- #1

tom.stoer

Science Advisor

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First I will sketch the standard argument that one should

*not*use the rocket engine and try to accelerate away from the singularity. Then I will try to identify the problematic part of this argument and ask for your comments.

1) For any two points P and Q in spacetime the worldline C

_{PQ}connecting these two points and maximizing proper time τ

_{PQ}= τ[C

_{PQ}] is a geodesic C⁰

_{PQ}.

2) The problem is that once one uses the engine this affects the point at which one will hit the singularity. In an appropriate coordinate system we may have Q = (t,r=0) but Q' = (t', r=0) with t' ≠ t. Therefore we must not refer to a single geodesic connecting P and Q. Now one could try to find a

*different*geodesic C⁰C

_{PQ'}connecting P and Q'. This geodesic would of course maximize the proper time τ

_{PQ'}, but a new geodesic is equivalent to a new initial condition at P. So in the very end with given P and an initial condition at P we cannot say anything about maximizing survival time based on geodesics.

Any comments?

Here's paper that addresses this topic numerically and shows that one can find curves with acceleration with longer survival time larger than for geodesaics.

https://arxiv.org/PS_cache/arxiv/pdf/0705/0705.1029v1.pdf

**No Way Back: Maximizing survival time below the Schwarzschild event horizon**

Authors:

__Geraint F. Lewis__,

__Juliana Kwan__

Abstract: It has long been known that once you cross the event horizon of a black hole, your destiny lies at the central singularity, irrespective of what you do. Furthermore, your demise will occur in a finite amount of proper time. In this paper, the use of rockets in extending the amount of time before the collision with the central singularity is examined. In general, the use of such rockets can increase your remaining time, but only up to a maximum value; this is at odds with the ``more you struggle, the less time you have'' statement that is sometimes discussed in relation to black holes. The derived equations are simple to solve numerically and the framework can be employed as a teaching tool for general relativity.

published in Publications of the Astronomical Society of Australia, Volume 24 Number 2 2007, pp. 46-52.