The Dirac equation in Kerr spacetime, spheroidal coordinates and the MIT bag model of hadrons. (English) Zbl 0795.53076
Summary: The Dirac equation in Kerr spacetime is separated using the rotating tetrad formalism. This allows solutions of the Dirac equation, in flat spacetime, written in oblate and prolate spheroidal coordinates to be extracted. The usual MIT bag boundary condition, \(-i \gamma^ \mu n_ \nu \Psi = \Psi\) is then found to be incompatible with a non-vanishing separated wavefunction except in the spherical limit. However, it is shown that an alternative boundary condition exists that is physically motivated and allows for a nontrivial solution.
MSC:
53Z05 | Applications of differential geometry to physics |
83C20 | Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory |
35Q75 | PDEs in connection with relativity and gravitational theory |