Newtonian analogue of a Kerr black hole

Areti, Eleni,; Apostolatos, Theocharis A.

doi:10.1103/physrevd.101.044056

Cited by 16 publications

(10 citation statements)

References 37 publications

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“…A first step towards this direction could be the augmentation of the numerical kludge scheme utilized here, with an effective resonance model, such as the one recently proposed in [77]. Another direction would be to utilize Newtonian analogs, such as the one in [78], to understand the phenomenology of island crossings under instantaneous self-force dissipation, though a Newtonian analog prescription of a non-Kerr spacetime is still lacking.…”

Section: Discussionmentioning

confidence: 99%

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals

Destounis,

Kokkotas

2021

Preprint

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The detection of gravitational waves from extreme-mass-ratio inspirals with upcoming space-borne detectors will allow for unprecedented tests of general relativity in the strong-field regime. Aside from assessing whether black holes are unequivocally described by the Kerr metric, such detections may place constraints on the degree of spacetime symmetry. In particular, depending on exactly how a hypothetical departure from the Kerr metric manifests, the Carter symmetry, which implies the integrability of the geodesic equations, may be broken. Here, we examine the gravitational waveforms associated with non-integrable extreme-mass-ratio inspirals involving a small-mass companion and a supermassive compact object of general relativity, namely the Manko-Novikov spacetime. We show that the waveforms displays sudden frequency jumps, when the companion transverses resonant islands. These findings demonstrate that such abrupt manifestations in the gravitational-wave frequencies are generic, have a genuine astrophysical origin and function as a distinctive signature of chaotic phenomena in extreme-mass-ratio binaries.

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Section: Discussionmentioning

confidence: 99%

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals

Destounis,

Kokkotas

2021

Preprint

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“…Let us also establish a direct correspondence with the discussion of Birkhoff chains in section 2.5.1. If we go back to the initial system (17) and choose a Poincaré section on the plane 10 θ 2 = 0, then from the transformation (18) we get θ 1 = k 1 θ 1 everywhere on the section. This implies that on the surface of section and at the k 1 ω 1 + k 2 ω 2 = 0 resonance there will appear a total of nk 1 islands of stability and nk 1 unstable points.…”

Section: Tools To Study Resonancesmentioning

confidence: 99%

“…Even on the level of a Newtonian and electromagnetic analogue of Kerr, the Carter constant appears to be a unique feature of the Kerr-like Newtonian and electromagnetic fields [36,18,33]. This implies that in the framework of General Relativity any deviation from Kerr spacetime destroys the integrability of the geodesic motion.…”

Section: Deviating Spacetimesmentioning

confidence: 99%

Non-linear effects in EMRI dynamics and their imprints on gravitational waves

Lukes-Gerakopoulos,

Witzany

2021

Preprint

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The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this conservative system is smooth and there are no "topological transitions" in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral. However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play. In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model. Even though many of the developments of this chapter apply to general inspirals, we focus on a particular scenario known as the Extreme mass ratio inspiral (EMRI). An EMRI consists of a compact stellar-mass object inspiralling into a supermassive black hole. At leading order, the referential conservative system is simply geodesic motion in the field of the supermassive black hole and the rate of the drift is given by radiation reaction. In Einstein gravity the supermassive black hole field is the Kerr space-time in which the geodesic motion is integrable. However, the equations of motion can be perturbed in various ways so that prolonged resonances and chaos appear in phase space as well as the inspiral, which we demonstrate in simple physically motivated examples.

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“…With general relativity being a strongly nonlinear theory, chaos is often more visible, either emerging even for systems that are integrable in Newtonian theory, such as the case of a fixed binary system [16,61,73] (also known in Newtonian theory as the "Euler" problem [33,31,32,57,2,30]), or being amplified such as in the case of a Schwarzschild black hole endowed with a quadrupole [42]. Chaos in GR can be studied by investigating the geodesic dynamics of test particles in a given spacetime.…”

Section: Chaotic Orbits In the Hartle-thorne Spacetimementioning

confidence: 99%

Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle-Thorne spacetime

Kostaros,

Pappas

2021

Preprint

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The data from the event horizon telescope (EHT) have provided a novel view of the vicinity of the horizon of a black hole (BH), by imaging the region around the light-ring. They have also raised hopes for measuring in the near future, features of the image (or the shadow) related to higher order effects of photons traveling in these regions, such as the appearance of higher order bright rings produced by more than one windings of photons around the light-ring. While the prospect of measuring these fine features of Kerr BHs is very interesting in itself, there are some even more intriguing prospects for observing novel features of possible non-Kerr objects, in the case that the subjects of our images are not the BH solutions of general relativity. In the hope of sufficient resolution being available in the future, we explore in this work the structure and properties of null geodesics around a Hartle-Thorne spacetime that includes a deformation from the Kerr spacetime characterised by the quadrupole deformation δq. These spacetimes have been found to exhibit a bifurcation of the equatorial light-ring to two off-equatorial light-rings in a range of δqs and spin parameters. In addition to this, there is a range of parameters where both the equatorial and the off-equatorial light-rings are present. This results in the formation of a pocket that can trap photon orbits. We investigate the properties of these trapped orbits and find that chaotic behaviour emerges. Some of these chaotic orbits are additionally found to be "sticky" and get trapped close to periodic orbits for long times. We also explore how these novel features affect the shadow and find that the off-equatorial light-rings produce distinctive features that deform its circular shape, while the chaotic behaviour associated to the pocket creates features with fractal structure.

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Newtonian analogue of a Kerr black hole

Cited by 16 publications

References 37 publications

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals

Non-linear effects in EMRI dynamics and their imprints on gravitational waves

Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle-Thorne spacetime

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