A nonlinear Klein–Gordon equation on Kerr metrics

Discovering the Kerr and Kerr-Schild metrics

The story of this metric begins with a paper by Alexei Zinovievich Petrov (1954) where the simultaneous invariants and canonical forms for the metric and conformal tensor are calculated at a general point in an Einstein space. This paper took a while to be appreciated in the West, probably because the Kazan State University journal was not readily available, but Felix Pirani (1957) used it as t...

Kerr - Schild Structure and Harmonic 2 - forms on ( A ) dS - Kerr - NUT Metrics

We demonstrate that the general (A)dS-Kerr-NUT solutions in D dimensions with ([D/2], [(D + 1)/2]) signature admit [D/2] linearly-independent, mutually-orthogonal and affinely-parameterised null geodesic congruences. This enables us to write the metrics in a multi-Kerr-Schild form, where the mass and all of the NUT parameters enter the metrics linearly. In the case of D = 2n, we also obtain n h...

Dirac Equation in Kerr Geometry

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 19...

Canonical Hamiltonian formulation of the nonlinear Schrödinger equation in a one-dimensional, periodic Kerr medium.

A canonical Hamiltonian formulation of the nonlinear Schrödinger equation has been derived in this paper. This formulation governs the dynamics of pulse propagation in a one-dimensional, periodic Kerr medium when the frequency content of the pulse is sufficiently narrow relative to a carrier frequency, and sufficiently far removed from a photonic band gap of the medium. Our Hamiltonian is numer...

A Novel Generalized Nonlinear Dispersion Equation for Five-Layer Waveguides with Kerr-like Nonlinearity