Constraining the rotating Simpson-Visser spacetime from the observed quasi-periodic oscillations in black holes

TL;DR

This study tests the rotating Simpson-Visser regular BH against observed HFQPOs by computing orbital and epicyclic frequencies $f_{\phi}$, $f_{r}$, and $f_{\theta}$ in the SV metric and assessing 11 HFQPO models against HFQPO data from six BHs. The SV deviation is encoded in the parameter $\beta=l^2$, and parameter estimation is performed using grid search and Bayesian MCMC to jointly constrain $\beta$, spin $a$, mass $M$, and emission radius $r_{\rm em}$. Across sources, no single model decisively rules out Kerr, though several models provide nontrivial constraints on $\beta$ and show occasional preference for SV (e.g., GRO J1655-40 under RPM/PRM/KRM variants), while others remain compatible with Kerr within uncertainties. The results suggest possible beyond-GR effects in the strong gravity regime and underscore the need for higher-precision timing data from future missions to robustly discriminate between Kerr and SV spacetimes. Ultimately, the work highlights the utility—and current limitations—of HFQPOs as probes of near-horizon geometry and potential BH hair.

Abstract

Regular black holes (BHs) which are singularity-free alternatives to the standard black hole paradigm in General Relativity (GR), offer effective models for probing the interface between classical and quantum gravity. They serve as promising candidates for exploring the nature of strong gravity and potential extensions of GR by providing testing grounds to understand how quantum corrections might manifest in astrophysical black holes. In the present work, we investigate the regular BH scenario described by the Simpson-Visser (SV) spacetime and explore its imprints on the high-frequency quasi-periodic oscillations (HFQPOs) observed in the black hole power spectrum. The Simpson-Visser spacetime represent the simplest, globally regular extensions of the Schwarzschild scenario, through the presence of a regularizing parameter. We explore the imprints of the regularizing parameter on the orbital and epicyclic frequencies associated with the motion of test particles in the rotating SV spacetime. Models aimed to explain the observed HFQPOs often invoke these fundamental frequencies and hence can potentially constrain the regularizing parameter from the available HFQPO data. We test eleven well-established HFQPO models against available observations from six black hole sources, obtaining spin constraints that, when compared with previous independent estimates, help identify the observationally favored models for each source. Based on the present data, we report that the observationally favored models cannot discriminate between the Kerr and the Simpson-Visser scenario. This when coupled with the large discrepancy in previous spin estimates of these sources, may plausibly indicate some deviation from GR in the strong gravity regime near BHs which requires further investigation.

Figures (20)

• Figure 1: The above figure shows radial variation of $f_{\phi}$ for (a) l=0.2 and (b) l= 1.2 for different choices of spin, a=0.3(red), a=0.6(orange), a=0.9(blue)
• Figure 2: The above figure shows the radial variation of $f_r$ for (a) l=0.2 and (b) l= 1.2 for different choices of spin, a=0.3 (red), a=0.6(orange), a=0.9 (blue)
• Figure 3: The above figure shows the radial variation of $f_{\theta}$ for (a) l=0.2 and (b) l= 1.2 for different choices of spin, a=0.3(red), a=0.6(orange), a=0.9(blue)
• Figure 4: The above figure (a) demonstrates the variation of $\ln \chi^{2}$ with the regularisation parameter $\beta$ for the six black holes sources shown in \ref{['t1']} assuming PRM. Figure (b) plots the variation of $\ln\chi^{2}$ with $\beta$ (assuming the same model) along with the confidence lines. The grey dotted line corresponds to the 1-$\sigma$ contour, the grey short dashed line corresponds to the 2-$\sigma$ contour and the grey long dashed line is associated with the 3-$\sigma$ contour for GRO J1655-40, XTE J1550-564, GRS 1915+105, H 1743+322, XTE J1859+226. The green dotted, short dashed and long dashed lines are the 1-$\sigma$, 2-$\sigma$ and 3-$\sigma$ contours respectively, corresponding to the source Sgr A*.
• Figure 5: The above figure (a) demonstrates change of $\ln\chi^2$ with regularisation parameter $\beta$ for individual black holes in \ref{['t1']} assuming FRM1, figure (b) plots the variation of $\ln\chi^{2}$ with regularisation parameter $\beta$ (assuming the same model) but for a subset of the six black holes where $\chi^2$ values are large and the variation with $\beta$ is also substantial such that the confidence lines can be drawn. The grey dotted line corresponds to the 1-$\sigma$ contour, the grey short-dashed line corresponds to the 2-$\sigma$ contour and the grey long-dashed line is associated with the 3-$\sigma$ contour. The confidence contour lines are the same for all the three BHs as $\chi^2_{min}\sim0$ for all of them.