Infall time in the Eddington-Finkelstein metric, with application to Einstein-Rosen bridges

Abstract

The Eddington-Finkelstein metric is obtained from the Schwarzschild metric by a change of the time variable. It is well known that a test mass falling into a black hole does not reach the event horizon for any finite value of the Schwarzschild time variable $t$. By contrast, we show that the event horizon is reached for a finite value of the Eddington-Finkelstein time variable $t^{\prime }$. Then we study in Eddington-Finkelstein time the fate of a massive particle traversing an Einstein-Rosen bridge and obtain a different conclusion than recent proposals in the literature: we show that the particle reaches the wormhole throat for a finite value $t_1^{\prime }$ of the time marker $t^{\prime }$, and continues its trajectory across the throat for $t^{\prime }>t_1^{\prime }$. Such a behavior does not make sense in Schwarzschild time since it would amount to continuing the trajectory of the particle "beyond the end of time."

To appear in International Journal of Modern Physics D

Cited by in corpus (2)

• Closed timelike curves in PT-symmetric wormholes
• Characterization of exotic matter in PT-symmetric wormholes