Membrane paradigm

In black hole theory, the black hole membrane paradigm is a useful "toy model" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations. It models a black hole as a thin classically-radiating surface (or membrane) at or vanishingly close to the black hole's event horizon. This approach to the theory of black holes was created by Kip S. Thorne, R. H. Price and D. A. Macdonald.

The results of the membrane paradigm are generally considered to be "safe".

Electrical resistance

Thorne (1994) relates that this approach to studying black holes was prompted by the realisation by Hanni, Ruffini, Wald and Cohen in the early 1970s that since an electrically charged pellet dropped into a black hole should still appear to a distant outsider to be remaining just outside the critical r=2M radius, if its image persists, its electrical fieldlines ought to persist too, and ought to point to the location of the "frozen" image (1994, pp. 406). If the black hole rotates, and the image of the pellet is pulled around, the associated electrical fieldlines ought to be pulled around with it to create basic "electrical dynamo" effects (see: dynamo theory).

Further calculations yielded properties for a black hole such as apparent electrical resistance (pp. 408). Since these fieldline properties seemed to be exhibited down to the event horizon, and general relativity insisted that no dynamic exterior interactions could extend through the horizon, it was considered convenient to invent a surface at the horizon that these electrical properties could be said to belong to.

Hawking radiation

After being introduced to model the theoretical electrical characteristics of the horizon, the "membrane" approach was then pressed into service to model the Hawking radiation effect predicted by quantum mechanics.

In the coordinate system of a distant stationary observer, Hawking radiation tends to be described as a quantum-mechanical particle-pair production effect (involving "virtual" particles), but for stationary observers hovering nearer to the hole, the effect is supposed to look like a purely conventional radiation effect involving "real" particles. In the "membrane paradigm", the black hole is described as it should be seen by an array of these stationary, suspended noninertial observers, and since their shared coordinate system ends at r=2M (because an observer cannot legally hover at or below the event horizon under general relativity), this conventional-looking radiation is described as being emitted by an arbitrarily-thin shell of "hot" material at or just above the critical r=2M radius, where this coordinate system fails.

As in the "electrical" case, the membrane paradigm is useful because these effects should appear all the way down to the event horizon, but are not allowed by GR to be coming through the horizon – blaming them on a hypothetical thin radiating membrane at the horizon allows them to be modelled classically without explicitly contradicting general relativity's prediction that the r=2M surface is inescapable.

In 1986, Kip S. Thorne, Richard H. Price and D. A. Macdonald published an anthology of papers by various authors that examined this idea: "Black Holes: The membrane paradigm".

See also

• Holographic principle
• Black hole complementarity

References

• Price, Richard H. & Thorne, Kip (1988). "The Membrane Paradigm for Black Holes". Scientific American 258 (4): 69–77. doi:10.1038/scientificamerican0488-69. 
• Leonard Susskind, "Black holes and the information paradox", Scientific American, April 1997 (cover story). Also reprinted in the special edition "The edge of physics"
• Kip S. Thorne, R. H. Price and D. A. Macdonald (eds.) "Black Holes: The membrane paradigm" (1986)
• Thorne, Kip, Black Holes and Time Warps: Einstein's Outrageous Legacy, W. W. Norton & Company; Reprint edition, January 1, 1995, ISBN 0-393-31276-3, chapter 11, pp. 397–411