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In isotropic coordinates, the McVittie metric is given by [1] = (() / + / ()) + (+ / ()) () (+), where is the usual line element for the euclidean sphere, M is identified as the mass of the massive object, () is the usual scale factor found in the FLRW metric, which accounts for the expansion of the space-time; and () is a curvature parameter related to the scalar curvature of the 3-space as
The no-hair theorem (which is a hypothesis) states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, angular momentum, and electric charge.
A black hole is a region of spacetime where gravity is so strong that nothing, not even light, can escape it. [2] Albert Einstein's theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. [3] [4] The boundary of no escape is called the event horizon.
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 blueshifted energy of the infalling radiation should, in principle, have a significant impact on the spacetime geometry near the inner horizon. The backreaction of the blueshifted radiation leads to a runaway effect where the effective mass parameter (or energy density) of the black hole as measured near the inner horizon grows without bound.
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry. All celestial objects – planets, stars , galaxies, black holes – spin. [1] [2] [3] The boundaries of a Kerr black hole relevant to astrophysics. Note that there are no physical "surfaces" as such.
Stellar black hole – black hole formed by the gravitational collapse of a massive star. [1] They have masses ranging from about three to several tens of solar masses. Intermediate-mass black hole – black hole whose mass is significantly more than stellar black holes yet far less than supermassive black holes.
This paper predicted the existence of what are today known as black holes. [1] [7] The term "black hole" was coined decades later, in the fall of 1967, by John Archibald Wheeler at a conference held by the Goddard Institute for Space Studies in New York City; [7] it appeared for the first time in print the following year. [8]