Constraining Cubic Curvature Corrections to General Relativity with Quasi-Periodic Oscillations

TL;DR

The paper constrains cubic curvature corrections to general relativity using quasi-periodic oscillations (QPOs) from accreting black holes. It derives a perturbed Kerr metric including couplings $\beta_5$ and $\beta_6$ and computes QPO frequencies within the relativistic precession framework. A Bayesian analysis of GRO J1655-40 data yields 2-$\sigma$ bounds $-12.31<\frac{\beta_5}{(5 M_\odot)^4}<24.15$ and $-1.99<\frac{\beta_6}{(5 M_\odot)^4}<0.30$, tightening constraints beyond those from big-bang nucleosynthesis and the speed of gravitational waves. The results demonstrate QPOs as a viable probe of strong-field gravity and highlight degeneracies with mass and spin that future multi-messenger and spectral observations could help to break.

Abstract

We investigate observational constraints on cubic curvature corrections to general relativity by analyzing quasi-periodic oscillations (QPOs) in accreting black hole systems. In particular, we study Kerr black hole solution corrected by cubic curvature terms parameterized by $β_5$ and $β_6$. While $β_6$ corresponds to a field-redefinition invariant structure, the $β_5$ term can in principle be removed via a field redefinition. Nonetheless, since we work in the frame where the accreting matter minimally couples to the metric, $β_5$ is in general present. Utilizing the corrected metric, we compute the QPO frequencies within the relativistic precession framework. Using observational data from GRO J1655$-$40 and a Bayesian analysis, we constrain the coupling parameters to $-12.31<\frac{β_5}{(5 M_\odot)^4}<24.15$ and $-1.99<\frac{β_6}{(5 M_\odot)^4}<0.30$ at 2-$σ$. These bounds improve upon existing constraints from big-bang nucleosynthesis and the speed of gravitational waves.

Figures (2)

• Figure 1: Two dimensional and one dimensional marginal distributions for $\beta_5$. The contours show 68%, 95% and 99% credible intervals. Dashed lines are the 5%, 50%, and 95% percentiles of the distribution. At 2-$\sigma$ we have $-12.31<\frac{\beta_5}{(5 M_\odot)^4}<24.15$.
• Figure 2: Two dimensional and one dimensional marginal distributions for $\beta_6$. The contours show 68%, 95% and 99% credible intervals. Dashed lines are the 5%, 50%, and 95% percentiles of the distribution. At 2-$\sigma$ we have $-1.99<\frac{\beta_6}{(5 M_\odot)^4}<0.30$.