Schwarzschild-Like Wormholes as Accelerators

In a stationary spacetime $S$ consider a pair of free falling particles that collide with the energy $E_{\rm c.m.}$ (as measured in the center-of-mass system). Let the metric of $S$ or/and the trajectories of the particles depend on a parameter $k$. Then $S$ is said to be a "(super) accelerator" if $E_{\rm c.m.}$ grows unboundedly with $k$, even though the energies of the particles at infinity remain bounded. The existence of naturally occurring super accelerators would make it possible to observe otherwise inaccessible phenomena. This is why in recent years a lot of spacetimes were tested on being super accelerators. In this paper a wormhole $W$ of an especially simple---and hence, hopefully, realistic---geometry is considered: it is static, spherically symmetric, its matter source is confined to a compact neighbourhood of the throat, and the $tt$-component (in the Schwarzschild coordinates) of its metric has a single minimum. It is shown that such a wormhole is a super accelerator with $k\equiv \frac 13\ln |g_{tt\ \mathrm{min}}|$. In contrast to the rotating Teo wormhole, considered by Tsukamoto and Bambi, $W$ cannot accelerate the collision products on their way to a distant observer. On the other hand, in contrast to the black hole colliders, $W$ does not need such acceleration to make those products detectable.