The evolutions of spinning bodies moving in rotating black hole - - PowerPoint PPT Presentation

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The evolutions of spinning bodies moving in rotating black hole - - PowerPoint PPT Presentation

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The evolutions of spinning bodies moving in rotating black hole spacetimes Zoltn Keresztes Balzs Mikczi Department of Theoretical Physics, University of Szeged Research Institute for Particle and Nuclear Physics, Wigner RCP The work

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The evolutions of spinning bodies moving in rotating black hole spacetimes

Zoltán Keresztes Balázs Mikóczi

Department of Theoretical Physics, University of Szeged Research Institute for Particle and Nuclear Physics, Wigner RCP

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

  • The work of Z. K. was supported by the UNKP-18-4 New National Excellence Program of the Ministry of Human Capacities,

and by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences

  • The work of B. M. was supported by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences
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Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Mathisson-Papapetrou-Dixon Eqs.

Description of extended body with multipole moments:

(antisymmetric)

Kinematical mass: Dynamical mass: ( )

  • M. Mathisson, Acta. Phys. Polon. 6, 163 (1937).
  • A. Papapetrou, Proc. Phys. Soc. 64, 57 (1951).
  • W. Dixon, Nuovo Cim. 34, 317 (1964).
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Spin Supplementary Conditions (SSCs)

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Frenkel-Mathisson-Pirani (FMP) SSC Tulczyjew-Dixon (TD) SSC Constants: Constants: Velocity-momentum relation: Velocity-momentum relation:

L.F.O. Costa, G. Lukes-Gerakopoulos, O. Semerák, Phys. Rev. D 97, 084023 (2018).

  • J. Frenkel, Z. Phys. 37, 243 (1926).
  • M. Mathisson, Acta. Phys. Polon. 6, 163 (1937).

F.A.E. Pirani, Acta Phys. Polon. 15, 389 (1956). W.M. Tulczyjew, Acta Phys. Polon. 18, 393 (1959).

  • W. Dixon, Nuovo Cim. 34, 317 (1964).
  • O. Semerák, Mon. Not. Roy.
  • Astron. Soc. 308, 863 (1999).
  • O. Semerák, Mon. Not. Roy.
  • Astron. Soc. 308, 863 (1999).

K.P. Tod, F. de Felice, Il Nouvo Cimento 34, 365 (1976).

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Spin vectors with SSCs

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Spin vector: Spin vector: Frenkel-Mathisson-Pirani (FMP) SSC Tulczyjew-Dixon (TD) SSC Spin magnitude: Orthogonality relations: Equation of motion: Spin magnitude: Orthogonality relations: Equation of motion:

  • O. Semerák, Mon. Not. Roy. Astron. Soc. 308, 863 (1999).

, , , ,

  • The case of negligible acceleration

was investigated in Ref.

  • D. Bini, A. Geralico, R.T. Jantzen,
  • Phys. Rev. D 95, 124022 (2017).
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Kerr spacetime

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Line element squared:

Stationary limit surfaces: Constants of motion: Event horizons:

  • R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
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Rotating Bardeen-like and Hayward-like spacetimes

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Line element squared:

, Bardeen-like Hayward-like

  • B. Toshmatov, Z. Stuchlík, B. Ahmedov, Phys. Rev. D 95, 084037 (2017).
  • B. Toshmatov, Z. Stuchlík, B. Ahmedov, Phys. Rev. D 95, 084037 (2017).
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Comoving and zero 3-momentum frames

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Comoving frame: zero 3-momentum frame: TD SSC FMP or TD SSC SO: ZAMO: SO frame vectors: Boost transformation: Boost transformation: ( )

Related by a spatial rotation in U-frame:

( )

Rotation angle:

  • D. Bini, A. Geralico, R.T. Jantzen,
  • Phys. Rev. D 95, 124022 (2017).

, , ZAMO frame vectors:

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https://www.ligo.org/detections/GW170817.php https://www.ligo.org/detections/GW170817.php

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Spin equations in comoving and zero 3-momentum frames

FMP SSC: TD SSC: TD SSC: TD SSC:

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Cartesian-like triads

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

SO frame: Boosted SO frame: Boosted ZAMO frame: ZAMO frame:

  • D. Bini, A. Geralico, R.T. Jantzen,
  • Phys. Rev. D 95, 124022 (2017).
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Evolution equations for Cartesian-like triad components of the spin

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

FMP SSC: TD SSC: In the U-frame: ( ) ( , )

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Spherical-like orbits (Kerr BH)

Coordinate space:

Increasing spin magnitude

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Spherical-like orbits (Kerr BH)

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Increasing spin magnitude

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Unbound orbits

Initial spin directions are different.

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In boosted ZAMO frame

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

In boosted SO frame

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Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Rotation angle between the boosted SO and ZAMO frames (In the left side hand case)

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Precessional angular velocity Blue in boosted SO frame Red in boosted ZAMO frame

Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

(In the left side hand case) diverges

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Blue in boosted SO frame Red in boosted ZAMO frame

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Zoom-whirl orbits (Kerr and regular BHs)

Kerr BH Bardeen-like BH Hayward-like BH

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Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics 2019

Precessional angular velocity Kerr BH Bardeen-like BH Hayward-like BH

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Thank you for the attention

  • The work of Z. K. was supported by the UNKP-18-4 New National Excellence Program of the Ministry of Human Capacities,

and by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences

  • The work of B. M. was supported by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences