Construction and enlargement of traversable wormholes from Schwarzschild black holes

Analytic solutions are presented which describe the construction of a traversable wormhole from a Schwarzschild black hole, and the enlargement of such a wormhole, in Einstein gravity. The matter model is pure radiation which may have negative-energy density (phantom or ghost radiation) and the idealization of impulsive radiation (infinitesimally thin null shells) is employed.

Figure 1

Penrose diagrams of (a) a Schwarzschild black-hole and (b) a Hayward traversable wormhole [14]. The bold magenta and green lines represent the trapping horizons, ${\partial }_{+}r=0$ and ${\partial }_{-}r=0$, respectively, which constitute the event horizons of the black-hole and the throat of the wormhole. Yellow (light) and gray (dark) quadrants represent past trapped and future trapped regions, respectively. Wavy cyan lines represent the constant-profile radiation supporting the wormhole structure.

Figure 2

Matching domains: ${\eta }_1=1$ (left) and ${\eta }_1=-1$ (right).

Figure 3

Matching domains: ${\eta }_2=1$ (left) and ${\eta }_2=-1$ (right).

Figure 4

Matching domains: ${\eta }_1={\eta }_2=1$ (left) and ${\eta }_1={\eta }_2=-1$ (right).

Figure 5

Penrose diagram of the wormhole-construction model. The wavy blue bold lines represent impulsive radiation with negative-energy density. The region $S$ is Schwarzschild, $V$ is Vaidya and $W$ is static-wormhole. The boundary between $S$ and $V$ corresponds to $z=0$ and the boundary between $V$ and $W$ corresponds to $z=l$.

Figure 6

Penrose diagram of the wormhole-enlargement model. The wavy blue and red bold lines represent impulsive radiation with negative and positive-energy density, respectively. The regions $W1$ and $W2$ are static-wormhole, $V1$ and $V2$ are Vaidya, and $S$ is Schwarzschild. The boundary between $W1$ and $V1$ corresponds to $z=l$, the boundary between $V1$ and $S$ corresponds to $z=0$, the boundary between $S$ and $V2$ corresponds to $w=0$, and the boundary between $V2$ and $W2$ corresponds to $w=l$.

Figure 7

An infinitesimal box across which two radiative impulses (arrows) intersect.