## Black to white hole tunneling: An exact classical solution

H. M. Haggard and C. Rovelli

*International Journal of Modern Physics A* **30** (1545015), 2015.

We present a metric that describes conventional matter collapsing into a black hole, bouncing and emerging from a white hole, and that satisfies the vacuum Einstein equations everywhere,

*including in the interior of the black hole and the subsequent white hole*, except for a small compact 4d “quantum tunneling” zone. This shows that a black hole can tunnel into a white hole without violating classical general relativity where this can be trusted. We observe that quantum gravity can affect the metric in a region outside the horizon without violating causality because small quantum effects might pile up over time. We study how quantum theory can determines the bouncing time.DOI: 10.1142/S0217751X15450153

Full text: HaRoBlackHoleTunneling.pdf