Gravitational Focusing of Non−Relativistic Dark Matter Streams by the Earth.

In this report, we investigate how monochromatic streams of low-velocity dark matter are gravitationally lensed by the Earth. Specifically, it is found that an incoming Dark Matter stream from sufficiently far away, exhibits significant amplification in its original flux at the Earth's surface when is initiated with a speed of 8.8 km s$^{-1}$. The computational evolution of the equations of motion was performed with the Velocity$-$Verlet algorithm with a time$-$discretization parameter of $\Delta t = 0.1$ s.