Consider one of the classical observables of General Relativity, the precession of the perihelion of an elliptical orbit: $$ \delta\varphi=\frac{6\pi G^2M^2m^2}{c^2L^2} $$

I am interested in known corrections to this formula, either classical or quantum-mechanical, coming from more general descriptions of General Relativity. More precisely, what is the value of $\delta\varphi$ in

  • $f(R)$ gravity?
  • naïve quantum gravity (i.e., from the one-loop correction to the Hilbert Lagrangian, in the form $c_1 R^{abcd}R_{abcd}+c_2 R^{ab}R_{ab}+c_3 R^2$)?
  • Supergravity and low-energy effective String Theory (e.g., the effect of a non-trivial dilaton, etc.)?

Corrections to other classical observables, such as the deflection of light by a massive body, or the gravitational redshift of light are of interest as well.

  • 1
    $\begingroup$ $f(R)$ are more of a family of theories but if you accept series in $R$, then this paper should qualify: arxiv.org/abs/1104.0819 $\endgroup$ – user154997 Oct 11 '17 at 15:29
  • $\begingroup$ Wouldn't quantum gravity effects be too small to observe by many, many orders of magnitude? $\endgroup$ – Ben Crowell Oct 11 '17 at 15:33
  • $\begingroup$ @LucJ.Bourhis I guess I was hoping that a result of $\delta\varphi$ for arbitrary $f$ was known, but now I realise I was being far too optimistic. A series expansion it is then. Thanks! $\endgroup$ – AccidentalFourierTransform Oct 11 '17 at 15:34
  • $\begingroup$ @BenCrowell yes, of course. From the theoretical point of view, the prediction is very interesting anyway, even if untestable in practice. $\endgroup$ – AccidentalFourierTransform Oct 11 '17 at 15:35
  • $\begingroup$ The main result I had taken from that paper I cited is that it predicts that light deflection is not modified, and that is depressing! $\endgroup$ – user154997 Oct 11 '17 at 15:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.