Solution of Dirac equation around a spinning Black Hole
Banibrata Mukhopadhyay, Sandip K. Chakrabarti
TL;DR
This paper develops an analytical WKB method to solve the Dirac equation in Kerr spacetime, providing explicit wave functions and reflection/transmission coefficients for spinning black holes.
Contribution
It introduces a WKB approximation approach for the full radial Dirac equation in Kerr geometry, extending previous asymptotic solutions.
Findings
Derived analytical radial wave functions for Dirac particles around Kerr black holes.
Calculated local reflection and transmission coefficients for various Kerr parameters.
Enhanced understanding of fermionic wave behavior in rotating black hole backgrounds.
Abstract
Chandrasekhar separated the Dirac equation for spinning and massive particles in Kerr geometry in radial and angular parts. Chakrabarti solved the angular equation and found the corresponding eigenvalues for different Kerr parameters. The radial equations were solved asymptotically by Chandrasekhar. In the present paper, we use the WKB approximation to solve the spatially complete radial equation and calculate analytical expressions of radial wave functions for a set of Kerr and wave parameters. From these solutions we obtain local values of reflection and transmission coefficients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.