Epicyclic Oscillations around Simpson–Visser Regular Black Holes and Wormholes

Zdeněk Stuchlík,Jaroslav Vrba

doi:10.3390/universe7080279

Zdeněk Stuchlík, Jaroslav Vrba

Open Access

https://doi.org/10.3390/universe7080279

Copy DOI

Abstract

We study epicyclic oscillatory motion along circular geodesics of the Simpson–Visser meta-geometry describing in a unique way regular black-bounce black holes and reflection-symmetric wormholes by using a length parameter l. We give the frequencies of the orbital and epicyclic motion in a Keplerian disc with inner edge at the innermost circular geodesic located above the black hole outer horizon or on the our side of the wormhole. We use these frequencies in the epicyclic resonance version of the so-called geodesic models of high-frequency quasi-periodic oscillations (HF QPOs) observed in microquasars and around supermassive black holes in active galactic nuclei to test the ability of this meta-geometry to improve the fitting of HF QPOs observational data from the surrounding of supermassive black holes. We demonstrate that this is really possible for wormholes with sufficiently high length parameter l.

Highlights

We study in the Simpson–Visser meta-geometry the circular geodesic motion and related epicyclic oscillations that are relevant for oscillations of the Keplerian disks
A static and spherically symmetric metric describing the Simpson–Visser meta-geometry governing in a simple way the transition between the regular black-bounce black holes through the null wormhole to the traversable reflection-symmetric wormhole takes in the standard Schwarzschild coordinates the form dr2 + h(r ) dθ 2 + sin2 θ dφ2 (1)
The epicyclic frequencies are applied in the special version of the geodesic models of the twin high-frequency quasi-periodic oscillations (HF QPOs), namely the epicyclic resonance model

Summary

Introduction

Simpson and Visser introduced a very simple theoretically attractive spherically symmetric model of meta-geometry, coming from the Schwarzschild geometry and enabling a unique description of regular black holes and wormholes by smooth interpolation between these two possibilities using a length-scale parameter l responsible for regularization of the central singularity and potentially reflecting in a maximally simple way the possible influence of quantum gravity effects; its rotation version has recently been presented [1,2]. SgrA* by GRAVITY, and in the central region of M87 in [15] by EHT These observations of the assumed close vicinity of the black hole horizon inspired a variety of theoretical works representing precision tests of General Relativity in the strongest field limit enabling distinguishing of black hole mimickers of the type of the wormholes from the alternatives as superspinars [16,17,18] when the shadow qualitatively (topologically) differs from those corresponding to black holes [19], and these astrophysical phenomena are extraordinary even if related to their black hole counterparts [20,21,22,23]. We determine frequencies of the orbital motion and the radial and vertical epicyclic oscillations and apply them in the so-called geodesic models of HF QPOs [31,32] to test their applicability for explanation of the HF QPOs observed in the microquasars [33], and especially around supermassive black holes in active galactic nuclei [34]

Simpson–Visser Meta-Geometry

Equations of Motion

Circular Geodesics

Epicyclic Orbital Motion and Its Frequencies

The Epicyclic Frequencies Applied in the Epicyclic Resonance Model to Fit the

Conclusions