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

TL;DR

This paper investigates how non-Kerr, exotic compact objects like Zipoy-Voorhees spacetimes affect gravitational wave signals from extreme-mass-ratio inspirals, revealing unique glitch signatures that could distinguish them from black holes.

Contribution

It demonstrates the impact of Zipoy-Voorhees deformations on orbital dynamics and gravitational waveforms, highlighting potential observational signatures of exotic compact objects.

Findings

Resonant islands cause multiple glitches in gravitational wave signals.

Non-integrability of Zipoy-Voorhees spacetime affects inspiral trajectories.

Glitches could help differentiate exotic objects from black holes.

Abstract

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical 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. The well-established presence of accretion disks and astrophysical environments around supermassive objects can 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 traverse 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.