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Title: Particle motion near high-spin black holes

Abstract

General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Surprisingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. Furthermore, we review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle's polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  2. Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature and Society of Fellows
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
OSTI Identifier:
1596657
Grant/Contract Number:  
SC0009988
Resource Type:
Accepted Manuscript
Journal Name:
Classical and Quantum Gravity
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Journal ID: ISSN 0264-9381
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; black hole; Kerr geodesics; NHEK

Citation Formats

Kapec, Daniel, and Lupsasca, Alexandru. Particle motion near high-spin black holes. United States: N. p., 2019. Web. doi:10.1088/1361-6382/ab519e.
Kapec, Daniel, & Lupsasca, Alexandru. Particle motion near high-spin black holes. United States. doi:https://doi.org/10.1088/1361-6382/ab519e
Kapec, Daniel, and Lupsasca, Alexandru. Tue . "Particle motion near high-spin black holes". United States. doi:https://doi.org/10.1088/1361-6382/ab519e. https://www.osti.gov/servlets/purl/1596657.
@article{osti_1596657,
title = {Particle motion near high-spin black holes},
author = {Kapec, Daniel and Lupsasca, Alexandru},
abstractNote = {General relativity predicts that the Kerr black hole develops qualitatively new and surprising features in the limit of maximal spin. Surprisingly, the region of spacetime near the event horizon stretches into an infinitely long throat and displays an emergent conformal symmetry. Understanding dynamics in this NHEK (Near-Horizon Extreme Kerr) geometry is necessary for connecting theory to upcoming astronomical observations of high-spin black holes. Furthermore, we review essential properties of NHEK and its relationship to the rapidly rotating Kerr black hole. We then completely solve the geodesic equation in the NHEK region and describe how the resulting trajectories transform under the action of its enhanced symmetries. In the process, we derive explicit expressions for the angular integrals appearing in the Kerr geodesic equation and obtain a useful formula, valid at arbitrary spin, for a particle's polar angle in terms of its radial motion. These results will aid in the analytic computation of astrophysical observables relevant to ongoing and future experiments.},
doi = {10.1088/1361-6382/ab519e},
journal = {Classical and Quantum Gravity},
number = 1,
volume = 37,
place = {United States},
year = {2019},
month = {12}
}

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Cited by: 2 works
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Works referenced in this record:

Microscopic origin of the Bekenstein-Hawking entropy
journal, June 1996


The Kerr/CFT correspondence
journal, December 2009


Remarks on the Sachdev-Ye-Kitaev model
journal, November 2016


Conformal symmetry and its breaking in two-dimensional nearly anti-de Sitter space
journal, November 2016

  • Maldacena, Juan; Stanford, Douglas; Yang, Zhenbin
  • Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 12
  • DOI: 10.1093/ptep/ptw124

Observation of Gravitational Waves from a Binary Black Hole Merger
journal, February 2016


First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
journal, April 2019

  • Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter
  • The Astrophysical Journal, Vol. 875, Issue 1
  • DOI: 10.3847/2041-8213/ab0ec7

Force-free electrodynamics around extreme Kerr black holes
journal, December 2014

  • Lupsasca, Alexandru; Rodriguez, Maria J.; Strominger, Andrew
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)185

Towards an understanding of the force-free magnetosphere of rapidly spinning black holes
journal, December 2014


Exact solutions for extreme black hole magnetospheres
journal, July 2015

  • Lupsasca, Alexandru; Rodriguez, Maria J.
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)090

Near-horizon extreme Kerr magnetospheres
journal, January 2016


Near-horizon Kerr magnetosphere
journal, May 2016


Separating metric perturbations in near-horizon extremal Kerr spacetimes
journal, September 2017


Scaling and universality in extremal black hole perturbations
journal, June 2018

  • Gralla, Samuel E.; Zimmerman, Peter
  • Journal of High Energy Physics, Vol. 2018, Issue 6
  • DOI: 10.1007/JHEP06(2018)061

Near-extremal black holes at late times, backreacted
journal, January 2019


Gravity waves from the Kerr/CFT correspondence
journal, August 2014


Gravity waves from extreme-mass-ratio plunges into Kerr black holes
journal, September 2014

  • Hadar, Shahar; Porfyriadis, Achilleas P.; Strominger, Andrew
  • Physical Review D, Vol. 90, Issue 6
  • DOI: 10.1103/PhysRevD.90.064045

Fast plunges into Kerr black holes
journal, July 2015

  • Hadar, Shahar; Porfyriadis, Achilleas P.; Strominger, Andrew
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)078

Whirling orbits around twirling black holes from conformal symmetry
journal, March 2017

  • Hadar, Shahar; Porfyriadis, Achilleas P.
  • Journal of High Energy Physics, Vol. 2017, Issue 3
  • DOI: 10.1007/JHEP03(2017)014

Gravitational waves from plunges into Gargantua
journal, April 2018

  • Compère, Geoffrey; Fransen, Kwinten; Hertog, Thomas
  • Classical and Quantum Gravity, Vol. 35, Issue 10
  • DOI: 10.1088/1361-6382/aab99e

