On a Reconstruction Procedure for Special Spherically Symmetric Metrics in the Scalar-Einstein–Gauss–Bonnet Model: the Schwarzschild Metric Test

Abstract: The 4D gravitational model with a real scalar field, Einstein and Gauss–Bonnet terms is considered. The action contains the potential and the Gauss–Bonnet coupling function. For a special static spherically symmetric metric, with (is a radial coordinate), we verify the so-called reconstruction procedure suggested by Nojiri and Nashed. This procedure presents certain implicit relations for and which lead to exact solutions to the equations of motion for a given metric governed by. We confirm that all relations in the approach of Nojiri and Nashed for and are correct, but the relation for contains a typo which is eliminated in this paper. Here we apply the procedure to the (external) Schwarzschild metric with the gravitational radius and. Using the “no-ghost” restriction (i.e., reality of), we find two families of. The first one gives us the Schwarzschild metric defined for, while the second one describes the Schwarzschild metric defined for (is the radius of the photon sphere). In both cases the potential is negative. © Pleiades Publishing, Ltd. 2024.