The geometric basis of generalized theories of gravity and geometrical methods in string cosmology

• Applicant: Dr. Mattias Wohlfarth
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2006 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 24941599

• Final Report Year: 2015

Final Report Abstract

The Emmy Noether research group “Geometry in gravity and cosmology” successfully completed its work on many of the projects proposed in the application and developed several new lines of research. We extended previous results on the local and global properties of manifolds with sectional curvature bounds which arise from the physical requirement of bounded relative gravitational accelerations. We could prove completeness theorems for spherically symmetric spacetimes and for cosmology. Moreover, we could rigourously demonstrate the absence of black hole singularities in static spherical symmetry. We investigated the structure of area metric manifolds which are a generalization of metric manifolds motivated from string and gauge theory. We could solve all problems of principle, by classifying area metric backgrounds and formulating physicality criteria, in the definition of observers, and in constructing exemplary gravitational dynamics. Thus we can now uphold the conjecture that spacetime can be described as an area metric manifold which was shown to have consequences for the cosmology of dark energy while being consistent with solar system physics. Further details and an area metric gravity more convincingly motivated from first principles will have to be the subject of future research work. We newly developed the notion of Finsler spacetimes that consistently generalize the causal structure of Lorentzian metric spacetimes. The geometry is now described by a rather general function on the tangent bundle instead of the very specific metric type. We defined observers and could show that the transformations between them have the structure of a groupoid generalizing the Lorentz group. An action based gravity theory was constructed that reduces to Einstein gravity in the limit of metric geometry. Preliminary consequences for solar system observations like the fly-by anomaly were studied. Besides all these mathematical and physical results we studied questions on the geometry behind quantization, the geometry of the stability of solutions of dynamical systems, a multi-copied standard model scenario of potential relevance to explain astrophysical observations, and proposed experiments of gyroscope system transports that locally distinguish between rotating Kerr and non-rotating Schwarzschild spacetimes.

Publications

• Area metric gravity and accelerating cosmology, J. High Energy Phys. 02 (2007) 030
  R. Punzi, F. P. Schuller and M. N. R. Wohlfarth
  
• Geometric obstruction of black holes, Ann. Phys. 322 (2007) 1335-1372
  R. Punzi, F. P. Schuller and M. N. R. Wohlfarth
  
• Geometry and stability of dynamical systems, Phys. Rev. E 79 (2009) 046606
  R. Punzi and M. N. R. Wohlfarth
  
• Causal structure and algebraic classification of non-dissipative linear optical media, Ann. Phys. 325 (2010) 1853-1883
  F. P. Schuller, C. Witte and M. N. R. Wohlfarth
  
• Consistent matter couplings for Plebanski gravity, Phys. Rev. D 82 (2010) 104052
  F. Tennie and M. N. R. Wohlfarth
  
• Multimetric extension of the PPN formalism: experimental consistency of repulsive gravity, Phys. Rev. D 82 (2010) 084028
  M. Hohmann and M. N. R. Wohlfarth
  
• Repulsive gravity model for dark energy, Phys. Rev. D 81 (2010) 104006
  M. Hohmann and M. N. R. Wohlfarth
  
• Causal structure and electrodynamics on Finsler spacetimes, Phys. Rev. D 84 (2011) 044039
  C. Pfeifer and M. N. R. Wohlfarth
  
• Finsler geometric extension of Einstein gravity, Phys. Rev. D 85 (2012) 064009
  C. Pfeifer and M. N. R. Wohlfarth
  
• Local spacetime effects on gyroscope systems, Phys. Rev. D 87 (2013) 024031
  M. N. R. Wohlfarth and C. Pfeifer