Gravitational dynamics for all tensorial spacetimes carrying predictive, interpretable, and quantizable matter

Kristina Giesel, Frederic P. Schuller, Christof Witte, and Mattias N. R. Wohlfarth
Phys. Rev. D 85, 104042 – Published 24 May 2012

Abstract

Only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry matter field equations which are predictive, interpretable, and quantizable. These three conditions on matter translate into three corresponding algebraic conditions on the underlying tensorial geometry: the latter must be hyperbolic, time-orientable, and energy-distinguishing. Lorentzian metrics, on which general relativity and the standard model of particle physics are built, present just the simplest tensorial spacetime geometry satisfying these conditions. The problem of finding gravitational dynamics—for the general tensorial spacetime geometries satisfying the above minimum requirements—is reformulated in this paper as a system of linear partial differential equations, in the sense that their solutions yield the actions governing the corresponding spacetime geometry. Thus, the search for modified gravitational dynamics is reduced to a clear mathematical task.

  • Received 14 March 2012

DOI:https://doi.org/10.1103/PhysRevD.85.104042

© 2012 American Physical Society

Authors & Affiliations

Kristina Giesel1, Frederic P. Schuller2,*, Christof Witte2, and Mattias N. R. Wohlfarth3

  • 1Universität Erlangen, Institut für Theoretische Physik III, Lehrstuhl für Quantengravitation, Staudtstraß 7, 91058 Erlangen, Germany
  • 2Albert Einstein Institut, Max-Planck-Institut für Gravitationsphysik Am Mühlenberg 1, 14476 Potsdam, Germany
  • 3Zentrum für Mathematische Physik and Institut für Theoretische Physik Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

  • *Corresponding author: fps@aei.mpg.de

See Also

Geometry of physical dispersion relations

Dennis Rätzel, Sergio Rivera, and Frederic P. Schuller
Phys. Rev. D 83, 044047 (2011)

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Vol. 85, Iss. 10 — 15 May 2012

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