Rahaman and colleagues, in their work taking cosmic fluid as source, have provided a new class of wormhole solutions under the framework of general relativity. Here, this matter source would supply fuel to construct the exact wormhole spacetime. Their matter sources consists of two non-interacting fluids, as follows: the first one is real matter in the form of perfect fluid and the second one is anisotropic dark energy which is phantom energy type. The mining of this second ingredient can be done from cosmic fluid that is responsible for acceleration of the Universe.
1.1. Energy Conditions
By checking the material compositions comprising the wormhole, whether it will satisfy or not the null energy condition (NEC), weak energy condition (WEC) and strong energy condition (SEC) simultaneously at all points outside the source, they found that the null energy condition (NEC), weak energy condition (WEC) are violated, however, the strong energy condition (SEC) is satisfied marginally. Hence, in their models, the null energy condition (NEC) is violated to hold a wormhole open.
1.2. Equilibrium condition
By obtaining modified TOV equation they showed that, equilibrium stage for the wormhole can be achieved due to the combined effect of 3 forces: gravitational force, hydrostatic force, plus another force due to the anisotropic nature (Fa) of the matter comprising the wormhole.
1.3. Effective gravitational mass
They also calculated effective mass of the wormhole, and found that it was up to radius 8 km from the throat (assuming the throat radius r0 = 4 km) is obtained as Meff = 0.828 km = 0.561 M (where 1 Solar Mass = 1.475 km). They noted from the effective gravitational mass equation that though wormholes are supported by the exotic matter, but the effective mass is positive. This implies that for an observer sitting at large distance could not distinguish the gravitational nature between wormhole and a compact mass M.
1.4. Total gravitational energy
It is known that total gravitational energy of a localized real matter obeying all energy conditions is negative. Naturally, authors would like to know how the gravitational energy behaves for the matters that supply fuel of their wormhole structure.
They found that the total gravitational energy from the throat r0 = 4 to the embedded radial space 1.5r0 = 7 (i.e. a = 1.5) as Eg = 1.9397, which indicates that Eg > 0, in other words, there is a repulsion around the throat. This result is very much expected for constructing a physically valid wormhole.
1.5. Traversability conditions
If the tidal gravitational forces felt by a traveler be reasonably small, then travel through wormhole is possible. It means that, acceleration felt by a traveler should less than the gravitational acceleration at earth surface. In their model, they found that the condition imposed by morris et al.
is automatically satisfied, the traveler feels a zero gravitational acceleration since ν = 0.
Based on the all these observations they concluded that their wormhole model with anisotropic dark energy and real matter is fascinating in several aspects and hence very promising one.
However, they observed in the present investigation that anisotropic dark energy with different energy density and radial pressure may also provide the exotic fuel in constructing the wormhole. So, interpretations within dark energy or other than dark energy is needed for exotic sector of the energy-momentum tensor which can be sought for in a future work.
Reference: Rahaman, F., Ray, S. & Islam, S. Wormholes supported by two non-interacting fluids. Astrophys Space Sci 346, 245–252 (2013). https://link.springer.com/article/10.1007/s10509-013-1423-4 https://doi.org/10.1007/s10509-013-1423-4
Copyright of this article totally belongs to our author S. Aman. One is allowed to reuse it only by giving proper credit either to him or to us.