Hamilton-Jacobi equation for spinning particles near black holes

Witzany, Vojtěch

doi:10.1103/physrevd.100.104030

Cited by 44 publications

(64 citation statements)

References 93 publications

(124 reference statements)

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“…We can also employ the non-linear oscillator model to estimate the rate at which resonances of a spinning particle near a black hole grow. It has been shown that for MPD equations with the TD SSC to linear order in spin in the Kerr spacetime (of which Schwarzschild is a special case) approximate constants of motion exist that allow for an (approximate) separation of the Hamilton-Jacobi equation (see [18,33]). It is not clear whether this means that no resonances appear at linear-in-spin order.…”

Section: Growth Of Resonancesmentioning

confidence: 99%

“…These equations correspond in general to a non-integrable system, which exhibits chaotic behavior and prolonged resonances [16,17]. However, when MPD are linearized in spin, it appears that under certain conditions they are approximately separable [18]. It is unclear whether this means that chaos and prolonged resonances do not appear at linear order in spin [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

et al. 2020

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Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear.We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source.

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Section: Growth Of Resonancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

et al. 2020

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“…However, due to the long duration of the inspiral they can accumulate to give a measurable phase shift in the waveforms. In the case where the inspiralling object is compact, like a BH or NS, we can deduce a component of the spin [ 246 , 247 ] from the respective waveforms. Some quadrupole terms could be measured for less compact objects [ 239 ].…”

Section: Emris: Ideal Probes Of Black-hole Physicsmentioning

confidence: 99%

Probing the nature of black holes: Deep in the mHz gravitational-wave sky

et al. 2021

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Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo’s telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein’s gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our Universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature.

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“…While chaos has been established to appear at second order in the spin [25], numerical simulations suggest that no chaos occurs at linear order in the spin [25][26][27]. From the solution of the Hamilton-Jacobi equations at linear order in the spin, one can infer that chaotic motion at linear order is negligible [28]. In this paper, we will relate the existence of new quasi-conserved quantities homogeneously linear in the spin to the existence of a new tensorial structure on the background, that we will refer to as a mixed-symmetry Killing tensor.…”

Section: Introductionmentioning

confidence: 99%

Complete set of quasi-conserved quantities for spinning particles around Kerr

Compère

Druart

2022

SciPost Phys.

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We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

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Hamilton-Jacobi equation for spinning particles near black holes

Cited by 44 publications

References 93 publications

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

Probing the nature of black holes: Deep in the mHz gravitational-wave sky

Complete set of quasi-conserved quantities for spinning particles around Kerr

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