Abstract
Wormhole solutions in classical general relativity are unstable and hence non traversable. Morris and Thorne discovered a traversable wormhole solution that required the energy momentum tensor of matter sources to violate various energy conditions and are out of the purview of the standard model of particle physics. The search for traversable wormhole solutions in modified theories of gravity has been of significant interest in the decades after Morris and Thorne first published their results as such violations may be avoided in such theories. This work comprehensively reviews traversable wormhole solutions in higher dimensional extensions of general relativity that satisfy the various energy conditions with an in depth look at the matter sources and the various constraints on the parameters of the theories to make the energy momentum of the matter sources respect the energy conditions.
Highlights
Wormhole solutions to the Einstein’s Field Equations (EFE) have been studied since the early days of the General Theory of Relativity (GTR)
Einstein and Rosen in their seminal 1935 work [3] tried to develop a unified theory of electromagnetism and gravity and therein were the first to interpret such a solution as two asymptotically flat regions of space-time connected by a tube or ‘bridge’
The costraints on the metric parameters of the Morris-Thorne wormhole discussed above, demands an abnormally high tension at the throat where it is required that τ0 > ρ0c2. This means an observer moving through the throat with arbitrarily high velocities, observes a negative density of mass energy which is unphysical. This is the violation of the Weak Energy Condition (WEC) ρ = TμνXμXν ≥ 0, where X is any time-like vector field and Tμν is the Energy Momentum Tensor (EMT) of the matter source
Summary
Wormhole solutions to the Einstein’s Field Equations (EFE) have been studied since the early days of the General Theory of Relativity (GTR). This means an observer moving through the throat with arbitrarily high velocities, observes a negative density of mass energy which is unphysical This is the violation of the Weak Energy Condition (WEC) ρ = TμνXμXν ≥ 0, where X is any time-like vector field and Tμν is the Energy Momentum Tensor (EMT) of the matter source. In modified theories of gravity, as the structure of the field equations are different from those in classical General Relativity, a violation of the Null Convergence Condition Rμνkμkν ≥ 0 (which all Lorentzian wormholes violate) does not necessarily lead to a violation of the Null Energy Condition (NEC) and spherically symmetric wormhole solutions have been extensively studied in theories such as f (R) Gravity [14, 15]. We hereafter use natural system of units where the constants such as G, c etc. have been set to unity. the metric signature under consideration in the rest of the paper is (−, +, +, +)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
