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The Volume of 2D Black Holes

Daniel Grumiller
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Abstract

It is shown that the definition for the volume of stationary black holes advocated in hep-th/0508108 readily generalizes to the case of dilaton gravity in D=2. The dilaton field is included as part of the measure. A feature observed in D=3 and 4 has been the impossibility to obtain infinite volume while retaining finite area without encountering some kind of pathology. It is demonstrated that this also holds in D=2. Consistency with spherically reduced gravity is shown. For the Witten black hole it is found that the area is proportional to the volume.

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Daniel Grumiller. 2005-09-20. The Volume of 2D Black Holes. https://doi.org/10.1088/1742-6596%2F33%2F1%2F044

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