Analytic solutions of equations of motion in General Relativity

• Antragstellerinnen / Antragsteller: Professorin Dr. Jutta Kunz-Drolshagen; Professor Dr. Claus Lämmerzahl
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2009 bis 2014
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 157461990

• Erstellungsjahr: 2014

Zusammenfassung der Projektergebnisse

Within the frame of the project we have achieved most of the defined goals. We have systematically and thoroughly investigated the classical spacetimes of General Relativity. Namely, we have solved analytically equations of motion in the generalized four dimensional axially symmetric black hole spacetime, presented a compehensive analysis of the spherically and axially symmetric spacetimes as Reissner-Nordström for charged test particles and Taub-NUT spacetimes, Kerr-Newmann and Kerr-de Sitter spacetimes. Moreover, we have studied higher dimensional spacetimes with various horizon topologies like Myers-Perry spacetimes or black ring spacetimes. We have also considered cosmic string spacetimes and analysed the dynamics of test particles analytically for spherically and axially symmetric cases. But our main and most important result is the solution of hyperelliptic integrals of arbitrary genus (i.e. power of the underlying polynomial) for the holomorphic and meromorphic differentials, which has a very wide range of applications not only in the classical but also in other theories or models of gravity as for example a theory motivated by quantum gravity – Hořava-Lifshitz. With our work within this project, where we have developed new approaches and techniques, we have contributed significantly to a very important research field, namely, the analysis of spacetime properties by studying analytically the general dynamics of test particles with various physical properties (but without structure). Our main results were achieved in classical general relativity but the derived solutions have a much wider scope of applications stretching to String Theory and realistic models of motion. Our research was innovative and is well recognized at the national and international level. Two theses received the Prize of the University of Oldenburg as the best bachelor and master theses of the physics faculty.

Projektbezogene Publikationen (Auswahl)

• Analytic treatment of complete and incomplete geodesics in Taub–NUT space–times, Phys. Rev. D 81 124044 (2010)
  V. Kagramanova, J. Kunz, E. Hackmann and C. Lämmerzahl
  
• Test particle motion in the space-time of a Kerr black hole pierced by a cosmic string, Phys. Rev. D 82 044024 (2010)
  E. Hackmann, B. Hartmann, C. Lämmerzahl, P. Sirimachan
  
• Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: analytical solutions, Phys. Rev. D 83 044009 (2011)
  S. Grunau, V. Kagramanova
  
• Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity, Journal of Geometry and Physics 61 899 (2011)
  V. Enolski, E. Hackmann, V. Kagramanova, J. Kunz and C. Lämmerzahl
  
• Analytic treatment of geodesics in five-dimensional Myers- Perry space–times, Phys. Rev. D 86 084029 (2012)
  V. Kagramanova, S. Reimers
  
• Inversion of a general hyperelliptic integral and particle motion in Hořava-Lifshitz black hole space-times, Journal of mathematical physics 53, 012504 (2012)
  V. Enolski, B. Hartmann, V. Kagramanova, J. Kunz, C. Lämmerzahl and P. Sirimachan
  
• Observables for bound orbital motion in axially symmetric space-times, Phys. Rev. D 85 044049 (2012)
  E. Hackmann, C. Lämmerzahl
  
• Charged particle motion in Kerr-Newmann space-times, Phys. Rev. D 87 124030 (2013)
  E. Hackmann, H. Xu
  
• Dynamics of test particles in thin-shell wormhole spacetimes, Class.Quantum Grav. 30, 175014 (2013)
  V. Diemer (née Kagramanova), E. Smolarek