Non-existence of a dilaton gravity action for the exact string black hole
Daniel Grumiller and Dmitri Vassilevich
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Submission date: 25. Oct. 2002
published in: Journal of high energy physics, 2002 (2002) 11, art-no. 018
PACS-Numbers: 04.60.-m, 11.25.-w, 04.70.-s
Keywords and phrases: dilaton gravity, strings, black holes
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We prove that no local diffeomorphism invariant two-dimensional theory of the metric and the dilaton without higher derivatives can describe the exact string black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One of the key points in this proof is the concept of dilaton-shift invariance. We present and solve (classically) all dilaton-shift invariant theories of two-dimensional dilaton gravity. Two such models, resembling the exact string black hole and generalizing the CGHS model, are discussed explicitly.