Energy transfer in the collision of two scalar wave packets in spherical symmetry

Abstract

We study the collisions of two scalar wave packets in the asymptotically flat spacetime and asymptotically anti-de Sitter spacetime in spherical symmetry. An energy transfer formula is obtained, $y=Cm_{i}m_{o}/r$, where $y$ is the transferred energy in the collisions of the two wave packets, $m_i$ and $m_o$ are the Misner-Sharp energies for the ingoing and outgoing wave packets, respectively, $r$ is the areal radius and collision place, and $C=1.873$ and $C=1.875$ for the asymptotically flat spacetime and asymptotically anti-de Sitter spacetime circumstances, respectively. The formula is universal, independent of the initial profiles of the scalar fields.