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The first [1] is given by = where M BH is the mass of the black hole, σ is the stellar velocity dispersion of the host bulge, and G is the gravitational constant. The second definition [ 2 ] is the radius at which the enclosed mass in stars equals twice M BH , i.e. M ⋆ ( r < r h ) = 2 M BH . {\displaystyle M_{\star }(r<r_{h})=2M_{\text{BH}}.}
(Supermassive black holes up to 21 billion (2.1 × 10 10) M ☉ have been detected, such as NGC 4889.) [17] Unlike stellar mass black holes, supermassive black holes have comparatively low average densities. (Note that a (non-rotating) black hole is a spherical region in space that surrounds the singularity at its center; it is not the ...
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 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.
The black hole event horizon bordering exterior region I would coincide with a Schwarzschild t-coordinate of + while the white hole event horizon bordering this region would coincide with a Schwarzschild t-coordinate of , reflecting the fact that in Schwarzschild coordinates an infalling particle takes an infinite coordinate time to reach the ...
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.
Scientists made that point anew on Monday in a study that used observations of a ferocious class of black holes called quasars to demonstrate "time dilation" in the early universe, showing how ...
Both of these facts would also be true if we were considering a set of observers hovering outside the event horizon of a black hole, each observer hovering at a constant radius in Schwarzschild coordinates. In fact, in the close neighborhood of a black hole, the geometry close to the event horizon can be described in Rindler coordinates.