Minimal Extension of Einstein's Theory: The Quartic Gravity

Understand

We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level.

• The extended higher derivative theory, just like Einstein's gravity, has only a massless spin-two graviton about its unique maximally symmetric vacuum.
• The extended theory does not admit the Schwarzschild or Kerr metrics as exact solutions, hence there is no issue of Schwarzschild type singularity but, approximately, outside a source, spherically symmetric metric with the correct Newtonian limit is recovered.
• We also show that for all Einstein space-times, square of the Riemann tensor (the Kretschmann scalar or the Gauss-Bonnet invariant) obeys a non-linear scalar Klein-Gordon equation.