Chandrasekhar–Page equations

Chandrasekhar–Page equations describe the wave function of the spin-½ massive particles, that resulted by seeking a separable solution to the Dirac equation in Kerr metric or Kerr–Newman metric. In 1976, Subrahmanyan Chandrasekhar showed that a separable solution can be obtained from the Dirac equation in Kerr metric. Later, Don Page extended this work to Kerr–Newman metric, that is applicable to charged black holes. In his paper, Page notices that N. Toop also derived his results independently, as informed to him by Chandrasekhar.

By assuming a normal mode decomposition of the form ${\displaystyle e^{i(\omega t+m\phi )}}$ for the time and the azimuthal component of the spherical polar coordinates ${\displaystyle (r,\theta ,\phi )}$, Chandrasekhar showed that the four bispinor components can be expressed as product of radial and angular functions. The two radial and angular functions, respectively, are denoted by ${\displaystyle R_{+{\frac {1}{2}}}(r)}$, ${\displaystyle R_{-{\frac {1}{2}}}(r)}$ and ${\displaystyle S_{+{\frac {1}{2}}}(\theta )}$, ${\displaystyle S_{-{\frac {1}{2}}}(\theta )}$. The energy as measured at infinity is ${\displaystyle \omega }$ and the axial angular momentum is ${\displaystyle m}$ which is a half-integer.