Jacobi and Lyapunov Stability Analysis of Circular Geodesics around a Spherically Symmetric Dilaton Black Hole

We analyze the stability of geodesic curves in geometry Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing space time a charged hole low energy limit string theory. The analysis is performed by using both linear (Lyapunov) method, as well notion Jacobi stability, based on Kosambi–Cartan–Chern Brief reviews two methods are also presented. After obtaining equations spherical symmetry, we reformulate them two-dimensional dynamic system. considering important geometric invariants that can be used for description this system (the nonlinear and Berwald connections), deviation curvature tensor, respectively. characteristic values tensor specifically calculated, given second derivative effective potential motion. Lyapunov leads to same results. Hence, conclude that, particular case motion circular orbits Gibbons–Maeda–Garfinkle–Horowitz–Strominger, gives equivalent