Stress-energy tensor of quantized scalar fields in a zero-tidal wormhole

Abstract

To create a static traversable wormhole, exotic matter that meets the Morris-Thorne conditions is required. It is well known that the expectation value of the vacuum stress-energy tensor can violate the null energy condition, and thus has long been considered the best candidate for exotic matter. In this paper, we investigate whether the renormalized stress-energy tensor of a non-minimally coupled massive scalar field in a zero-tidal wormhole can satisfy the Morris-Thorne conditions. Within the Hadamard renormalization framework, we calculate the renormalized stress-energy tensor using the pragmatic mode-sum regularization method recently established by Levi and Ori. By varying the scalar field mass $m_0$ and coupling constant $ξ$, we find that there are three disconnected regions in this two-dimensional parameter space that satisfy the Morris-Thorne conditions. We identify two intervals in the scalar field mass $m_0$, within which the Morris-Thorne conditions cannot be satisfied irrespective of the value of the coupling constant $ξ$. This establishes two mass exclusion regions that constitute a no-go regime for the construction of traversable wormholes.

Figures (6)

• Figure 1: The curve in this figure displays the value of $F_{\text{1tt}}$ for $r=r_0$, $\xi=0$ and $m_0=0$ in the zero-tidal wormhole.
• Figure 2: The curve in this figure displays the value of $F_{\text{1ttreg}}$ for $r=r_0$, $\xi=0$ and $m_0=0$ in the zero-tidal wormhole.
• Figure 3: The curve in this figure displays the value of $H_{\text{1tt}}$ for $r=r_0$, $\xi=0$ and $m_0=0$ in the zero-tidal wormhole.
• Figure 4: The curve in this figure displays the value of $G_{\text{1tt,rem,k}}$ for $r=r_0$, $\xi=0$ and $m_0=0$ in the zero-tidal wormhole.
• Figure 5: The curves in this figure display the numerical values of $\tau_{\text{rem}}$ and $\eta_{\text{rem}}$ for $m_0=0$.