Dirac Equation in Kerr Geometry

TL;DR

This paper reviews the development of the Dirac equation in Kerr geometry, highlighting key solutions and methods used to analyze half-integer spin particles in curved spacetime around rotating black holes.

Contribution

It systematically summarizes historical and recent solutions of the Dirac equation in Kerr geometry, emphasizing the progression of analytical methods and solutions.

Findings

Solutions to the Dirac equation in Kerr geometry are complex and have been progressively developed over decades.

Separation of variables into radial and angular parts has been crucial for solving the Dirac equation in this context.

Recent work provides a more complete understanding of the behavior of spin-half particles in rotating black hole backgrounds.

Abstract

We are familiar with Dirac equation in flat space by which we can investigate the behaviour of half-integral spin particle. With the introduction of general relativistic effects the form of the Dirac equation will be modified. For the cases of different background geometry like Kerr, Schwarzschild etc. the corresponding form of the Dirac equation as well as the solution will be different. In 1972, Teukolsky wrote the Dirac equation in Kerr geometry. Chandrasekhar separated it into radial and angular parts in 1976. Later Chakrabarti solved the angular equation in 1984. In 1999 Mukhopadhyay and Chakrabarti have solved the radial Dirac equation in Kerr geometry in a spatially complete manner. In this review we will discuss these developments systematically and present some solutions.