Vacuum stress-energy tensor of a massive scalar field in a wormhole spacetime

The vacuum average value of the stress-energy tensor of a massive scalar field with nonminimal coupling $\xi$ to the curvature on the short-throat flat-space wormhole background is calculated. The final analysis is made numerically. It was shown that the energy-momentum tensor does not violate the null energy condition near the throat. Therefore, the vacuum polarization cannot self-consistently support the wormhole.

Figure 1

Plots of $⟨{\varphi }^2⟩a^2$ for $\xi =0$, $\frac{1}{8}$, $\frac{1}{6}$, 0.2, 0.4 from bottom to top are shown in panel (a). The value of the field mass $m$ is fixed: $m=1$. The $⟨{\varphi }^2⟩a^2$ behavior is shown on panel (b) for small distances at the throat. All lines fall down to minus infinity near the throat.

Figure 2

Plots of $⟨{\varphi }^2⟩a^2$ for $m=0$, 1, 2 from bottom to top. The value of $\xi$ is fixed: $\xi =0$.

Figure 3

Plots of $p{a}^4$ for $m=1$ and $\xi =0$, $\frac{1}{8}$, $\frac{1}{6}$, 0.2, 0.3. The thicker the line, the greater is the value of $\xi$.

Figure 4

Plots of $\epsilon a^4$ for $m=1$ and $\xi =0$, $\frac{1}{8}$, $\frac{1}{6}$, 0.2, 0.3 are shown in panel (a). The thicker the line, the greater is the value of $\xi$. The $\epsilon a^4$ behavior is shown on panel (b) for small distances at the throat. All lines fall down to infinity near the throat.

Figure 5

Plots of $(\epsilon +p)a^4$ for $m=1$ and $\xi =0$, $\frac{1}{8}$, $\frac{1}{6}$, 0.2, 0.3 are shown in panel (a). The thicker the line, the greater is the value of $\xi$. The $(\epsilon +p)a^4$ behavior is shown on panel (b) for small distances at the throat. All lines fall down to infinity near the throat.