2008
DOI: 10.1103/physrevlett.100.171101
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Complete Analytic Solution of the Geodesic Equation in Schwarzschild–(Anti-)de Sitter Spacetimes

Abstract: The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti) de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta-divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The solutions are completely classified by the structure of the zeros of the characteristic polynomial which depends on the energy, angular momentum, and the cosmological constant.

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Cited by 129 publications
(128 citation statements)
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“…In General Relativity (GR), the curvature and geometry of the space-time play crucial role as space-time is curved with the presence of matter fields [26,27,28,29]. A number of studies related to the geodesic motion in the background of various spacetimes has been performed time and again due to its astrophysical importance [30,31,32,33,34,35]. In general, the effects of the curvature in a given space-time is studied through the Geodesic Deviation Equations (GDE) [36,37,38], the equations which describe the relative acceleration of two neighbouring geodesics in diversified scenario [28,29,39,40,41,42].…”
Section: Introductionmentioning
confidence: 99%
“…In General Relativity (GR), the curvature and geometry of the space-time play crucial role as space-time is curved with the presence of matter fields [26,27,28,29]. A number of studies related to the geodesic motion in the background of various spacetimes has been performed time and again due to its astrophysical importance [30,31,32,33,34,35]. In general, the effects of the curvature in a given space-time is studied through the Geodesic Deviation Equations (GDE) [36,37,38], the equations which describe the relative acceleration of two neighbouring geodesics in diversified scenario [28,29,39,40,41,42].…”
Section: Introductionmentioning
confidence: 99%
“…It can be shown [3,8] that φ ∞ is an element of the theta-divisor, that is, the set of zeroes of the theta function. It follows σ( φ) = 0 and a functional relation between the components φ ∞,1 and φ ∞,2 of φ ∞ .…”
Section: The Geodesic Equationmentioning
confidence: 99%
“…Second, the functional relation between the components of φ ∞ can be used to get rid of φ ∞,j = f (φ ∞,i+1 ), where j = i + 1 and i given by (3). The function f has to be chosen such that φ ∞ is an element of the theta-divisor, i.e.…”
Section: The Geodesic Equationmentioning
confidence: 99%
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