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Periodic Orbits and Gravitational Radiation from Extreme Mass-Ratio Inspirals as Probes of Black Hole Quantum Hair

Yiru Zhang, Meirong Tang, Zhaoyi Xu

Abstract

The classical no-hair theorem states that stationary black holes in general relativity can be completely described by only a small set of global parameters. Within this framework, no additional geometric structures are expected to persist outside the event horizon. However, quantum vacuum polarization may introduce small modifications to the near-horizon geometry, effectively giving rise to what is known as quantum hair. Such corrections may provide a possible window into the microscopic structure and thermodynamic properties of black holes. In this work, we examine how the quantum hair parameter γ influences the periodic orbital dynamics of test bodies in extreme mass-ratio inspirals (EMRIs) and their associated gravitational-wave emission. We find that γ significantly modifies the characteristic radii and angular momenta of two important circular orbits, namely the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO), leading to a shift in the allowed region of the energy-angular momentum (E-L) phase space. Based on the rational number q classification, we further show that quantum corrections tend to enhance the zoom-whirl orbital behavior.Gravitational-wave calculations using the Numerical Kludge approach indicate that quantum hair alters the effective spacetime potential, produces small drifts in the fundamental orbital frequencies, and consequently leads to observable phase dephasing in longduration signals. These results provide a dynamical signature for distinguishing quantum-corrected black holes from classical Schwarzschild ones and offer theoretical motivation for testing quantum gravity effects with future space-based gravitational-wave observatories.

Periodic Orbits and Gravitational Radiation from Extreme Mass-Ratio Inspirals as Probes of Black Hole Quantum Hair

Abstract

The classical no-hair theorem states that stationary black holes in general relativity can be completely described by only a small set of global parameters. Within this framework, no additional geometric structures are expected to persist outside the event horizon. However, quantum vacuum polarization may introduce small modifications to the near-horizon geometry, effectively giving rise to what is known as quantum hair. Such corrections may provide a possible window into the microscopic structure and thermodynamic properties of black holes. In this work, we examine how the quantum hair parameter γ influences the periodic orbital dynamics of test bodies in extreme mass-ratio inspirals (EMRIs) and their associated gravitational-wave emission. We find that γ significantly modifies the characteristic radii and angular momenta of two important circular orbits, namely the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO), leading to a shift in the allowed region of the energy-angular momentum (E-L) phase space. Based on the rational number q classification, we further show that quantum corrections tend to enhance the zoom-whirl orbital behavior.Gravitational-wave calculations using the Numerical Kludge approach indicate that quantum hair alters the effective spacetime potential, produces small drifts in the fundamental orbital frequencies, and consequently leads to observable phase dephasing in longduration signals. These results provide a dynamical signature for distinguishing quantum-corrected black holes from classical Schwarzschild ones and offer theoretical motivation for testing quantum gravity effects with future space-based gravitational-wave observatories.
Paper Structure (8 sections, 22 equations, 12 figures, 2 tables)

This paper contains 8 sections, 22 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Vacuum Quantum-Corrected Black Hole Metric Based on Effective Field Theory
  3. Orbital Dynamics in a Quantum-Corrected Black Hole Background
  4. Critical Orbital Features and Parameter Space Analysis
  5. Classification of Periodic Orbits in a Quantum-Corrected Background
  6. Gravitational Wave Radiation from Periodic Orbits in a Quantum-Corrected Black Hole Background
  7. Conclusion
  8. acknowledgements

Figures (12)

  • Figure 1: Radial behavior of the metric function $B(r)$ for different values of the quantum hair parameter $\gamma$. The event horizon corresponds to the root of $B(r)=0$.
  • Figure 2: Behavior of the marginally bound orbit radius and the corresponding angular momentum as functions of the quantum hair parameter
  • Figure 3: Variation of the ISCO radius and its angular momentum with the quantum hair parameter.
  • Figure 4: Effective potential distributions under different angular momenta and quantum hair parameters.
  • Figure 5: Allowed orbital regions for particles under different quantum hair parameters.
  • ...and 7 more figures