Einstein-Grisaru-Zanon gravity

The leading $(\alpha')^3$-correction to the gravitational low-energy effective action of closed (type II) superstring theory in four-spacetime dimensions defines the Einstein-Grisaru-Zanon gravity action that is applied for a calculation of the leading corrections to the Schwarzschild solution and the Hubble function in the Friedmann-Lemaitre-Robertson-Walker universe, in the first order with respect to the effective string-generated coupling. The solutions found are compared to the corresponding solutions in the Einstein-Bel-Robinson gravity that also modifies the Einstein gravity by the terms quartic in the spacetime curvature. We consider the black hole shadows in the Einstein-Grisaru-Zanon gravity theory and derive the upper bound on the string coupling parameter from the Hawking temperature of a black hole.