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The relation between event horizons and trapping horizons is investigated ina number of different situations with emphasis on their role in thermodynamics.A notion of constant change is introduced that in certain situations allows thelocation of the event horizon to be found locally. When the black hole isaccreting matter the difference in area between the two different horizons canbe many orders of magnitude larger than the Planck area. When the black hole isevaporating the difference is small on the Planck scale. A model is introducedthat shows how trapping horizons can be expected to appear outside the eventhorizon before the black hole starts to evaporate. Finally a modifieddefinition is introduced to invariantly define the location of the trappinghorizon under a conformal transformation. In this case the trapping horizon isnot always a marginally outer trapped surface.

The spatial relation between the event horizon and trapping horizon