whether the radiation flux from the disc could not accelerate test particles and/or collimate them in the direction perpendicular to the disc plane. Hence, consider a test particle moving in the Schwarzschild field and influenced by interaction with radiation described by the null dust energy-momentum tensor of equation (\[Tmunu\]). If the interaction is dominated by Thomson scattering, it is convenient to approximate its effect on the particle in terms of the fraction of transferred radiation momentum, as seen in the particle’s rest frame, i.e., by the equation of motion $$\label{equation-of-motion}
  \frac{{\rm D}u^\mu}{{\rm d}\tau}
        =-\tilde{\sigma}\,(\delta^\mu_\nu+u^\mu u_\nu)\,T^\nu{}_\lambda u^\lambda
        =\tilde{\sigma}\,\Phi^2\hat{E}\,\hat{p}^\mu \,,$$ where $\tau$, $u^\mu$ and $a^\mu={{\rm D}u^\mu}/{{\rm d}\tau}$ are the test-particle proper time, four-velocity and four-acceleration, $(\delta^\mu_\nu+u^\mu u_\nu)$ is the projector onto the particle’s local rest space and $\tilde{\sigma}$ is an effective constant scaling the interaction strength (with dimensions of length); the second version of the right hand side is written in terms of the relative photon energy and momentum with respect to the particle, $\hat{E}\equiv -p_\nu u^\nu$ and $\hat{p}^\mu$, which result from the decomposition $$p^\mu=-u^\mu u_\nu p^\nu+(\delta^\mu_\nu+u^\mu u_\nu)\,p^\nu
        =\hat{E}u^\mu+\hat{p}^\mu \,.$$

Despite the elegant form (\[equation-of-motion\]) of the equation of motion, the expressions for $\hat{E}$ and $\hat{p}^\mu$ make it rather cumbersome to be 