Asymmetric thin-shell wormholes in the Kalb-Ramond background: Observational characteristics and extra photon rings

TL;DR

This work studies observational signatures of an asymmetric thin-shell wormhole (ATSW) in Kalb-Ramond (KR) gravity and how to distinguish it from black holes using high-resolution imaging. It develops the KR-field ATSW metric, derives null geodesics and the effective potential, and analyzes photon-sphere radii $r_{ph_i}$ and critical parameters $b_{c_i}$ as functions of charge $Q$ and Lorentz-violation parameter $l$, with fixed masses $M_1$ and $M_2$. Through ray-tracing and transfer-function analysis, the study reveals additional transfer-function branches and extra photon rings unique to the ATSW, whose locations move inward as $Q$ and $l$ increase. Using two thin-disk emission models, it demonstrates distinctive multi-ring structures in ATSW images compared to BHs, offering concrete observational discriminants and showing that the Lorentz-violation parameter $l$ exerts a stronger influence than $Q$ on optical signatures.

Abstract

In this paper, we utilize the ray-tracing method to conduct an in-depth study of the observational images of asymmetric thin-shell wormholes in the Kalb-Ramond field. Initially, we calculate the null geodesics and effective potential energy of the asymmetric thin-shell wormhole, and investigate the variations in the photon sphere radius and critical impact parameter under different values of charge $Q$ and Lorentz-violation parameter $l$. Based on these calculations, we determine the photon deflection angles and trajectories within this space-time structure. Specifically, depending on the photon impact parameters, the photon trajectories can be categorized into three types. By using a thin accretion disk as the sole background light source and incorporating two classical observational radiation models, we find that under conditions of equal mass $M$, charge quantity $Q$, and Lorentz-violation parameter $l$, the asymmetric thin-shell wormholes exhibit unique observational features such as additional lensing rings and photon ring clusters. Furthermore, distinct from black holes, as the charge quantity $Q$ and the Lorentz-violation parameter $l$ increase, the coverage area of the specific additional halo also expands correspondingly.

Figures (14)

• Figure 1: (color online) In spacetime $M_1$, panels (a), (b), and (c) respectively depict the variation of the photon sphere radius $r_{p_{1}}$, impact parameter $b_{c_{1}}$, and the enclosed area $S_{p_{1}}$ of the photon sphere with the Lorentz-violation parameter $l$.
• Figure 2: (color online) In spacetime $M_2$, the variation of the photon sphere radius $r_{p_{2}}$, impact parameter $b_{c_{2}}$, and the area $S_{p_{2}}$ enclosed by the photon sphere with the Lorentz-violation parameter $l$, is depicted in panels (a), (b), and (c), respectively.
• Figure 3: (color online) With Lorentz-violation parameter $l=0.01$, we analyze the effective potential of the BH and ATSW in the KR field as functions of $Q$. The left plot shows the effective potential for BH, while the right plot displays that for ATSW. Various $Q$ values are considered, specifically $Q=$$0,\,0.1,\,0.3,\,0.5$, respectively. In the right plot, the solid and dashed lines correspond to the effective potentials for$M_1$ and $M_2$, respectively, with parameters set as $M_1=1$, $M_2=1.2$, and $R=2.6$.
• Figure 4: (color online)The effective potential energy of BH (with charge $Q=0.3$) and ATSW (with charge $Q=0.3$) in the KR field varies with the value of $l$. On the left, the effective potential energy of BH is depicted, while on the right, that of ATSW is shown. We have designed different $Q$ values and set $l$ to $0$, $0.01$, $0.05$, and $0.1$. In the right figure, the solid and dashed lines represent the effective potential energies of $M_1$ and $M_2$, respectively. Specifically, we have set $M_1$,$M_2$, and $R$ to $1$, $1.2$, and $2.6$, respectively.
• Figure 5: (color online) The influence of the charge $Q$ on photon trajectories in polar coordinates $\left(r_1, \varphi\right)$, specifically for impact parameters in the range $Zb_{c_2}<b_1<b_{c_1}$. The first, second, and third rows correspond to the cases of $Q = 0.1$, $Q = 0.3$, and $Q = 0.5$, respectively. The trajectories are denoted as follows: the red lines represent incident photons in spacetime $M_1$, the green lines represent outgoing photons in spacetime $M_1$, and the blue dashed lines depict the photon trajectories within spacetime $M_2$. The parameters are fixed at $l = 0.01$, $R = 2.6$, $M_2=1$, and $M_2=1.2$.