The Paczyński–Wiita potential is an approximation of the gravitational potential around a non-rotating

black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...

. It was introduced by

Bohdan Paczyński Bohdan Paczyński or Bohdan Paczynski (8 February 1940 – 19 April 2007) was a Polish astronomer notable for his theories and work in the fields of stellar evolution, accretion discs, and gamma ray bursts. He is the recipient of the Eddington ...

and Paul Wiita in 1980. The article is one of the 40 most-cited from the first 40 years of the journal

Astronomy & Astrophysics ''Astronomy & Astrophysics (A&A)'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. It is operated by an editorial team under the supervision of a board of directors re ...

. The mathematical form of the potential is :

\Phi_ (r)=-\frac

where

r

is the radial distance from the black hole,

G

is the gravitational constant,

M

is the mass of the black hole, and

r_S=2GM/c^2

is its Schwarzschild radius. (

c

is the speed of light.) The potential exactly reproduces the locations of the innermost stable circular orbit and the marginally bound orbit. It also exactly reproduces the form of the angular momentum distribution and accurately approximates the Keplerian angular velocity and epicyclic frequency. Because the Paczyński–Wiita potential reproduces these general relativistic effects and is easy to calculate, it is widely used in analytical studies and numerical simulations of black hole

accretion Accretion may refer to: Science * Accretion (astrophysics), the formation of planets and other bodies by collection of material through gravity * Accretion (meteorology), the process by which water vapor in clouds forms water droplets around nucl ...

References

* * General relativity Black holes 1980 introductions {{black-hole-stub