**Authors**: Christopher P. L. Berry, Jonathan R. Gair

**Date**: 5 Apr 2011

**Abstract**: We investigate the linearized form of metric f(R)-gravity, assuming that f(R) is analytic about R = 0 so it may be expanded as f(R) = R + a_2 Rˆ2/2 + … Gravitational radiation is modified, admitting an extra mode of oscillation, that of the Ricci scalar. We derive an effective energy-momentum tensor for the radiation. We also present weak-field metrics for simple sources. These demonstrate that Kerr (or Schwarzschild) black holes do not exist in f(R)-gravity. We apply the metrics to tests that could constrain f(R). We show that light deflection experiments cannot distinguish f(R)-gravity from general relativity as both have an effective post-Newtonian parameter gamma = 1. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound |a_2| < 1.2 \times 10ˆ{18} mˆ2. Gravitational wave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extreme-mass-ratio inspiral about a 10ˆ6 M_sol black hole if |a_2| > 10ˆ{17} mˆ2. However Eot-Wash experiments provide the strictest bound |a_2| < 2 \times 10ˆ{-9} mˆ2. Although the astronomical bounds are weaker, they are still of interest in the case that the effective form of f(R) is modified in different regions, perhaps through the chameleon mechanism. Assuming the laboratory bound is universal, we conclude that the propagating Ricci scalar mode cannot be excited by astrophysical sources.

1104.0819
(/preprints)

2011-04-06, 12:16
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*