Hyperbolicity constraints in extended gravity theories

Yotam Sherf

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We study the characteristic structure of the Einstein-Hilbert (EH) action when modifications of the form of R2, Rmn 2 , Rmnrs 2 and Cmnr 2 s are included. We show that when these quadratic terms are significant, the initial value problem is generically ill-posed. We do so by demanding the hyperbolicity of the effective metric for propagation of perturbations. Here, we find a general expression for the effective metric in field space and calculate it explicitly about the cosmological Friedman-Robertson-Walker spacetime, and the spherically symmetric Schwarzschild solution. We find that when these quadratic contributions are non-negligible, the signature of the effective metric becomes non-Lorentzian and hence non-hyperbolic. As a consequence, we conclude that theories suggesting the inclusion of these terms can only be considered as a perturbative extension of the EH action and therefore cannot constitute a true alternative to general relativity.

Original languageEnglish
Article number085005
JournalPhysica Scripta
Issue number8
StatePublished - 4 Jun 2019


  • General relativity
  • alternative gravity theories
  • causality and hyperbolicity
  • gravitation
  • relativistic wave equation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics


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