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A classification of black holes by mass: Micro black hole and extra-dimensional black hole; Planck length; Primordial black hole, a hypothetical leftover of the Big Bang; Stellar black hole, which could either be a static black hole or a rotating black hole; Supermassive black hole, which could also either be a static black hole or a rotating ...
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.
The Kerr–Newman metric describes the spacetime geometry around a mass which is electrically charged and rotating. It is a vacuum solution which generalizes the Kerr metric (which describes an uncharged, rotating mass) by additionally taking into account the energy of an electromagnetic field, making it the most general asymptotically flat and stationary solution of the Einstein–Maxwell ...
The formula for the Bekenstein–Hawking entropy (S) of a black hole, which depends on the area of the black hole (A). The constants are the speed of light ( c ), the Boltzmann constant ( k ), Newton's constant ( G ), and the reduced Planck constant ( ħ ).
The Carter constant is a conserved quantity for motion around black holes in the general relativistic formulation of gravity. Its SI base units are kg 2 ⋅m 4 ⋅s −2 . Carter's constant was derived for a spinning, charged black hole by Australian theoretical physicist Brandon Carter in 1968.
Although charged black holes with r Q ≪ r s are similar to the Schwarzschild black hole, they have two horizons: the event horizon and an internal Cauchy horizon. [8] As with the Schwarzschild metric, the event horizons for the spacetime are located where the metric component diverges; that is, where + = =
In the mathematical description of general relativity, the Boyer–Lindquist coordinates [1] are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole. The Hamiltonian for particle motion in Kerr spacetime is separable in Boyer–Lindquist coordinates.