The angular size θ of a Black hole , i.e. its apparent size in the sky, is larger than that of a traditional object of the same ray. Indeed, for an ordinary object, its angular size (i.e. the plane Angle on the sky) is obtained by the usual formula:

$\backslash \; theta\; =\; 2\; R/D$

where R and D is respectively the ray and the distance from the object, both expressed in physical units like the Mètre. In the case of a black hole, the effects of deflection of the light (described by the theory of the General relativity) let it “appear” larger than its real size. This results owing to the fact that a luminous ray passing sufficiently near to the black hole can be sufficiently deflected by this one at the point to be absorbed. Calculations show that the angular size underlain by a black hole is given by:

$\backslash \; theta\; =\; 3\; \backslash \; sqrt\; \{3\}\; R\_\; \{\backslash \; rm\; S\}/D$,

where $R\_\; \{\backslash \; rm\; S\}$ is the Rayon of Schwarzschild of the black hole, who can be regarded here as delimiting the “surface” of the black hole (even if actually, the black hole does not have material surface). The formula thus gives an angular diameter 3 √ 3/2 $\backslash \; approx$2,5 time larger than than the usual estimate gives.

For example, the supermassif Black hole located at the center of our Galaxie is at a distance from 8,5 Kiloparsec S approximately. Its mass, about 2,6 million solar masses confers to him a ray of Schwardzschild of approximately 7 million and half of Kilomètre S. At a distance from 8,5 kpc, is 2,6× 10 20 meters, its apparent diameter should naively be 5,9× 10 -11 Radian, is 12 microphone seconds of arc. While adding factor 3 √ 3/2 lack, the angular diameter passes then to its exact value of approximately 30 microseconds of arc, quantifies which does not seem from now on inaccessible to the Interférométrie at very long base in the field radio.

See too

• solid Angle

• Sgr A* (the black hole of the galactic Center)

Reference

• Subrahmanyan Chandrasekhar, The mathematical theory off black holes , Oxford University Close (1983).

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