Hyperelliptic Functions and Motion in General Relativity

被引：0

作者：

Grunau, Saskia ^{[1
]}

Kunz, Jutta ^{[1
]}

机构：

[1] Carl von Ossietzky Univ Oldenburg, Inst Phys, D-26111 Oldenburg, Germany

来源：

MATHEMATICS | 2022年 / 10卷 / 12期

关键词：

hyperelliptic functions; geodesic motion; black holes; SUPERMASSIVE BLACK-HOLES; GRAVITATIONAL COLLAPSE; GEODESIC EQUATIONS; KERR; KERR-(ANTI); DIMENSIONS; INVERSION; ORBITS; BINARY; LIGHT;

D O I：

10.3390/math10121958

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g=2: higher dimensional Schwarzschild black holes, rotating dyonic U(1)(2) black holes, and black rings.

引用

页数：20

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