Two-dimensional higher derivative gravity and conformal transformations

Mignemi, Salvatore; Schmidt, Hans-Jurgen

doi:10.1088/0264-9381/12/3/021

Two-dimensional higher derivative gravity and conformal transformations

Sep 26, 1994

14 pages

Published in:

Class.Quant.Grav. 12 (1995) 849-858

e-Print:

gr-qc/9501024 [gr-qc]

DOI:

10.1088/0264-9381/12/3/021

Report number:

INFN-CA-TH-94-22

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Abstract: (arXiv)

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 = c_1 R\sp {k+1} and a divergence for

F=c_2 R

. The field equation is scale-invariant not only for the sum of them, but also for

F=R\ln R

. We prove this to be the only exception and show in which sense it is the limit of \frac{1}{k} R\sp{k+1} as

k\rightarrow 0

. More generally: Let

H

be a divergence and

F

a scale-invariant lagrangian, then

L= H\ln F

has a scale-invariant field equation. Further, we comment on the known generalized Birkhoff theorem and exact solutions including black holes.

gravitation: action
dimension: 2
transformation: conformal
Einstein equation: solution

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