Possibility of hyperbolic tunneling

Abstract

Traversable wormhole are primarily useful as "gedanken-experiments" and as a theoretician's probe of the foundations of general relativity. In this work, we analyse the possibility of having tunnels in a hyperbolic spacetime. We obtain exact solutions of static and pseudo-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class A. The physical properties and characteristics of these intriguing solutions are explored, and through the mathematics of embedding it is shown that particular constraints are placed on the shape function, that differ significantly from the Morris-Thorne wormhole. In particular, it is shown that the energy density is always negative and the radial pressure is positive, at the throat, contrary to the Morris-Thorne counterpart. Specific solutions are also presented by considering several equations of state, and by imposing restricted choices for the shape function or the redshift function.

7 pages, 1 figure. V2: 8 pages, changes in title and throughout the text; to appear in PRD

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• Influence of Electromagnetic Field on Hyperbolically Symmetric Source
• Non-static hyperbolicallly symmetric fluids
• Characterising exotic matter driving wormhole
• IDEAL characterization of higher dimensional spherically symmetric black holes
• Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation
• An anti-Schwarzshild solution: wormholes and scalar-tensor solutions
• Extension of Buchdahl's Theorem on Reciprocal Solutions
• The variation of G in a negatively curved space-time
• Dynamics of hyperbolically symmetric fluids