Shadow of regularized compact objects without a photon sphere

TL;DR

This work investigates shadows in Simpson-Visser regularized spacetimes that lack a photon sphere, by applying SV regularization to null singularity and charged null singularity metrics. The analysis shows that shadows can form from central regular cores or wormhole throats, with the SV parameter $L$ controlling the geometry and shadow size; in several cases the shadow size is of order $\sim 3\sqrt{3}\,M$ even when no photon sphere exists. By comparing with EHT observations of Sgr A$^*$ and M87*, the authors constrain $L/M$ and $q/M$ and highlight that photon rings are not unambiguous indicators of photon spheres, which has implications for interpreting strong-field measurements and potential quantum-gravity effects encoded in $L$. The results broaden the set of viable compact-object models compatible with current observations and motivate further observational tests to distinguish between black holes and regularized exotic spacetimes.

Abstract

Recent observations by the Event Horizon Telescope (EHT) indicate that the shadow of the compact object at our Galaxy's center (Sgr A*) closely resembles that of a Schwarzschild black hole. However, identifying the presence and exact location of a photon sphere observationally remains challenging. Motivated by this, we investigate shadow formation in spacetimes that lack a photon sphere by applying the Simpson-Visser (SV) regularization technique (originally designed to smooth black hole singularities) to null singularity and charged null singularity metrics. Remarkably, these regularized null and charged null singularity spacetimes can produce a shadow without a photon sphere. We analyze how the SV regularization parameter influences their geometry and shadow size, and show that the regularized null and charged null singularity spacetimes can correspond either to two-way traversable wormholes or retain singularities. Our results reveal that shadows arising from these regularized 'null singularity spacetimes' closely mimic those of Schwarzschild and charged black-bounce spacetimes, despite the absence of a photon sphere. We also constrain parameters in these geometries using observational data of Sgr A* and M87.

Figures (5)

• Figure 1: In Figs. (\ref{['fig1a']}), (\ref{['fig1b']}), (\ref{['fig1c']}), and (\ref{['fig1d']}) we show the nature of effective potentials of the null geodesics, light trajectory, intensity distribution, and shadow image in black-bounce (SV) spacetime. The effective potential of light-like geodesics for different impact parameters in the black-bounce spacetime is shown in Fig. (\ref{['fig1a']}). In Fig. (\ref{['fig1b']}), the light trajectories in these spacetimes are shown, and the blue lines are the null geodesics. In Figs. (\ref{['fig1c']}) and (\ref{['fig1d']}), the intensity map in observer sky and the shadow of the central object are shown for the black-bounce geometry. The shadow shown in the right bottom corner is the shadow cast by the black-bounce spacetime.
• Figure 2: In Figs. (\ref{['fig2a']}), (\ref{['fig2b']}), (\ref{['fig2c']}), and (\ref{['fig2d']}) we show the nature of effective potentials of the null geodesics, light trajectory, intensity distribution, and shadow image in charged black-bounce (SV) spacetime. Effective potential of light-like geodesics for different impact parameter in charged black-bounce spacetime is shown in Fig. (\ref{['fig2a']}). In Fig. (\ref{['fig2b']}) the light trajectories in these spacetimes are shown, the blue lines are the null geodesics. In Figs. (\ref{['fig2c']}) and (\ref{['fig2d']}), the intensity map in observer sky and the shadow of the central object are shown for charged black-bounce spacetime. The shadow shown in the right bottom corner is the shadow cast by the charged black-bounce spacetime.
• Figure 3: In Figs. (\ref{['fig3a']}), (\ref{['fig3b']}), (\ref{['fig3c']}), and (\ref{['fig3d']}) we show the nature of effective potentials of the null geodesics, light trajectory, intensity distribution and shadow image in modified null singularity spacetime. Effective potential of lightlike geodesics for different impact parameter in modified null singularity spacetime is shown in Fig. (\ref{['fig3a']}). In Fig. (\ref{['fig3b']}) the light trajectories in these spacetimes are shown, the blue lines are the null geodesics. In Figs. (\ref{['fig3c']}) and (\ref{['fig3d']}), the intensity map in observer sky and the shadow of the central object are shown for the modified null singularity spacetime. The shadow shown in the right bottom corner is the shadow cast by the modified null singularity spacetime.
• Figure 4: In Figs. (\ref{['fig4a']}), (\ref{['fig4b']}), (\ref{['fig4c']}), and (\ref{['fig4d']}) we show the nature of effective potentials of the null geodesics, light trajectory, intensity distribution and shadow image in modified charged null singularity spacetime. Effective potential of lightlike geodesics for different impact parameter in modified charged null singularity spacetime is shown in Fig. (\ref{['fig4a']}). In Fig. (\ref{['fig4b']}) the light trajectories in these spacetimes are shown, the blue lines are the null geodesics. In Figs. (\ref{['fig4c']}) and (\ref{['fig4d']}), the intensity map in observer sky and the shadow of the central object are shown for modified charged null singularity spacetime. The shadow shown in the right bottom corner is the shadow cast by the modified charged null singularity spacetime.
• Figure 5: Shadow radius in null regular geometry compared with Sgr $A^{*}$ and M87 for $1\sigma$ and $2\sigma$ constraints derived from the EHT observations are presented in Figs. \ref{['a']} and \ref{['b']} respectively. Shadow radius in charged null regular geometry compared with Sgr $A^{*}$ and M87 for $1\sigma$ and $2\sigma$ constraints derived from the EHT observations are presented in Figs. \ref{['c']} and \ref{['d']} respectively.