1995/01/21 by S. Mignemi, Salvatore Mignemi, Hans‐Jürgen Schmidt +1 · 16 citations
Earth and Planetary Sciences · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical field theory #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Einstein #Geometry #Geophysics and Gravity Measurements #Gravitation #Lagrangian #Mathematical analysis #Mathematical physics #Physics #Quantum #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar theories of gravitation #Theoretical physics #f(R) gravity #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/3/021
published in Classical and Quantum Gravity 12(3), 849-857 (IOP Publishing) · 16 pages, latex, no figures, [email protected], Class. Quant. Grav. to appear
arxiv created 1995/01/21 · openalex publication_date 1995/03/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the Lagrangian L=F(R) in classical (i.e. 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 and diverges for . The field equation is scale invariant not only for both of these, but also for . We prove this to be the only exception, and show in what sense it is the limit of as . More generally: let H be a divergence and F a scale-invariant Lagrangian, then has a scale-invariant field equation. Furthermore, we comment on the known generalized Birkhoff theorem and exact solutions including black holes.