Although wormholes are still considered hypothetical, recent advances in precision measurements related to black holes have increased the significance for testing viable wormhole models (as black hole mimicker) as well. Studies on various phenomena, such as wormhole merger [43, 44] or their quasinormal modes [45, 46], can be beneficial for capturing wormhole signatures in the cosmos. In principle, one can also detect them through their lensing effects, shadows, Einstein ring etc. [47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62]. Interestingly, signatures like these may also favour the case for modified gravity theories over general relativity.
This paper is organized as follows. The wormhole spacetimes corresponding to our 5D model is introduced in Sect. 2. It contains a brief description of the Wormhole characteristics and the warping factor and embedding diagrams for both wormhole models. In Sect. 3, through analytic approach (wherever possible), dynamical systems analysis and embedding diagrams we built intuitions about the trajectories and corresponding effective potentials. In Sect. 4, we solve the geodesic equations for various initial conditions numerically and presented the geodetic potentials and particle trajectories for both 4D-GEB and 5D-WGEB geometries. Finally, we compare the 4D and 5D models based on our key findings and provide conclusion of this study with a summary of the results in Sect. 5.
Black holes and wormholes are two typical fascinating solutions of General Relativity. Recently, progress in astrophysical experiments has attracted a lot of interest in black hole physics. Two breakthroughs in this field are the first image of a black hole with the Event Horizon Telescope [1,2,3] and the observation of gravitational waves from a binary black hole merger . Especially, there is a growing number of detected cases of GWs reported by LIGO Scientific Collaboration and Virgo Collaboration [5,6,7], which provides a lot of concrete examples to study the properties of black holes. 2b1af7f3a8