Narrow Results

It is well-known that traversable wormholes are valid solutions of the Einstein field equations, but these structures can only be maintained by violating the null energy condition. In this paper, we have obtained such wormhole solutions in an isothermal galactic halo, as well as in a void. We have shown that the null energy condition is violated, with the help of a suitable redshift function obtained from flat galactic rotation curves.

The concept of dark matter has been imported to explain the observed velocity profile of the spiral galaxies, the flat rotational velocity. Taking the flatness of rotation curves as an input and assuming that the galactic halo is filled with charged perfect fluid having known mass density function, we obtain a space time metric in the galactic halo region. The acquired solution indicates to a (nearly) flat universe, consistent with the present day cosmological observations. Various other aspects of the solution such as attractive gravity in the halo region, stability of the circular orbit, etc., are also analyzed.

The concept of dark matter (DM) hypothesis comes out as a result from the input of the observed flat rotational velocity. With the assumption that the galactic halo is pseudo-spheroidal and filled with charged perfect fluid, we have obtained a solution which has inkling to a (nearly) flat universe, compatible with the modern day cosmological observations. Various other important aspects of the solution such as attractive gravity in the halo region and the stability of the circular orbit are also explored. Also, the matter in the halo region satisfies the known equation of state which indicates its non-exotic nature.

Using the observed flat galactic rotation curve feature and taking into account the presence of anisotropic dark matter with a Hernquist density profile, the space-time geometry of the halo region in galaxies is derived. The gravitational field inside the halo is attractive in nature, and the resultant space-time is flat. We find that our solution affirms the existence of stable circular orbits in the dark halo region. The expression for the equation of state parameter indicates that the matter within the dark halo is non-exotic in nature. An analysis is also conducted on several other aspects of the solution.

Based on the widely recognized Karmarkar condition, or embedding class 1 technique, this work searches for charged wormhole solutions with spherical symmetry for the Einstein field equations. With charged traversable wormhole geometry, we use the Karmarkar condition to derive a wormhole shape function. The obtained shape function satisfies the necessary traversability conditions. In addition, we discuss the embedding diagram in Euclidean space, in both two and three dimensions, and verify the proper radial distance to display the wormhole configurations. Next, we examine a model with a quintessence field and a second field that represents regular matter and has an anisotropic pressure, providing energy for developing wormhole spacetime. Then, we obtain the Einstein field equations to verify the energy conditions. After that, we take three density profiles, which are the pseudo-isothermal density profile, the Navarro–Frenk–White density profile, and the density profile of Einasto Dark Matter of the galactic halo, and observe that for all of these density profiles, the NEC is violated. Hence, wormhole structures are firmly maintained by the composition of exotic matter within them. Furthermore, we use the volume integral quantifier to determine the necessary quantity of exotic matter near the wormhole throat.