Two-dimensional higher-derivative gravity and conformal transformations

Details Two-dimensional higher-derivative gravity and conformal transformations Two-dimensional higher-derivative gravity and conformal transformations

1995-01-21

arxiv.org/abs/gr-qc/9501024v1

Class.Quant.Grav.12:849-858,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, latex, no figures, hjschmi@rz.uni-potsdam.de, Class. Quant. Grav. to appear

Scientific paper

10.1088/0264-9381/12/3/021

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 $k\to 0$. 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.

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