Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator
arXiv:2207.10658 · doi:10.1088/1361-6382/ac9f9f
Abstract
We consider the massive Dirac equation in the exterior region of the 5-dimensional Myers-Perry black hole. Using the resulting ODEs obtained from the separation of variables of the Dirac equation, we construct an integral spectral representation for the solution of the Cauchy problem with compactly supported smooth initial data. We then prove that the probability of presence of a Dirac particle to be in any compact region of space decays to zero as , in analogy with the case of the Dirac operator in the Kerr-Newman geometry.
arXiv commentMinor corrections and improvements, published version, 15 pages
References in corpus (10)
- Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry
- The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry
- Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry
- Separability of the massive Dirac's equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor
- Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry
- The Massive Dirac Equation in the Kerr Geometry: Separability in Eddington-Finkelstein-type Coordinates and Asymptotics
- Scattering for massive Dirac fields on the Kerr metric
- Self-Adjointness of the Dirac Hamiltonian for a Class of Non-Uniformly Elliptic Boundary Value Problems
- Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
- An Integral Spectral Representation of the Massive Dirac Propagator in the Kerr Geometry in Eddington-Finkelstein-type Coordinates