@article{Schmidt2011,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Gauss-Bonnet lagrangian G lnG and cosmological exact solutions},
  series = {Physical review : D, Particles, fields, gravitation, and cosmology},
  volume    = {83},
  journal   = {Physical review : D, Particles, fields, gravitation, and cosmology},
  number    = {8},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1550-7998},
  doi       = {10.1103/PhysRevD.83.083513},
  pages     = {7},
  year      = {2011},
  abstract  = {For the Lagrangian L = G lnG where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedmann models using a state-finder parametrization. Further we show that among all Lagrangians F(G) this L is the only one not having the form G(r) with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R) theories in two-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n = 4.},
  language  = {en}
}
@article{Schmidt2011,
  author    = {Schmidt, Hans-J{\"u}rgen},
  title     = {Perihelion advance for orbits with large eccentricities in the Schwarzschild black hole},
  series = {Physical review : D, Particles, fields, gravitation, and cosmology},
  volume    = {83},
  journal   = {Physical review : D, Particles, fields, gravitation, and cosmology},
  number    = {12},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1550-7998},
  doi       = {10.1103/PhysRevD.83.124010},
  pages     = {9},
  year      = {2011},
  abstract  = {We deduce a new formula for the perihelion advance Theta of a test particle in the Schwarzschild black hole by applying a newly developed nonlinear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure Theta = c(1) - c(2) ln(c(3)(2) - e(2)) with positive constants c(1,2,3) depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities e < c(3) < 1 showing that Theta -> infinity as e -> c(3).},
  language  = {en}
}