Advanced Digital Design with the Verilog HDL by Michael D. Ciletti

By Michael D. Ciletti

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A more correct definition of ‘thermal’ radiation is that if the body has an absorption cross section σ (k) for quanta of a certain wavenumber, then the emission rate for the same wavenumber is Γ = σ (k) 1 d3k . 77) The semiclassical radiation from the hole is ‘thermal’ in this sense. But the essential problem that we have is not created by this ‘thermality’, but by the entangled nature of the state. 74), which is very different from ‘thermal’, we face the same problem. 76) for the radiation which is order Sbek .

9 we sketch the evolution in the r − τ diagram that we discussed above. The initial slice is drawn again, with the outgoing wavemode on it. The lines of constant phase are drawn too, but now they do not look like straight lines. We had seen that the horizon itself is an outgoing null geodesic that stays at all times at r = 2GM. The rays starting slightly outside the horizon eventually ‘peel off’ and go to spatial infinity, while those starting slightly inside ‘peel off’ and fall in toward small r.

At each point on the surface, the wavemode is a complex number given by an amplitude and a phase. Let this be an outgoing mode, of the type eik(r−t) at infinity. Take a point A on this spacelike surface, and suppose the phase of the wavemode is eiφ0 at this point. Draw a radial null geodesic through A, going out to infinity. Assign the phase eiφ0 to all points on this null geodesic. Do the same for all points on the initial surface. The amplitude of the wavemode at point A also determines the amplitude at all points along the null geodesic through A, but we should note that in d + 1 spacetime Fig.

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