Constructing spherical traversable wormholes: an initial value approach

Details Constructing spherical traversable wormholes: an initial value approach Constructing spherical traversable wormholes: an initial value approach

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cqgra..26j5011g&link_type=abstract

Classical and Quantum Gravity, Volume 26, Issue 10, pp. 105011 (2009).

Computer Science

3

Scientific paper

The construction of {\bb R}^{2}\times S^{2} spherical wormholes is formulated as an initial value problem with the throat serving as an initial value surface. We model exotic matter with a stress tensor that relative to the orthonormal frame of Killing observers reduces to a diagonal form. This assumption combined with staticity, spherical symmetry and a (2 + 1 + 1) decomposition of Einstein's equations yields a set of first-order, coupled ordinary differential equations and an algebraic constraint. The dynamical equations involve the gradient Λ of the red-shift factor, the tension τ, the area A and the extrinsic curvature K of the SO(3) orbits as embedded on the hypersurfaces orthogonal to the timelike Killing field. The throat dictates a set of initial conditions which in combination with the dynamical equations yield a well-defined initial value problem. We study this initial value problem for the special case where the energy density ρc2 and Λ are a priori specified. Provided that ρc2 does not become large and positive over extended domains, we demonstrate the global existence of asymptotically flat, {\bb R}^{2}\times S^{2} wormholes have a throat of prescribed area A(0). For any density profile decaying according to ρc2 = O(r-(2+epsilon)), where r is a radial coordinate tied to an asymptotic cartesian system, the resulting wormhole has finite Komar mass MK, but diverging ADM mass MADM. Finiteness of MADM requires \rho c^{2}=O(r^{-(3+\epsilon)}), \epsilon\gt\frac{1}{2} . Besides this discrepancy, the non-trivial topology of the spacelike hypersurfaces orthogonal to the Killing fields, inserts an element of ambiguity in the definition of the Komar mass originating in the inability to normalize simultaneously the timelike Killing vector at both asymptotically flat ends.

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