How to make a traversable wormhole from a Schwarzschild black hole

The theoretical construction of a traversable wormhole from a Schwarzschild black hole is described, using analytic solutions in Einstein gravity. The matter model is pure phantom radiation (pure radiation with negative-energy density) and the idealization of impulsive radiation is employed.

Figure 1

Penrose diagrams of a Schwarzschild black hole and a traversable wormhole [10]. The bold diagonal or vertical lines (magenta and green) represent the trapping horizons, ${\partial }_{+}A=0$ and ${\partial }_{-}A=0$. They constitute the Killing horizons of the black hole and the throat of the wormhole. Bottom (yellow) and top (gray) quadrants represent past trapped and future trapped regions, respectively. Wavy (cyan) lines represent the constant-profile phantom radiation supporting the wormhole structure.

Figure 2

Penrose diagram of the wormhole-construction model. The wavy bold (blue) lines represent impulsive radiation with negative-energy density. The region S is Schwarzschild, V is Vaidya, and W is static-wormhole.

Figure 3

An infinitesimal box around the intersection of two radiative impulses.

Figure 4

Penrose diagram of the wormhole enlargement model. Wavy bold lines represent impulsive radiation with positive (red) or negative (blue) energy density. The regions W1 and W2 are static-wormhole, V1 and V2 are Vaidya, and S is Schwarzschild.