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syp2001 committed Dec 22, 2023
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# Summary

In general relativity, the motion of a free falling test particle in a curved spacetime is
described by a geodesic - the generalization of a "straight line" path to a curved space.
[comment: maybe we just say "...by a geodesic - the minimal path between two points in a curved space"]
The geodesics of Kerr spacetime are of particular interest in the field of black
described by a timelike geodesic - a path that extremizes the proper time experienced by the
particle. Intuitively, geodesics are analogous to straight line paths in flat spacetime.
The timelike geodesics of Kerr spacetime are of particular interest in the field of black
hole perturbation theory because they describe the zeroth order motion of a small object
moving through the background spacetime of a much more massive spinning black hole. For this reason, computing
geodesics is an important step in modeling the gravitational radiation emitted by an
Expand All @@ -42,7 +42,7 @@ initial conditions [@schmidt]. Alternatively, geodesics can be identified using
version of the parameters used to define a Keplerian orbit (eccentricity, semi-latus rectum, and inclination angle).
Bound geodesics also possess fundamental frequencies since their radial, azimuthal, and polar motions are periodic.

`KerrGeoPy` is a Python package which computes both stable and plunging geodesics in Kerr spacetime using the
`KerrGeoPy` is a Python package which computes both stable and plunging timelike geodesics in Kerr spacetime using the
analytic solutions to the geodesic equation derived in [@fujita] and
[@dyson]. It mirrors and builds upon much of the functionality of the `KerrGeodesics` [@kerrgeodesics] Mathematica library.
Geodesic solutions are written in terms of Legendre elliptic integrals, which are
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