharge
Supercharge
In theoretical physics, a supercharge is a generator of supersymmetry transformations.Supercharge, denoted by the symbol Q, is an operator which transforms bosons into fermions, and vice versa...

s. This is a consequence of the BPS bound. Such black holes are stable and emit no Hawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

. Their black hole entropycan be calculated in string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

.

It has been suggested by Sean Carroll that the entropy of an extremal black hole is equal to zero. Carroll explains the lack of entropy by creating a separate dimension for the black hole to exist within. This theory is not held in high regard, however.

The hypothetical black hole electron
Black hole electron
In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength. This idea is substantiated within a series of papers published by...

is defined as an extremal black hole.

• Black hole electron
Black hole electron
In physics, there is a speculative notion that if there were a black hole with the same mass and charge as an electron, it would share many of the properties of the electron including the magnetic moment and Compton wavelength. This idea is substantiated within a series of papers published by...

The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...

• Black hole thermodynamics
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...