The Paczynski-Wiita potential: A step-by-step "derivation"

Marek A. Abramowicz

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The Paczynski-Wiita potential: A step-by-step "derivation"

Marek A. Abramowicz

High Energy Astrophysical Phenomena · Submitted 6 Apr 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The gravitational part differs from the Paczynski-Wiita potential only by a constant.

how it is stated · asserted 1.00 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,392 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.41 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Paczynski realized that a properly chosen gravitational potential may accurately model (in a "pseudo Newtonian" theory) general relativistic effects that determine motion of matter near a non-rotating 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 "out of nowhere" simple ideas that were brilliant, deep and useful. Paczynski has guessed intuitively the form of the potential. However, it could be also derived by a a step-by-step formal procedure. I show the derivation here. My derivation 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 differs from the Paczynski-Wiita potential only by a constant.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Paczynski realized that a properly chosen gravitational potential may accurately model (in a "pseudo Newtonian" theory) general relativistic effects that determine motion of matter near a non-rotating black hole.	background 1.00	0.04	0.13	hedged possibility 0.94
s1	Paczynski's choice, known today as the "Paczynski-Wiita potential", proved to be very practical.	background 0.97	0.05	0.09	asserted 1.00
s2	It was used by numerous researchers in the black hole accretion theory, and became a standard tool in relativistic astrophysics.	background 1.00	0.04	0.07	asserted 1.00
s3	The model is an example of Paczynski's admired ability to invent "out of nowhere" simple ideas that were brilliant, deep and useful.	background 0.68	0.06	0.06	asserted 1.00
s4	Paczynski has guessed intuitively the form of the potential.	background 0.92	0.06	0.07	asserted 0.99
s5	However, it could be also derived by a a step-by-step formal procedure.	contribution 0.47	0.29	0.17	hedged possibility 0.99
s6	I show the derivation here.	contribution 0.97	0.94	0.07	asserted 0.99
s7	My derivation is based on a standard definition of the relativistic "effective potential" in the Schwarzschild spacetime.	method 0.99	0.68	0.08	asserted 0.99
s8	The relativistic effective potential may be uniquely divided into its "gravitational" and "centrifugal" part.	method 0.84	0.35	0.13	hedged possibility 0.94
s9	The gravitational part differs from the Paczynski-Wiita potential only by a constant.	result 0.97	0.73	0.53	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Paczynski realized that a properly chosen gravitational potential may accurately model (in a "pseudo Newtonian" theory) general relativistic effects that determine motion of matter near a non-rotating 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 "out of nowhere" simple ideas that were brilliant, deep and useful. Paczynski has guessed intuitively the form of the potential. However, it could be also derived by a a step-by-step formal procedure. I show the derivation here. My derivation 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 differs from the Paczynski-Wiita potential only by a constant.

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How the literature uses it

1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 1 paper

Since these motions can be quite complicated, pseudo-Newtonian potentials have been introduced that give an effective simplified description of timelike geodesics around Schwarzschild and Kerr black holes [ref] .

Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land · Introduction · 0.90

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