Radiative-transfer variables along a particular null geodesic that intersects a radiating plasma near a Kerr black hole (see Fig. 2). Top: local specific intensity Iν (dashed red curve), which is computed by integrating Eq. (34) in the direction of increasing affine parameter λ, and of the specific intensity seen by the observer, Iν,obs (solid black curve), which is computed by integrating Eq. (37) in the direction of decreasing λ. The intensity is normalized with respect to the observed intensity in both cases, so that we expect both curves to approach unity with continued integration, which is illustrated using the blue guideline. We note that Iν is a non-monotonic function of λ while Iν,obs is a monotonic function of λ. We also notethat for Iν,obs and τν,obs, integration proceeds from right to left in these plots, and that Iν,obs converges much faster than Iν. Bottom: optical depth for the same ray.
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