Manuscript Hawk02-A@1 · Hawk02-A.tex · section · 7fbae745

Power and the quasistatic ledger

Stage 1: the fixed-background comparison object › Power and the quasistatic ledger · lines 418–442

Hawk02-A@1#eq:power, Hawk02-A@1#eq:massledger

For this scalar comparison, provided the sum and integral converge,

P_{sc} (M) = ℓ = 0 \sum^{\infty} (2 ℓ + 1) \int_{0}^{\infty} \frac{ω Γ _{ℓ} ( ω ; M )}{2 π ( e ^{8 π GM ω} - 1 )} d ω .

Finite species or angular cutoffs must be displayed when used. The quasistatic comparison ledger is

M ˙ (u) = - P_{sc} (M (u)), M (u) \geq M_{cut} .

It does not assert that (eq:schwarzschild) with $M$ replaced by $M (u)$ solves the semiclassical Einstein equations.

Displayed formulas in this passage

Hawk02-A@1#eq:power · line 421
$P_{sc} (M) = ℓ = 0 \sum^{\infty} (2 ℓ + 1) \int_{0}^{\infty} \frac{ω Γ _{ℓ} ( ω ; M )}{2 π ( e ^{8 π GM ω} - 1 )} d ω .$
Hawk02-A@1#eq:massledger · line 433
$M ˙ (u) = - P_{sc} (M (u)), M (u) \geq M_{cut} .$