Inversion of a general hyperelliptic integral and particle motion in Hořava–Lifshitz black hole space-times

DOI10.1063/1.3677831zbMath1273.83099arXiv1106.2408OpenAlexW2080996082MaRDI QIDQ2853648

Jutta Kunz, Parinya Sirimachan, Betti Hartmann, Valeria Kagramanova, Viktor Z.Enol'skij, Claus Lämmerzahl

Publication date: 16 October 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2408

Mathematics Subject Classification ID

Black holes (83C57) Elliptic curves (14H52) Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory (83C20) Kaluza-Klein and other higher-dimensional theories (83E15) Equations of motion in general relativity and gravitational theory (83C10) Inverse problems for integral equations (45Q05) Elliptic integrals as hypergeometric functions (33C75)

Related Items

On Jacobi inversion formulae for telescopic curves, Periods of second kind differentials of $(n,s)$-curves, On higher genus Weierstrass sigma-function, General derivative Thomae formula for singular half-periods, Filtration under a stepped dam and Riemann theta functions, Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\). II, Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves, Modular form representation for periods of hyperelliptic integrals, Ultraelliptic integrals and two-dimensional sigma functions, Geodesic equations for particles and light in the black spindle spacetime, Rosenhain-Thomae formulae for higher genera hyperelliptic curves, Relationships between hyperelliptic functions of genus 2 and elliptic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Gauge theory correlators from non-critical string theory
• Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity
• Dynamical systems on infinitely sheeted Riemann surfaces
• An extended Abel-Jacobi map
• Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\)
• Black holes in higher dimensional space-times
• Complex multiplication formulae for hyperelliptic curves of genus three
• Classical integrable systems and billiards related to generalized Jacobians
• Double pendulum and \(\theta\)-divisor
• On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
• On directional derivatives of the theta function along its divisor
• The large-\(N\) limit of superconformal field theories and supergravity
• Theta functions on Riemann surfaces
• Stratifications of hyperelliptic Jacobians and the Sato Grassmannian
• Rational analogues of Abelian functions.
• Newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve \(\mu^{2}= \nu^{n}-1, n \in \mathbb Z\): ergodicity, isochrony and fractals
• Complete Analytic Solution of the Geodesic Equation in Schwarzschild–(Anti-)de Sitter Spacetimes
• Formal groups in genus two.