Thin-shell wormhole with a background Kalb-Ramond Field

TL;DR

This work constructs a thin-shell wormhole by cutting and pasting two KR-field–modified black holes, where a non-minimal coupling between the Kalb-Ramond field and the Ricci tensor induces Lorentz-violating effects. The throat is supported by exotic matter, with NEC and WEC violated while the strong energy condition holds, and the shell exhibits dark-energy-like behavior (ω in (-1, -1/3)). A linearized stability analysis shows instability for the conventional speed-of-sound range, and the properties depend on the LV parameters λ and γ in a nuanced way; the study also rules out Casimir-like contributions for the throat and notes possible extensions to light deflection in a Gauss–Bonnet framework. Overall, the paper links string-inspired KR fields to wormhole physics, illuminating the role of LV in throat dynamics and stability, while acknowledging the speculative nature of these objects and suggesting future observational probes.

Abstract

The Kalb-Ramond field is a background tensor field that arises in string theory and violates local Lorentz symmetry of spacetime, upon acquiring the Vacuum Expectation Value. A non-minimal coupling between the Kalb-Ramond VEV and the Ricci tensor may give rise to a modified black hole solution. Considering two copies of such black holes, we construct a thin-shell wormhole using the Cut-and-Paste technique. Then we investigate key physical properties of the wormhole like pressure-density profile, equation of state, the geodesic motion of test particles near the wormhole throat, and the total amount of exotic matter in the throat, and examine how these properties vary with the Lorentz-Violating parameters. We find that the wormhole model violates the null and weak energy conditions, but satisfies the strong energy condition. On top of that, the velocity of the throat radius is found considering its time evolution. Finally, we analyze its linear stability against small radial perturbations.

Figures (12)

• Figure 1: The variation in the metric function $f(r$) with the radial coordinate $r$ is shown. We have taken three sets of values for the LV parameters $\gamma$ and $\lambda$ (which meet our given constraints) and plotted $f(r)$ (solid lines) for five different masses (M varies from $10^9$ to $5.10^9$ Kg) in each of these three cases. The dashed lines represent Schwarzschild Black Holes corresponding to each M, $\gamma$, and $\lambda$. Note that the r-intercepts of $f(r)$ (the points where $f(r)$=0) for each curve are the radial distances at which event horizons form. Since each curve cuts the r-axis at two points, each black hole has two event horizons (inner and outer, occurring at $r_-$ and $r_+$ respectively).
• Figure 2: The variation of the energy density $\bm{\sigma}$ with the throat radius $\bm{a(km)}$, for different masses and LV parameters. We choose typical wormholes whose radii fall within the range of 1 to 10 km. Since $\sigma<0$ from these plots, the first condition for the Weak Energy Condition (WEC) is violated.
• Figure 3: The variation of the thermodynamic pressure $\bm{p}$ with the throat radius $\bm{a(km)}$, for different masses and LV parameters.
• Figure 4: The variation of the $\bm{\sigma+p}$ with the throat radius $\bm{a(km)}$. In all three cases, $(\sigma+p) <0$; i.e., NEC is violated. This picture also provides the second condition for the violation of WEC.
• Figure 5: The variation of the $\bm{\sigma + 3p}$ with the throat radius $\bm{a(km)}$. The plots show that $(\sigma+3p)>0$; i.e., the wormhole satisfies the Strong Energy Condition.