Two-dimensional higher-derivative gravity and conformal transformations
نویسنده
چکیده
We consider the lagrangian L = F (R) in classical (=non-quantized) two-dimensional fourth-order gravity and give new relations to Einstein’s theory with a non-minimally coupled scalar field. We distinguish between scale-invariant lagrangians and scale-invariant field equations. L is scale-invariant for F = c1R k+1 and a divergence for F = c2R. The field equation is scale-invariant not only for the sum of them, but also for F = R lnR. We prove this to be the only exception and show in which sense it is the limit of 1 kR k+1 as k → 0. More generally: Let H be a divergence and F a scale-invariant lagrangian, then L = H lnF has a scale-invariant field equation. Further, we comment on the known generalized Birkhoff theorem and exact solutions including black holes. PACS numbers: 04.20, 04.50
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