Daemon sub Ponte: The Cost of a Second Black Hole (A Scholium on an ER=EPR Thought Experiment)

Abstract

A thought experiment in the ER=EPR and related literature involves collecting the Hawking radiation of an old black hole, then collapsing it into a second, entangled black hole. In this short note, we examine the resources required by this idealized conversion. More specifically, we are interested in answering the question: how much external energy is needed to form the second black hole? Assuming a semiclassical bound on the information capacity of the newly formed black hole, we derive a conditional lower bound on external energy and a complementary constraint on correlations retained by the exterior degrees of freedom. We also distinguish entropy-level feasibility from the requirements for exact and approximate purification. We illustrate these requirements via a Page curve analysis.