The Paczyński-Wiita potential. A step-by-step "derivation". Commentary on: Paczyński B. and Wiita P. J., 1980, A&A, 88, 23

• Paczynski realized that a properly chosen gravitational potential may accurately model (in a ``pseudo Newtonian'' theory) general relativistic effects that determine the motion of matter near a nonrotating black hole. Paczynski's choice, known today as the ``Paczynski-Wiita potential'', proved to be very practical. It was used by numerous researchers in the black-hole accretion theory and became a standard tool in relativistic astrophysics. The model is an example of Paczynski's admired ability to invent simple ideas that were brilliant, deep, and useful ``out of nowhere''. Paczynski has intuitively guessed the form of the potential. However, it could be also derived by a step-by-step formal procedure. I show the derivation here that is based on a standard definition of the relativistic ``effective potential'' in the Schwarzschild spacetime. The relativistic effective potential may be uniquely divided into its ``gravitational'' and ``centrifugal'' part. The gravitational part only differs from the Paczynski-Wiita potential by a constant.

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NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

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black holes

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