New features of circular geodesics in Kalb–Ramond gravity: an autonomous dynamical system approach

Abstract Kalb–Ramond gravity is expected to show the signatures of the low energy limit of the Lorentz violating extension of the standard model of particle physics. To understand the theory further, we study the circular geodesics belonging to a class of exact solutions [found recently by Lessa, Silva, Maluf, Almeida (LSMA)] by posing them as a Hamiltonian dynamical autonomous system. The analysis on the phase space for relevant values of the Lorentz violating parameters reveals for the first time a wealth of novel information that include prediction of homoclinic orbits, saddle points, separatrices that are not available from the conventional analysis. Their image on the actual physical space is discussed.