2025/02/28 by Ernazarov, K. K., Ivashchuk, V. D. · 2 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2503.00244
We consider the 4D gravitational model with a scalar field φ, Einstein and Gauss-Bonnet terms. The action of the model contains a potential term U(φ), Gauss-Bonnet coupling function f(φ) and a parameter ε = ±1 , where ε = 1 corresponds to ordinary scalar field and ε = -1 - to phantom one. Inspired by the recent works of Nojiri and Nashed, we explore a reconstruction procedure for a generic static spherically symmetric metric written in the Buchdal parametrization: ds2 = (A(u))-1du2 - A(u)dt2 + C(u)dΩ2, with given A(u) > 0 and C(u) > 0. The procedure gives the relations for U(φ(u)), f(φ(u)) and dφ/du, which lead to exact solutions to equations of motion with a given metric. A key role in this approach is played by the solutions to a second order linear differential equation for the function f(φ(u)). The formalism is illustrated by two examples when: a) the Schwarzschild metric and b) the Ellis wormhole metric, are chosen as a starting point. For the first case a) the black hole solution with a ``trapped ghost'' is found which describes an ordinary scalar field outside the photon sphere and phantom scalar field inside the photon sphere. For the second case b) the sEGB-extension of the Ellis wormhole solution is found when the coupling function reads: f(φ) = c1 + c0 ( tan ( φ) + (1)/(3) (tan ( φ))3), where c1 and c0 are constants.