Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Black Hole Quasi-Periodic Oscillations in the Presence of Gauss-Bonnet Trace Anomaly

Rupam Jyoti Borah, Umananda Dev Goswami

Abstract

We investigate the effects of the Gauss-Bonnet (GB) gravitational trace anomaly on the circular motion of test particles around black holes (BHs) and its implications for quasi-periodic oscillations (QPOs) in various theoretical models. Beginning with the equations of motion, we study the effects on effective potential, angular momentum, specific energy, and the innermost stable circular orbit (ISCO) induced by the anomaly parameter $α$. The fundamental frequencies are calculated. Moreover, we examine several QPO models, including PR, RP, WD, TD, and ER2-ER4, and study the relationship between the upper and lower QPO frequencies as well as the corresponding resonance radii for frequency ratios of 1:1, 3:2, 4:3, and 5:4. Our results show that increasing $α$ leads to deviations from the Schwarzschild case in both upper and lower QPO frequencies correlations and QPO orbital radii, with model-dependent trends. Further, we constrain the BH parameters using the observational data using MCMC analysis. Finally, we calculate the upper and lower QPO frequencies for a few BH candidates on the basis of the RP model using the constrained parameter values and find a good agreement with the observed results.

Black Hole Quasi-Periodic Oscillations in the Presence of Gauss-Bonnet Trace Anomaly

Abstract

We investigate the effects of the Gauss-Bonnet (GB) gravitational trace anomaly on the circular motion of test particles around black holes (BHs) and its implications for quasi-periodic oscillations (QPOs) in various theoretical models. Beginning with the equations of motion, we study the effects on effective potential, angular momentum, specific energy, and the innermost stable circular orbit (ISCO) induced by the anomaly parameter . The fundamental frequencies are calculated. Moreover, we examine several QPO models, including PR, RP, WD, TD, and ER2-ER4, and study the relationship between the upper and lower QPO frequencies as well as the corresponding resonance radii for frequency ratios of 1:1, 3:2, 4:3, and 5:4. Our results show that increasing leads to deviations from the Schwarzschild case in both upper and lower QPO frequencies correlations and QPO orbital radii, with model-dependent trends. Further, we constrain the BH parameters using the observational data using MCMC analysis. Finally, we calculate the upper and lower QPO frequencies for a few BH candidates on the basis of the RP model using the constrained parameter values and find a good agreement with the observed results.

Paper Structure

This paper contains 13 sections, 43 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Black Hole Solutions in Trace Anomaly-Induced Gravity
  3. Particle Motion Around Black Holes Modified by Trace Anomaly
  4. Fundamental Frequencies
  5. QPO models and QPO orbits in Black Holes
  6. Parametric Resonance (PR) Model
  7. Relativistic Precession (RP) model
  8. Warped Disk (WD) model
  9. Tidal Disruption (TD) Model
  10. ER2, ER3, and ER4 Models
  11. Monte Carlo Markov Chain Analysis
  12. Summery and Conclusion
  13. Expressions of $\mathcal{J}$, $\mathcal{E}$, $\Omega_r$, $\Omega_\theta$ and $\Omega_\phi$

Figures (9)

  • Figure 1: Variation of the effective potential \ref{['eqep']} with radial coordinate normalized by the BH mass $r\mathcal{M}^{-1}$ for different values of $\alpha$. Here we consider $\bar{M} = 0.003$.
  • Figure 2: Radial profiles of specific angular momentum and energy for circular orbits of test particles are shown for different values of $\alpha$, obtained by considering $\bar{M} = 0.003$.
  • Figure 3: Variation of the ISCO radius normalized by the BH mass $\mathcal{M}$ with respect to GB coupling constant $\alpha$ for different values of $\bar{M}$.
  • Figure 4: Variation of $\Omega_{\phi}\mathcal{M}^{-1}$ with respect to $r\mathcal{M}^{-1}$ for different values of $\alpha$ obatined by considering $\bar{M} = 0.003$.
  • Figure 5: Correlations between the upper ($\nu_U$) and lower ($\nu_L$) frequencies of twin-peak QPOs for different values of the coupling constant $\alpha$ as predicted by different QPO models mentioned in the text. In this analysis, we consider $\bar{M} = 0.003$ as a fixed parameter value.
  • ...and 4 more figures