Traversable wormholes in the bulge of Milky Way galaxy with Global Monopole Charge
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Regular Article - Theoretical Physics
Traversable wormholes in the bulge of Milky Way galaxy with Global Monopole Charge Susmita Sarkar1,a , Nayan Sarkar1,2,b , Farook Rahaman1,c 1 2
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700032, India Department of Mathematics, Karimpur Pannadevi College, Karimpur, Nadia, West Bengal 741152, India
Received: 15 June 2020 / Accepted: 5 September 2020 / Published online: 22 September 2020 © The Author(s) 2020
Abstract The present work looks for the existence of completely new wormhole geometries in the bulge of the Milky Way galaxy (MWG) situated on the dark matter (DM) density profile followed from MacMillan (MNRAS 76:465, 2017) and Boshkayev and Malafarina (MNRAS 484:3325, 2019) concerned with Global Monopole Charge. The obtained shape function is positively increasing against the radial coordinate and it increases faster with the increasing values of Global Monopole Charge. Moreover, the reported shape function satisfies all the essential criterions and hence it constructs wormhole geometry in the bulge of the MWG. Further, the DM candidate around bulge is suitable to harbor wormhole by violating the null energy condition(NEC) corresponding to three different redshift functions. The striking point of our solution is that for zero Global Monopole Charge the wormholes are asymptotically flat corresponding to the first two choices of redshift functions while for positive values of Global Monopole Charge wormhole becomes non asymptotically flat and Global Monopole Charge also has the crucial effect on the violation of NEC. In our solutions, one can note that the total amount of averaged NEC violating matter in the wormhole spacetime depends on the Global Monopole Charge η. Furthermore, the respective wormhole solutions are in equilibrium positions.
1 Introduction One of the fundamental properties of general relativistic wormhole geometry is that this spacetime is tunnel-like spacetime connecting two widely disconnected regions of a same universe or two different universes and supported by exotic matter, which can characterize by the stress–energy a e-mail:
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tensor of the spreading matter content in the wormhole that violates the null energy condition(NEC) Tμν v μ < 0, where v μ is a null vector [1,2]. Hochberg and Visser [3–5] showed that the wormhole generically violates the NEC after the wormhole throat and they also provided some striking theorems that generalized the Morris–Thorne seminal results on the exotic matter with the help of the theory of embedded hypersurfaces on the Riemann tensor and stress–energy tensor after the wormhole throat radius. The first wormhole solution, Einstein–Rosen bridge, was provided by Einstein and Rosen [6] and it was regarded as a mathematical product because of its non traversable property. Later in the year 1973, Ellis [7] provided a new spherically symmetric wormhole solution with a ghost
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