# Non-test-particle dynamics from inside a black hole horizon

It seems to me that most arguments in favor of impossibility of communication from beyond black hole horizon region are based on "test-particle" scenario, where the falling object is (very) light with respect to the black hole mass. Argument is as follows: everything, including gravitation, propagates at speed $$v \le c$$, so it is within future light-cone which (the light-cone) ends-up in singularity. QED.

Does, without exception, this argument hold also for very massive falling objects which importantly contribute by themselves to space-time modification? Imagine a neutron star which is just under the horizon divided into two parts (in non-gravitational way, using e.g. atomic explosion), which then fall separately onto singularity on different trajectories. In alternative scenario the neutron star is not divided....Are alternatives completely hidden to the external observer?

Let me forward a simplistic argument: Imagine the neutron star falls direct on the singularity. In non-divided scenario the neutron star goes quickly away from the horizon and produces no "polar angle" effects on space-time. In "divided" scenario two parts can (in extreme case) make many rotations (so very long time) just under the horizon (almost speed $$c$$) slowly falling. By continuity argument (functions are continuous) I would expect an effect on the horizon which is in their very proximity. And the horizon is an observable to the external viewer... Non-negligible masses do contribute during the fall to the horizon shape - do not they?

• It's not exactly clear what you're saying in the 2nd paragraph, particularly "Imagine a neutron star which is just under the horizon divided into two parts". Do you mean a binary pair of neutron stars, orbiting each other, which have just crossed the event horizon of an existing black hole? – PM 2Ring Apr 3 '19 at 12:50
• But anyway, forget about velocities, think about worldlines. Inside the EH (event horizon), the futureward direction of every worldline leads to the singularity, without exception. (Also, the singularity is not in the past of any worldline). – PM 2Ring Apr 3 '19 at 12:53
• "Imagine a neutron star which is just under the horizon divided into two parts" I mean exactly what I say. Neutron star is divided and parts are throw apart very rapidly. The mechanism is not important (I proposed some nuclear reaction inside the neutron star as an example). – F. Jatpil Apr 3 '19 at 13:04

I don't know about the specific mechanism you're describing, but more generally I'm pretty sure that either this is an open problem or the answer is known to be yes, that sufficiently energetic interactions can recover information from inside the horizon.

Cosmic censorship is an open problem, and in fact I'm not sure that there is agreement on what is the best way to formulate cosmic censorship -- it's more of an open-ended research program. One of the standard ways of trying to find a counterexample to cosmic censorship has been to look for ways to deposit too much charge or angular momentum into a black hole, turning it into a naked singularity. As far as I know people like Veronika Hubeny are still working on this, and last I heard they seemed pretty optimistic about working through the technical difficulties and proving that there are counterexamples to cosmic censorship involving adding too much charge to a black hole.

So unless the goal of Hubeny's research program has been proved to be impossible, it is certainly an open possibility that one can extract information from inside a black hole's event horizon (assuming the information hasn't been lost into the singularity already). The violation of cosmic censorship in this type of scenario eliminates the event horizon entirely.

I was a little confused about this at first because it seemed like it would violate the second law of black hole thermodynamics, i.e., Hubeny's program would be trivially impossible. But there are some assumptions in the statement of the second law, and one of these essentially seems to be that cosmic censorship holds. (See Jacobson, Introductory Lectures on Black Hole Thermodynamics, for this characterization. In Hawking and Ellis's proposition 9.2.7, p. 318, this assumption is probably hidden somewhere in the business about a Cauchy surface and a regular predictable space. I'm not technically adept enough to decode this.)

If there is an argument that the answer is no, and information cannot be recovered from inside the horizon, then I think at a minimum it is going to need a bunch of assumptions, including an energy condition. The nature of these global theorems is that they all assume some energy condition, so I think any argument that purports to answer this in the negative without invoking an energy conditions has to be wrong.

The penrose singularity theorem shows that gravitational collapse and trapped geodesics happen even if you remove the requirements for test particles or spherical symmetry from the standard Schwarzschild arguments.

Similarly, one could make arguments from black hole thermodynamics (i.e., objects emerging from the black hole interior will necessarily decrease the entropy of the universe) to the same effect without making any appeal to test particles or perturbations.

• So the answer is: "The two alternatives are from outside the horizon the same" ? – F. Jatpil Apr 3 '19 at 16:19
• I don't see how these global theorems tell us anything about the question. The OP isn't asking whether a singularity can fail to exist. (And the Penrose singularity theorem doesn't say what kind of singularity exists or where -- only that there must be at least one incomplete geodesic.) The second law of black hole thermodynamics talks about the net change of the area of the horizon, so consistent with it, we could have a process in which information escapes from a black hole, but something else is going on that causes the area to increase. – user4552 Apr 3 '19 at 21:23