Flux module

API

The time-averaged rate of change of the orbital energy \(\langle \dot{E}\rangle\), angular momentum \(\langle \dot{L}_z\rangle\), and Carter constant \(\langle \dot{Q}\rangle\) can be expressed in terms of the Teukolsky amplitudes \(Z^\mathrm{Up/In}_{sjmkn}\),

\[\begin{split} \begin{align} \langle \dot{\mathcal{J}} \rangle & = \langle \dot{\mathcal{J}} \rangle^\mathrm{inf} + \langle \dot{\mathcal{J}} \rangle^\mathrm{hor}, \\ &= \sum_{jmkn} \langle \dot{\mathcal{J}} \rangle^\mathrm{inf/hor}_{jmkn}, \\ &= \sum_{jmkn} \alpha_{sjmkn}^{(\mathcal{J})\mathrm{inf/hor}}\left| Z^\mathrm{Up/In}_{sjmkn} \right|^2, \end{align}\end{split}\]

where \(\mathcal{J} = (E, L_z, Q)\), \(\alpha_{sjmkn}^{(\mathcal{J})\mathrm{inf}/\mathrm{hor}}\) are known coefficients, and \(s=0, \pm 2\) produce either scalar or gravitational fluxes, respectively.

The FluxMode class takes as input an instances of the Kerr geodesic class and the Teukolsky class for a mode \((s,j,m,k,n)\), and produces the flux contribution for that given mode.