What is the stretched horizon of a black hole? What is the stretched horizon of a black hole? Is it related to the proposed "firewall" at the event horizon?
 A: Stretched horizon is a surface located a short distance outside the true event horizon of a black hole.
This notion is closely related to “membrane paradigm” of black hole physics, which treats the black hole horizon as a physical membrane, possessing such characteristics as temperature, charge density, resistivity, viscosity etc. However the surface of true event horizon is singular from some viewpoints, so in practice it is more convenient to consider instead a stretched horizon: a surface slightly outside the true horizon. Writing equations (boundary conditions) for stretched horizon is easier than for a true one, since this surface is timelike, has a non-degenerate induced metric, and so there is a set of fiducial observers whose worldlines would generate this surface. Such observers would have a finite if large redshift relative to observers at infinity, and physical quantities that are diverging at the true horizon would remain finite at the stretched one.
More details could be found in


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*Price, R. H., & Thorne, K. S. (1986). Membrane viewpoint on black holes: properties and evolution of the stretched horizon. Physical Review D, 33(4), 915, doi, non-paywalled pdf.

*Parikh, M. K., & Wilczek, F. (1998). An action for black hole membranes. Physical Review D, 58(6), 064011, doi, arXiv:gr-qc/9712077.

Is it related to the proposed "firewall" at the event horizon?

As a mathematical gadget, stretched horizon could be useful in considering processes described by purely classical general relativity as well as in discussing quantum effects near the event horizon such as black hole complementarity or firewalls.
