Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers

Abstract

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.

Resonant dynamics of extreme mass-ratio inspirals in a perturbed Kerr spacetime

“…The near-resonance orbits can be classified into three categories: orbits in the rotation regime (blue line), chaotic transitional orbits (orange line), and orbits in the libration regime (green horizontal line). Similar features in the rotation curve have been found in previous studies on various non-Kerr metrics (see, e.g., [38][39][40][41][42][43][44][45][46][47][48]). These features (including both the plateau and jumps in the rotation curve) were believed to be the signatures of chaos.…”

“…In the resonant regime, i.e., kΩ r þ mΩ ϕ þ nΩ θ ≈ 0 for k; m; n ∈ Z, where Ω r;θ;ϕ are geodesic orbital frequencies in r; θ; ϕ directions, the KAM theorem no longer applies and orbital chaos can occur. In fact, signatures of chaotic orbits near resonances have been observed in studies of various modified Kerr spacetimes [38][39][40][41][42][43][44][45][46][47][48][49], e.g., in the vertical jumps of rotation numbers and volume-filling features in the phase space of the trajectory. A plateau in rotation number is sometimes observed, which should be associated with the resonant islands in the phase space.…”

“…II. This Hamiltonian governs the essential dynamics of the EMRI system within the resonant islands (commonly referred to as the "libration" regime for planetary systems), and it applies for generic metric perturbations h, including all the specific examples mentioned in previous studies [38][39][40][41][42][43][44][45][46][47][48][49]. The physical essence of this effective Hamiltonian-similar to the cases of mean motion resonances widely studied in planetary systems-is that there is a single resonant d.o.f.…”