Backreaction of accreting matter onto a black hole in the Eddington-Finkelstein coordinates

Abstract

We study backreaction of accreting matter onto a spherically symmetric black hole in a perturbative way, when accretion is in a quasi-steady state. General expressions for corrections to the metric coefficients are found in the Eddington-Finkelstein coordinates. It is shown that near the horizon of a black hole, independently of the form of the energy-momentum tensor, the leading corrections to the metric are of the Vaidya form. The relation to other solutions is discussed and particular examples are presented.

12 pages, v.2: references added, typos corrected, matches published version

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• Are black holes a serious threat to scalar field dark matter models?
• Ultra-hard fluid and scalar field in the Kerr-Newman metric
• Galileon accretion
• The spatial relation between the event horizon and trapping horizon
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