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{{Orphan|date=September 2013}}
 
The '''Paczyński–Wiita potential''' is an approximation of the gravitational potential around a non-rotating [[black hole]]. It was introduced by [[Bohdan Paczyński]] and Paul Wiita in 1980. The article is one of the 40 most-cited from the first 40 years of the journal [[Astronomy & Astrophysics]]. The mathematical form of the potential is
 
: <math>\Phi_{PW} (r)=-\frac{GM}{r-r_g}</math>
 
where <math>r</math> is the radial distance from the black hole, <math>G</math> is the gravitational constant, <math>M</math> is the mass of the black hole, and <math>r_g=2GM/c^2</math> is its Schwarzschild radius. (<math>c</math> 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 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 numerical simulations of black hole [[accretion disc|accretion]].
 
== References ==
* {{Citation | last1=Paczyński | first1=Bohdan | author1-link=Bohdan Paczyński | last2=Wiita | first2=Paul J.
| title=Thick accretion disks and supercritical luminosities | journal=Astronomy & Astrophysics | volume=88 | pages=23–31 | date=August 1980 | url=http://adsabs.harvard.edu/abs/1980A%26A....88...23P |bibcode = 1980A&A....88...23P }}
* {{Citation | last=Abramowicz | first=Marek A.
| title=The Paczyński–Wiita potential. A step-by-step "derivation". Commentary on: Paczyński B. and Wiita P. J., 1980, A&A, 88, 23
| journal=Astronomy & Astrophysics | volume=500 | pages=213–214 | date=June 2009 | url=http://adsabs.harvard.edu/abs/2009A%26A...500..213A |bibcode = 2009A&A...500..213A |doi = 10.1051/0004-6361/200912155 |arxiv = 0904.0913 }}
 
{{DEFAULTSORT:Paczynski-Wiita potential}}
[[Category:General relativity]]
[[Category:Black holes]]
[[Category:1980 introductions]]
 
{{relativity-stub}}

Revision as of 20:44, 1 August 2013

Template:Orphan

The Paczyński–Wiita potential is an approximation of the gravitational potential around a non-rotating black hole. It was introduced by Bohdan Paczyński and Paul Wiita in 1980. The article is one of the 40 most-cited from the first 40 years of the journal Astronomy & Astrophysics. The mathematical form of the potential is

ΦPW(r)=GMrrg

where r is the radial distance from the black hole, G is the gravitational constant, M is the mass of the black hole, and rg=2GM/c2 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 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 numerical simulations of black hole accretion.

References

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