Particle on the innermost stable circular orbit of a rapidly spinning black hole
journal, September 2015

  • Gralla, Samuel E.; Porfyriadis, Achilleas P.; Warburton, Niels
  • Physical Review D, Vol. 92, Issue 6
  • DOI: 10.1103/PhysRevD.92.064029

Inspiral into Gargantua
journal, July 2016


Gravitational waves from a plunge into a nearly extremal Kerr black hole
journal, October 2016


Transient instability of rapidly rotating black holes
journal, October 2016


Self-similar accretion in thin discs around near-extremal black holes
journal, March 2017

  • Compère, Geoffrey; Oliveri, Roberto
  • Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 4
  • DOI: 10.1093/mnras/stx748

Observational signature of high spin at the Event Horizon Telescope
journal, January 2018

  • Gralla, Samuel E.; Lupsasca, Alexandru; Strominger, Andrew
  • Monthly Notices of the Royal Astronomical Society, Vol. 475, Issue 3
  • DOI: 10.1093/mnras/sty039

Photon emission near extreme Kerr black holes
journal, March 2017


Critical emission from a high-spin black hole
journal, March 2018


Global Structure of the Kerr Family of Gravitational Fields
journal, October 1968


Optical caustics in a kerr spacetime and the origin of rapid X-ray variability in active galactic nuclei
journal, January 1994

  • Rauch, Kevin P.; Blandford, Roger D.
  • The Astrophysical Journal, Vol. 421
  • DOI: 10.1086/173625

Frame dragging and bending of light in Kerr and Kerr–(anti) de Sitter spacetimes
journal, October 2005


A fast new Public code for Computing Photon Orbits in a kerr Spacetime
journal, April 2009


Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
journal, June 2009


Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses
journal, April 2011


Bound Geodesics in the Kerr Metric
journal, February 1972


A note on Killing tensors
journal, September 1978

  • Stephani, Hans
  • General Relativity and Gravitation, Vol. 9, Issue 9
  • DOI: 10.1007/BF00760867

On the Reciprocal Modulus Relation for Elliptic Integrals
journal, November 1970

  • Fettis, Henry E.
  • SIAM Journal on Mathematical Analysis, Vol. 1, Issue 4
  • DOI: 10.1137/0501045

Gedanken experiments to destroy a black hole. II. Kerr-Newman black holes cannot be overcharged or overspun
journal, November 2017


Appearance of Keplerian discs orbiting Kerr superspinars
journal, October 2010


Observing black holes spin
journal, January 2019


Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation
journal, December 1972

  • Bardeen, James M.; Press, William H.; Teukolsky, Saul A.
  • The Astrophysical Journal, Vol. 178
  • DOI: 10.1086/151796

Disk-Accretion onto a Black Hole. Time-Averaged Structure of Accretion Disk
journal, July 1974

  • Page, Don N.; Thorne, Kip S.
  • The Astrophysical Journal, Vol. 191
  • DOI: 10.1086/152990

The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole
journal, December 1975

  • Cunningham, C. T.
  • The Astrophysical Journal, Vol. 202
  • DOI: 10.1086/154033

Thin-disc theory with a non-zero-torque boundary condition and comparisons with simulations: Thin-disc theory and simulations
journal, December 2011

  • Penna, Robert F.; Sądowski, Aleksander; McKinney, Jonathan C.
  • Monthly Notices of the Royal Astronomical Society, Vol. 420, Issue 1
  • DOI: 10.1111/j.1365-2966.2011.20084.x

Extreme Kerr throat geometry: A vacuum analog of AdS 2 × S 2
journal, October 1999


Particle dynamics near extreme Kerr throat and supersymmetry
journal, November 2010


Particle Dynamics in Weakly Charged Extreme kerr Throat
journal, May 2011

  • Al Zahrani, A. M.; Frolov, Valeri P.; Shoom, Andrey A.
  • International Journal of Modern Physics D, Vol. 20, Issue 05
  • DOI: 10.1142/S0218271811018986

Warped AdS 3 black holes
journal, March 2009


Third Law of Black-Hole Dynamics: A Formulation and Proof
journal, July 1986


Black hole superradiance from Kerr/CFT
journal, April 2010

  • Bredberg, Irene; Hartman, Thomas; Song, Wei
  • Journal of High Energy Physics, Vol. 2010, Issue 4
  • DOI: 10.1007/JHEP04(2010)019

Kerr-CFT and gravitational perturbations
journal, August 2009


No dynamics in the extremal Kerr throat
journal, September 2009


The Kerr/CFT Correspondence and its Extensions
journal, October 2012


Time evolution of entanglement entropy from a pulse
journal, December 2012


Symplectic and Killing symmetries of AdS3 gravity: holographic vs boundary gravitons
journal, January 2016


Anti-de Sitter fragmentation
journal, February 1999


    Works referencing / citing this record:

    Photon emission near Myers-Perry black holes in the large dimension limit
    journal, January 2020


    Observational signature of a near-extremal Kerr-Sen black hole in the heterotic string theory
    journal, January 2020


    Null geodesics of the Kerr exterior
    journal, February 2020