Just how long can you live in a black hole and what can be done about it?

We study the problem of how long a journey within a black hole can last. Based on our observations we make two conjectures. First, for observers that have entered a black hole from an asymptotic region, we conjecture that the length of their journey within is bounded by a multiple of the future asymptotic ‘‘size’’ of the black hole, provided the spacetime is globally hyperbolic and satisfies the dominant-energy and non-negative-pressure conditions. Second, for spacetimes possessing openR³ Cauchy surfaces (or an appropriate generalization thereof) and satisfying the dominant energy and non-negative-pressure conditions, we conjecture that the length of a journey anywhere within a black hole is again bounded, although here the bound requires a knowledge of the initial data for the gravitational field on a Cauchy surface. We prove these conjectures in the spherically symmetric case. We also prove that there is an upper bound on the lifetimes of observers lying ‘‘deep within’’ a black hole, provided the spacetime satisfies the timelike-convergence condition and possesses a maximal Cauchy surface. Further, we investigate whether one can increase the lifetime of an observer that has entered a black hole, e.g., by throwing additional matter into the hole. Lastly, in an appendix, we prove that the surface area A of the event horizon of a black hole in a spherically symmetric spacetime with an ADM mass M_ADM is always bounded by A≤16πM_ADM², provided that future null infinity is complete and the spacetime is globally hyperbolic and satisfies the dominant-energy condition.