Speaker
Description
The $4d$ gravitational model with real scalar field $\varphi$, Einstein and Gauss-Bonnet terms
is considered. The action contains potential term $U(\varphi)$ and Gauss-Bonnet coupling function $f(\varphi)$.
For a special (static) spherically symmetric metric
$ds^2 = \left(A(u)\right)^{-1}du^2 - A(u)dt^2 + u^2 d\Omega^2$
with $A(u) > 0$ ($u > 0$ is a radial coordinate)
we verify and correct the so-called reconstruction procedure suggested by
Nojiri and Nashed. This procedure presents certain implicit relations
for $U(\varphi)$, $f(\varphi)$ which lead to exact solutions
to the equations of motion for a given metric governed by $A(u)$.
Here we apply the procedure to (external) Schwarzschild metric with gravitational radius $2 \mu $ and $u > 2 \mu$. Using ``no-ghost'' restriction (i.e. reality of $\varphi(u)$) we find two family of $(U(\varphi), f(\varphi))$. The first one gives us the Schwarzschild metric defined for $u > 3 \mu$ and the second one describes the Schwarzschild metric defined for $ 2 \mu < u < 3 \mu$ ($3 \mu$ is the radius of photonic sphere). In both cases potential $U(\varphi)$ is negative.
