By George Whitefield
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Extra info for A letter to ... dr. Durell ... occasioned by a late expulsion of six students from Edmund hall
Then, as x → 0, 1 xK → √ . 48) Combining this with Eqs. 46), we have S= When b = 1 , 8π 1 8π √ i d3 x −h K = − 2 r2 u i dψ = − ∆r 2 . 49) we obtain the desired result, Eq. 18). This may be fixed by matching it with the rate exp(−4πM) for emission of the entire mass of the hole. 6. Emissions from the Membrane there is no scale other than the mass of the hole. Since the instanton simply scales the horizon radius, we must have KH = gH = 1 4M throughout the motion. Hence √ the proper length along the stretched horizon, dτ ≡ udψ, must also scale.
The equations of motion are now determined by Hamilton’s equations and the constraint: δH δH δH ˙ =A, =0. 69) In the bulk these equations are simply Maxwell’s equations but, because of the inner boundary, the usually discarded surface terms that arise during integration by parts now need to be canceled. It is easy to show then that the above equations hold only if additional surface terms are added to the Hamiltonian: H = Hout − √ d2 x γ js · A . 5. Hamiltonian Formulation tangential magnetic fields at the stretched horizon.
So too is the region on one side of a null plane in flat space; this is just the infinite-mass limit of a black hole. The region outside the stretched horizon is strictly speaking not dynamically closed since a signal originating in the thin region between the stretched horizon and the true horizon can propagate out beyond the stretched horizon. However, in the limit that the stretched horizon goes to the true horizon, α → 0, this region becomes vanishingly thin so that in this limit, which is in any case assumed throughout, we are justified in restricting the action.