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Published February 15, 1986 | public
Journal Article Open

Membrane viewpoint on black holes: Properties and evolution of the stretched horizon


This paper derives the ''membrane formalism'' for black holes. The membrane formalism rewrites the standard mathematical theory of black holes in a language and notation which (we hope) will facilitate research in black-hole astrophysics: The horizon of a black hole is replaced by a surrogate ''stretched horizon,'' which is viewed as a 2-dimensional membrane that resides in 3-dimensional space and evolves in response to driving forces from the external universe. This membrane, following ideas of Damour and Znajek, is regarded as made from a 2-dimensional viscous fluid that is electrically charged and electrically conducting and has finite entropy and temperature, but cannot conduct heat. The interaction of the stretched horizon with the external universe is described in terms of familiar laws for the horizon's fluid, e.g., the Navier-Stokes equation, Ohm's law, a tidal-force equation, and the first and second laws of thermodynamics. Because these laws have familiar forms, they are likely to help astrophysicists understand intuitively and compute quantitatively the behaviors of black holes in complex external environments. Previous papers have developed and elucidated electromagnetic aspects of the membrane formalism for time-independent rotating holes. This paper derives the full formalism for dynamical, evolving holes, with one exception: In its present form the formalism is not equipped to handle horizon caustics, where new generators attach themselves to the horizon.

Additional Information

©1986 The American Physical Society Received 20 June 1985 The authors are grateful to Thibaut Damour, Igor Novikov, Roman Znajek, and members of the Caltech Paradigm Society (Ronald Crowley, Douglas Macdonald, Ian Redmount, Wai-Mo Suen, Xiao-He Zhang, and Wojciech Zurek) for many useful discussions, and to Xiao-He Zhang for assistance with some computations. This work was supported in part by the National Science Foundation under Grants Nos. PHY81-06909 and AST82-14126.


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