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Extreme mass-ratio inspirals and extra dimensions: Insights from modified Teukolsky framework

Shailesh Kumar, Tieguang Zi, Arpan Bhattacharyya

TL;DR

This work investigates extreme mass-ratio inspirals as probes of extra dimensions by modeling equatorial eccentric EMRIs around a spherically symmetric braneworld black hole with tidal charge $Q$ using the Modified Teukolsky Equation (MTE). The authors derive a decoupled, gauge-invariant master equation for the radiative Weyl scalar $\Psi_4^{(1)}$ on a $tr$-symmetric, non-Ricci-flat background, incorporating nonlocal bulk effects via $\Phi_{11}$ and a beyond-GR potential $V_s(r)$ controlled by a switch $\varepsilon$ (with $\varepsilon=0$ reproducing the Dudley-Finley case). They compute GW fluxes and adiabatic orbital evolution, generate waveforms with FEW/AAK for LISA, and quantify observable effects through dephasing and mismatch as functions of the tidal charge $Q$ and initial eccentricity $e_0$. The key finding is that the tidal-charge bounds from the MTE are broadly consistent in order of magnitude with those from the DF approximation, but the MTE yields larger dephasings and mismatches, particularly for higher eccentricities, underscoring the need for the MTE in precision tests of gravity beyond GR and for future high-accuracy GW modeling of braneworld scenarios.

Abstract

Extreme mass-ratio inspirals (EMRIs) offer a promising avenue to test extra-dimensional physics through gravitational wave (GW) observations. In this work, we study equatorial eccentric EMRIs around a spherically symmetric braneworld black hole, focusing on the influence of a tidal charge parameter arising from extra dimensions. Using the fact of tr-symmetry of the spacetime under consideration, we implement the Modified Teukolsky Equation (MTE) framework, incorporating the non-Ricci-flat nature of the spacetime. We compute the relevant observables and perform a comparative analysis with the results obtained from the Dudley-Finley (DF) approximation. Our findings indicate that the constraint on the tidal charge remains nearly the same in both approaches MTE and DF thus supporting previous studies on EMRIs in braneworld scenarios within the DF approximation. Furthermore, the difference in the mismatch between the two formulations exhibits deviations as the orbital eccentricity increases. Therefore, these findings highlight not only the observational potential of future low-frequency detectors like the Laser Interferometer Space Antenna (LISA) but also bring out the effectiveness of the DF approximation as well as the importance of the MTE framework for accurately modeling binaries in theories beyond GR.

Extreme mass-ratio inspirals and extra dimensions: Insights from modified Teukolsky framework

TL;DR

This work investigates extreme mass-ratio inspirals as probes of extra dimensions by modeling equatorial eccentric EMRIs around a spherically symmetric braneworld black hole with tidal charge using the Modified Teukolsky Equation (MTE). The authors derive a decoupled, gauge-invariant master equation for the radiative Weyl scalar on a -symmetric, non-Ricci-flat background, incorporating nonlocal bulk effects via and a beyond-GR potential controlled by a switch (with reproducing the Dudley-Finley case). They compute GW fluxes and adiabatic orbital evolution, generate waveforms with FEW/AAK for LISA, and quantify observable effects through dephasing and mismatch as functions of the tidal charge and initial eccentricity . The key finding is that the tidal-charge bounds from the MTE are broadly consistent in order of magnitude with those from the DF approximation, but the MTE yields larger dephasings and mismatches, particularly for higher eccentricities, underscoring the need for the MTE in precision tests of gravity beyond GR and for future high-accuracy GW modeling of braneworld scenarios.

Abstract

Extreme mass-ratio inspirals (EMRIs) offer a promising avenue to test extra-dimensional physics through gravitational wave (GW) observations. In this work, we study equatorial eccentric EMRIs around a spherically symmetric braneworld black hole, focusing on the influence of a tidal charge parameter arising from extra dimensions. Using the fact of tr-symmetry of the spacetime under consideration, we implement the Modified Teukolsky Equation (MTE) framework, incorporating the non-Ricci-flat nature of the spacetime. We compute the relevant observables and perform a comparative analysis with the results obtained from the Dudley-Finley (DF) approximation. Our findings indicate that the constraint on the tidal charge remains nearly the same in both approaches MTE and DF thus supporting previous studies on EMRIs in braneworld scenarios within the DF approximation. Furthermore, the difference in the mismatch between the two formulations exhibits deviations as the orbital eccentricity increases. Therefore, these findings highlight not only the observational potential of future low-frequency detectors like the Laser Interferometer Space Antenna (LISA) but also bring out the effectiveness of the DF approximation as well as the importance of the MTE framework for accurately modeling binaries in theories beyond GR.

Paper Structure

This paper contains 9 sections, 34 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Braneworld Spacetime and Geodesic Motion
  3. Modified Teukolsky Perturbation and Method
  4. The MTE
  5. Flux and Evolution
  6. Waveform and Mismatch
  7. Results
  8. Discussion
  9. Source

Figures (5)

  • Figure 1: The dephasing due to tidal charge is shown for initial eccentricity $e_0\in\{0.1,0.4,0.85\}$, in which the changing of evolution is derived by the fluxes from the standard Teukolsky equation of GR. The other intrinsic parameters are set as the mass of the central MBH $M=10^6M_\odot$, the initial orbital semi-latus rectum $p_0=12.0$ and tidal charge $Q\in\{10^{-7},5\times 10^{-7},10^{-6}, 5\times 10^{-6}, 10^{-5}, 5\times 10^{-5}\}$.
  • Figure 2: The dephasing due to tidal charge as a function of observation time is plotted for initial eccentricity $e_0\in\{0.1,0.4,0.85\}$, in which the changing of evolution is derived by the fluxes from MTE.
  • Figure 3: Mismatch as a function of observation time for four initial orbital eccentricities $e_0 = (0.1,0.3,0.4,0.85)$ is plotted; the other parameters are $p_0=12.0$, $Q\in\{5\times 10^{-7}, 10^{-6}, 5\times 10^{-6}, 10^{-5}, 5\times10^{-5}, 10^{-4}\}$. Note that the mismatch is obtained from EMRI evolution using DF-Teukolsky fluxes in the presence and absence of $Q$.
  • Figure 4: Mismatch as a function of observation time for four initial orbital eccentricities $e_0 = (0.1,0.3,0.4, 0.85)$ is plotted, the other parameters are $p_0=12.0$, $Q\in\{5\times 10^{-7}, 10^{-6}, 5\times 10^{-6}, 10^{-5}, 5\times10^{-5}, 10^{-4}\}$. Note that $h^{\rm MTE}$ is the waveform from EMRIs evolution using modified Teukolsky fluxes and $h^{\rm GR}$ denotes to the waveform obtained from the standard GR fluxes.
  • Figure 5: Difference of mismatch as a function of observation time for four initial orbital eccentricitiy $e_0\in\{0.1,0.4,0.85\}$ is plotted, the other parameters are same with Fig. \ref{['Fig:mismatch1']}.