Abstract
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 language | English |
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Article number | 085005 |
Journal | Physica Scripta |
Volume | 94 |
Issue number | 8 |
DOIs | |
State | Published - 4 Jun 2019 |
Keywords
- 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