## The fourth black hole law

Using this new theory, we can thus formulate a new fourth law of black hole dynamics

it is never possible to change the angular velocity of a black hole

and its resulting corollary:

every black hole grows towards its ultimate maximum size, set by the maximal limit when the circumference reaches the speed of light.

The laws of black hole mechanics are numbered from zero to three in keeping with thermodynamic laws. This new law thus becomes law number four.

For an understanding of the other black hole laws, take this overview from Wikipedia.

The four laws of black hole mechanics are physical properties that black holes are believed to satisfy. The laws, analogous to the laws of thermodynamics, were discovered by Brandon CarterStephen Hawking and James Bardeen. (The four laws are numbered from zero to three)

## Statement of the laws

The laws of black hole mechanics are expressed here using geometrised units.

#### The Zeroth Law

The horizon has constant surface gravity for a stationary black hole.

#### The First Law

For perturbations of stationary black holes, the change of energy is related to change of area, angular momentum, and electric charge by:

$dE=\frac{\kappa}{8\pi}dA+\Omega dJ+\Phi dQ$

where $$E$$ is the energy, $$\kappa$$ is the surface gravity, $$A$$ is the horizon area, $$\Omega$$ is the angular velocity, $$J$$ is the angular momentum, $$\Phi$$ is the electrostatic potential and $$Q$$ is the electric charge.

#### The Second Law

The horizon area is, assuming the weak energy condition, a non-decreasing function of time,

$\frac{dA}{dt}\geq 0$

This "law" was superseded by Hawking's discovery that black holes radiate, which causes both the black hole's mass and the area of its horizon to decrease over time.

#### The Third Law

It is not possible to form a black hole with vanishing surface gravity. $$\kappa=0$$ is not possible to achieve.

For a fuller discussion and interpretation of these laws see Wikipedia.

The Fourth Law

It is never possible to change the angular velocity of a black hole

and its resulting corollary:

every black hole grows towards its ultimate maximum size, set by the maximal limit.

SBH=A4.