Membrane paradigm
Encyclopedia
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".
).
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.
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".
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
theory, the black hole membrane paradigm is a useful "toy model
Toy model
In physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....
" method or "engineering approach" for visualising and calculating the effects predicted by quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
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
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...
. This approach to the theory of black holes was created by Kip S. Thorne
Kip Thorne
Kip Stephen Thorne is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists...
, R. H. Price
Richard H. Price
Richard H. Price is an American physicist specializing in general relativity.Price graduated from Stuyvesant High School in 1960, and went on to earn a dual degree in physics and engineering from Cornell University in 1965. He earned his Ph.D. in 1971 from Caltech under the supervision of Kip...
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 theoryDynamo theory
In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time...
).
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 radiationHawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
effect predicted by quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
In the coordinate system of a distant stationary observer, Hawking radiation tends to be described as a quantum-mechanical particle-pair production
Pair production
Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...
effect (involving "virtual" particles
Virtual particle
In physics, a virtual particle is a particle that exists for a limited time and space. The energy and momentum of a virtual particle are uncertain according to the uncertainty principle...
), 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
Paradigm
The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...
", 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
Richard H. Price
Richard H. Price is an American physicist specializing in general relativity.Price graduated from Stuyvesant High School in 1960, and went on to earn a dual degree in physics and engineering from Cornell University in 1965. He earned his Ph.D. in 1971 from Caltech under the supervision of Kip...
and D. A. Macdonald published an anthology of papers by various authors that examined this idea: "Black Holes: The membrane paradigm".