Null geodesic structure for the Barriola–Vilenkin spacetime via k-essence

Based on the work of Chandrasekhar [The Mathematical Theory of Black Holes, Chap. 3, Sec. 20 (Oxford University Press, 1992)], we investigate the null geodesic structure of the emergent Barriola–Vilenkin (BV) spacetime in the context of k-essence theory. For k-essence, the emergent gravity metric is a one-to-one correspondence with the BV metric connected to the Schwarzschild background, where the global monopole charge is replaced by the dark energy density. This equivalence holds specifically for a certain class of k-essence scalar fields that have been constructed by Gangopadhyay and Manna [Eur. Phys. Lett. 100, 49001 (2012)]. We have traced out different trajectories for null geodesic in the presence of dark energy for the k-essence emergent BV spacetime. It is demonstrated that the outcomes deviate from the typical Schwarzschild spacetime owing to the fundamental configuration with a constant dark energy density.