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The Black Hole Membrane Paradigm in f(R) Gravity · Around

2010

The Black Hole Membrane Paradigm in f(R) Gravity

Chatterjee, Saugata, Parikh, Maulik, Sarkar, Sudipta

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To an outside observer, a black hole's event horizon appears to behave exactly like a dynamical fluid membrane.

We extend this membrane paradigm to black holes in general $f(R)$ theories of gravity.
We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity.
Using Euclidean methods, we study the thermodynamics of the membrane.

Built on

Landau, L. D. and Lifshitz, E. M. Fluid mechanics
1959
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Damour, T. “Black-hole eddy currents,” Phys. Rev. D 18
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Thorne, K. S. Price, R. H. and MacDonald, D. A. Black holes: The membrane paradigm
1986
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Wald, R. M, “Black hole entropy is Noether charge,” Phys. Rev. D 48
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Earlier work this paper cites.
Iyer, V. and Wald, R. M. “Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes,” Phys. Rev. D 52
1995
Earlier work this paper cites.

Similar

Parikh, M. K. and Wilczek, F. “An action for black hole membranes,” Phys. Rev. D 58
1998
Cited alongside, same era.
Fox, R. McDonald, A. and Pritchard, P. Introduction to Fluid Mechanics
2004
Cited alongside, same era.
Kovtun, P. Son, D. T. and Starinets, A. O. “Viscosity in strongly interacting quantum field theories from black hole physics,” Phys. Rev. Lett. 94
2005
Cited alongside, same era.
Deruelle, N. Sasaki, M. and Sendouda, Y. “Junction Conditions in f(R) Theories of Gravity,” Prog. Theor. Phys. 119
Original
2008
Cited alongside, same era.

Then

Dyer, E. and Hinterbichler, K. “Boundary Terms, Variational Principles and Higher Derivative Modified Gravity” Phys. Rev. D 79
Original
2009
Later among the works it cites.
Brustein, R and Medved, A.J.M. “The ratio of shear viscosity to entropy density in generalized theories of gravity,” Phys. Rev. D 79
Original
2009
Later among the works it cites.
Sotiriou, T. P. and Faraoni, V. “f(R) Theories Of Gravity,” Rev. of Mod. Phys. (2010) 451; arXiv:0805.1726
Original
2010
Closest in time.
Eling, C. and Oz, Y. “Relativistic CFT Hydrodynamics from the Membrane Paradigm,” JHEP 1002
Original
2010
Closest in time.

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