Gravitational waves from regular black holes in extreme mass-ratio inspirals

TL;DR

This work investigates gravitational waves from extreme mass-ratio inspirals around a rotating regular (Kerr-like) black hole with an asymptotically Minkowski core, introducing a non-Kerr deviation parameter $\ell$. Using a slow-rotation, PN framework, it derives equatorial eccentric orbital dynamics, computes radiation-reaction driven evolution, and constructs approximate waveforms to quantify dephasing and detectability with LISA. The main result is that LISA can distinguish $\ell$ down to about $10^{-6}$ for favorable EMRIs, with parameter estimation constraining $\ell$ to roughly $10^{-5}$ precision, highlighting the potential to test Kerr-like deviations and the no-hair theorem. The study also emphasizes the need for more complete PN corrections, non-equatorial dynamics, perturbative flux calculations, and Bayesian inference to tighten constraints in future analyses.

Abstract

We analyze a rotating regular black hole spacetime with an asymptotically Minkowski core, focusing on extreme mass-ratio inspiral (EMRIs) where a stellar-mass object inspirals a supermassive black hole under consideration. Such spacetimes are also called Kerr-like spacetimes, which motivate the investigation of black holes beyond general relativity and the test of the no-hair theorem. In the present article, we consider the eccentric equatorial motion of an inspiralling object in the background of a rotating regular black hole. The dynamics generate gravitational waves (GWs) that imply a loss in energy and angular momentum of the orbiting body. In this scenario, as a result of the radiation reaction, we analytically compute the orbital evolution of the moving object. Further, we generate the gravitational waveforms and constrain the non-Kerr parameter through dephasing and mismatch computations using Laser Interferometer Space Antenna (LISA) observations. Our result indicates that LISA can distinguish the effect of the additional non-Kerr/deviation parameter with the parameter as small as $\sim10^{-6}$. The constraint on the parameter in the regular black hole using the Fisher information matrix (FIM) can be obtained within a fraction error of $10^{-5}$. The estimates of our analysis with EMRIs present the possible detectability of Kerr-like geometries with future space-based detectors, and further open up ways to put a stringent constraint on non-Kerr parameters with more advanced frameworks.

Figures (6)

• Figure 1: The plots show the azimuthal (left) and radial (right) dephasings in one year of the observation period. We have taken mass-ratio $q=10^{-5}$ and the fixed initial eccentricity $e_{\textup{in}}=0.2$, together with distinct values of the parameter $\ell$.
• Figure 2: Effect of conservative regular parameter $\ell$ corrections on the long time phase evolution is plotted, including the cases of matched initial orbital parameters and frequencies, the label of "$\rm error$" the difference of two phase for those above cases. The other parameter keep same with the case of Fig. \ref{['dephasing1']}.
• Figure 3: Comparison between the polarizations $h_+$ of four EMRI waveforms for the standard Kerr and rotating regular black hole with a parameter $\ell \in\{10^{-5},10^{-4},5\times 10^{-4}\}$ case. The spin of the rotating regular black hole and the initial orbital parameters are set as $a=0.1, p_0=14, e_0\in\{0.1,0.3\}$ and mass-ratio $q=10^{-5}$ and initial phase $\Phi_{\phi,0}=3.0, \Phi_{r,0}=1.0$. The left panels are the initial stage of the time domain waveforms, the middle panels are time domain waveforms after orbital evolution of two weeks and the right panels denote the time domain waveforms after one month. The three subplots in the top panel show the EMRI waveform setting initial orbital eccentricity $e_0=0.1$, and the bottom panel displays the case of $e_0=0.3$.
• Figure 4: The plots show the mismatch as a function of observation time, which considers the mismatch related to a parameter $\ell \in \{10^{-9},5\times10^{-9},10^{-8},5\times 10^{-8},10^{-7},5\times10^{-7},10^{-6},3\times10^{-6},5\times 10^{-6},10^{-5},5\times10^{-5}\}$ in the left panel and an eccentricity $e_0\in \{0.001,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45\}$ in the right panel. We have taken mass-ratio $q=10^{-5}$ and the fixed initial eccentricity $e_{0}=0.3$ in the left panel, together with the parameter $\ell = 3\times 10^{-6}$ in the right panel. The horizontal black dashed lines denote the detection threshold of mismatch discerned by LISA.
• Figure 5: Mismatch as a function of mass $\log_{10} (M/M_\odot)$ and spin $a$ of regular MBH is plotted, which includes the cases of $\ell=3\times 10^{-6}$ (left panel) and $\ell= 10^{-7}$ (right panel); the mass-ratio is set $q=10^{-5}$. The sub-vertical black dashed lines denote the contour value of mismatches, among which the value $1.25\times 10^{-3}$ of the contour line is just distinguished by LISA.