Phantom stars and topology change

In this work, we consider time-dependent dark-energy star models, with an evolving parameter $\omega$ crossing the phantom divide $\omega =-1$. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark-energy star into a wormhole. The criteria for this topology change are discussed and, in particular, we consider a Casimir energy approach involving quasilocal energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark-energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.

Figure 1

Left plot: For this case, we considered the behavior of $\omega =\omega (0,t)$ at the center $r=0$; for the dashed curve we have $\sigma =0.3$ and for the solid curve $\sigma =0.1$. Right plot: For this case, we considered the $\omega =\omega (t,r)$ dependence with $\sigma =0.3$. For both cases, we have assumed the following numerical values: $R=1$, $\delta =1$, ${\omega }_0=3/4$, ${\overline{\omega }}_0=2/3$, and $t_0=8$.

Figure 2

Parameters for a sample stellar model presented in Sec. 3c. Plotted on the vertical axes (from left to right, starting from the top) are $\rho (r,t)$, $T_r^t(r,t)$ $p_r(r,t)$, $p_t(r,t)$, and finally $e^{2\beta (r,t)}$ and $-e^{2\alpha (r,t)}$.

Figure 3

The parameters $\omega (t)$ (left) and $a(t)$ (right) for a sample stellar model presented in Sec. 3c. For this particular evolution, the following values were used: ${\omega }_0=-0.9$, $k_1=0.01$, $a_0=5$, $ϵ=0.1$, $k_0=0.001$, ${\omega }_1=1$.

Figure 4

The figure depicts the null energy condition $\mathrm{NEC}=\rho +p_r+2f$ for the specific model with a nonzero flux term considered in the text.

Figure 5

A Penrose-Carter diagram illustrating the boundary location in a Schwarzschild metric. ${\mathcal{M}}_{+}$ and ${\mathcal{M}}_{-}$ are the two wedges, located in the right and left sectors of a Kruskal diagram, respectively, and bounded by two boundaries $B_{+}$ and $B_{-}$ located in ${\mathcal{M}}_{+}$ and ${\mathcal{M}}_{-}$, respectively. $\Sigma ={\Sigma }_{+}\cup {\Sigma }_{-}$ is a spacelike hypersurface. $H_{+}$ and $H_{-}$ are the future and past horizon, respectively. $S_0$ $(S_0=H_{+}\cap H_{-})$ is the bifurcation surface (wormhole throat), and $S_{+}$ and $S_{-}$ are the two-dimensional boundaries of ${\Sigma }_{+}$ and ${\Sigma }_{-}$, respectively.