Probing Black Hole Phase Transitions through Quasi-Periodic Oscillations

TL;DR

The paper investigates whether quasi-periodic oscillations (QPOs) can reveal the thermodynamic phase structure of black holes by analyzing upper and lower QPO frequencies as functions of Hawking temperature $T$ in RN AdS and Kerr spacetimes across multiple QPO models (RP, ER, WD). It derives QPO frequencies from small perturbations around unstable geodesics and demonstrates phase-dependent trends: QPOs decrease with $T$ in small black-hole branches, rise in intermediate branches, and level off in large black-hole branches, with spin in Kerr modulating these effects. The study emphasizes that these results are largely mathematical due to the undetermined observational relevance of Hawking temperature, yet they suggest that changes in near-horizon geometry associated with phase transitions can influence QPO signatures. Overall, QPOs may serve as indirect probes of black-hole thermodynamic state and geometry, motivating further theoretical and observational exploration within relativistic disk dynamics.

Abstract

In this work, we probe the well known thermodynamic phase structure of black hole through the lens of its quasi-periodic oscillations (QPOs). Can QPOs be influenced by black hole phase transi- tions? Do they carry any signature of such transitions in their observational patterns? These were the central questions guiding our study. Using both RN AdS and Kerr black hole backgrounds across different QPO models, we analyzed the behavior of upper and lower QPO frequencies as functions of the Hawking temperature. Our results shows that QPO frequencies trace out distinct thermo- dynamic phases and also reflect their stability properties. As the black hole transitions between different thermodynamic phases, the trend of QPO frequencies with respect to temperature also shifts. Due to lack of of observational data, the present work is primarily more on the mathematical side, as the underlying mechanism responsible for the Hawking temperature has not yet been fully understood or experimentally verified. Moreover, given the speculative nature of black hole phase transitions, it would be unfair to claim that our results establish a definitive connection between an observable quantity such as the QPO frequency and the thermodynamic phase behavior of black holes. Nevertheless, our analysis suggests a possibility that changes in black hole geometry could be one of the contributing factors influencing QPO behavior.

Figures (7)

• Figure 1: Radial and vertical oscillatory response of the particle in a unstable circular null geodesics with different values of $Q$. Gray area represents the non-physical region where temperature is negative.
• Figure 2: Behavior of the quasi-periodic oscillation (QPO) frequencies of both upper $\nu_U$ and lower $\nu_L$ for RN AdS black holes as functions of temperature, across different black hole branches: small (SBH), intermediate(IBH) and large (LBH). Here, we have considered $Q = 0.05$.
• Figure 3: Radial and vertical oscillatory response of the particle in a unstable circular timelike geodesics with different values of $Q$.We have considered L=20. Gray area represents the non-physical region where temperature is negative.
• Figure 4: Behavior of the quasi-periodic oscillation (QPO) frequencies of both upper $\nu_U$ and lower $\nu_L$ for RN black holes as functions of temperature, across different black hole branches: small (SBH), intermediate(IBH) and large (LBH). Here, we have considered $Q = 0.05$.
• Figure 5: Behavior of the quasi-periodic oscillation (QPO) frequencies of both upper $\nu_U$ and lower $\nu_L$ for Kerr black holes as functions of temperature, across different black hole branches in RP model : small (SBH) and large (LBH). Here, we have considered $a = 0.5$.