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Area of Science:

  • Theoretical physics
  • General relativity
  • Black hole physics

Background:

  • The behavior of massive vector fields (Proca fields) around black holes is crucial for understanding black hole physics.
  • Separability of field equations simplifies complex calculations in black hole spacetimes.

Purpose of the Study:

  • To demonstrate the separability of the Proca field equation in general Kerr-NUT-AdS black hole spacetimes.
  • To analyze the separated equations and calculate quasinormal modes.

Main Methods:

  • Mathematical derivation of field equation separability in higher-dimensional Kerr-NUT-AdS spacetimes.
  • Analysis of separated equations for the 4D Kerr black hole.
  • Calculation of Proca field quasinormal modes.

Main Results:

  • The Proca field equation is demonstrated to be separable in general Kerr-NUT-AdS black hole spacetimes.
  • Separated equations were derived and analyzed for the 4D Kerr geometry.
  • Quasinormal modes were calculated, showing excellent agreement with prior numerical studies.

Conclusions:

  • The separability of the Proca field equation in these black hole spacetimes is confirmed.
  • The method provides an analytical approach to studying Proca fields and their quasinormal modes.
  • This work bridges a gap in the literature concerning field equation separability in complex black hole geometries.