⚛️ general relativity

Optical appearance of regularized compact objects without an exterior photon sphere

This paper demonstrates that regularized compact objects lacking an exterior photon sphere can produce shadow appearances indistinguishable from Schwarzschild black holes, with their dark regions determined by the regular core rather than unstable photon orbits, while remaining consistent with Event Horizon Telescope observations of Sgr A* and M87.

Original authors: Ashok B. Joshi, Vishva Patel, Parth C. Varasani

Published 2026-07-28

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ashok B. Joshi, Vishva Patel, Parth C. Varasani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic stage where gravity is the ultimate director, bending light and time into shapes we can barely imagine. For decades, astronomers have been hunting for the most extreme actors on this stage: black holes. These are regions so dense that not even light can escape their grasp, leaving behind a perfect, dark circle in the sky known as a "shadow." But to understand these shadows, scientists usually look for a specific feature called a "photon sphere." Think of this like a cosmic racetrack right outside the black hole where light particles are forced to run in circles, sometimes looping around the object multiple times before escaping. This racetrack is what creates the bright ring of light we see in famous telescope images, framing the dark shadow in the middle.

However, nature might be playing a trick on us. What if a dark shadow appears in the sky without this racetrack? What if the dark spot isn't caused by light getting stuck in a circle, but by something else entirely? This is the big question scientists are asking as they try to figure out if the dark spots we see are truly black holes or something stranger, like "naked singularities" (points of infinite density without a protective event horizon) or "wormholes" (tunnels through space). The Event Horizon Telescope (EHT) has given us our first real pictures of these cosmic giants, but it's still hard to tell exactly what's making the shadow. If we can't find the racetrack, does the shadow even mean we're looking at a black hole?

This paper dives into that mystery by playing with a mathematical "fix" called the Simpson–Visser regularization technique. Imagine a black hole's center as a point where the laws of physics break down, like a glitch in a video game. The authors use this technique to "smooth out" that glitch, replacing the infinite singularity with a tiny, finite core or a throat that could connect two sides of the universe. They apply this fix to two specific types of weird objects: a "null singularity" (a point of infinite density) and a "charged null singularity" (the same thing, but with an electric charge).

The team ran simulations to see what these smoothed-out objects would look like to a telescope. They discovered something surprising: even though these objects lack the traditional "photon sphere" racetrack that usually defines a black hole's shadow, they still cast a dark shadow! In fact, for certain settings, the edge of the shadow is determined not by light circling outside, but by the geometry of the object's regular, smooth core itself. It's as if the object is so dense and structured that it swallows light directly, creating a dark silhouette without needing the light to get stuck in a loop first.

The researchers found that these "regularized" objects can look almost identical to standard black holes in telescope images. Depending on the size of the smoothing parameter (let's call it the "L" factor), these objects could act like two-way wormholes that you could theoretically travel through, or they could retain some singular features. Crucially, they showed that for specific ranges of mass and charge, the size of the shadow these objects cast matches the observations of the supermassive black holes at the center of our galaxy (Sgr A*) and the giant galaxy M87.

The paper suggests that just because we see a dark shadow with a bright ring, it doesn't guarantee we are looking at a black hole with a photon sphere. The shadow could be coming from a regular, smooth core of a wormhole or a naked singularity. While the authors didn't prove these objects exist, their simulations show that the universe might be hiding these "shadow mimics" right in plain sight, looking exactly like the black holes we think we know. This means that future telescopes will need to look for more than just the size of the shadow to tell the difference between a classic black hole and these exotic, regularized cosmic oddities.

Technical Summary: Optical Appearance of Regularized Compact Objects Without an Exterior Photon Sphere

Problem Statement
Recent Event Horizon Telescope (EHT) observations indicate that the shadow of the supermassive compact object at the center of our galaxy (Sgr A*) closely resembles that of a Schwarzschild black hole. However, the direct observational identification of the exterior photon sphere (an unstable circular null geodesic located outside the compact object) remains a significant challenge. While traditional black hole metrics (Schwarzschild, Reissner-Nordström, Kerr) possess exterior photon spheres that define their characteristic shadows, it is theoretically possible for other compact objects to cast shadows without such features. Previous studies have shown that certain regularized spacetimes (e.g., specific JNW and JMN1 configurations) can produce shadows without an exterior photon sphere. This paper addresses the fundamental question: what is the observed geometry around a compact object if an exterior photon sphere is absent? Specifically, the authors investigate whether shadow-like features can arise in spacetimes where the central singularity is regularized, yet no exterior photon sphere exists.

Methodology
The authors apply the Simpson–Visser (SV) regularization technique to two specific classes of metrics: the null singularity metric and the charged null singularity metric. The SV method replaces the central curvature singularity with a finite-area minimal surface (a "bounce") by performing the coordinate transformation $r \to \sqrt{r^2 + L^2}$ , where $L$ is a regularization parameter with dimensions of length.

Metric Construction:
- Black-Bounce Spacetimes: The authors first review the standard SV Schwarzschild and Reissner-Nordström geometries, which can describe regular black holes, one-way null throats, or two-way traversable wormholes depending on $L$ .
- Regularized Null Singularities: The SV transformation is applied to the static, spherically symmetric null singularity metric (an end-state of gravitational collapse) and its charged counterpart. The resulting metrics are asymptotically flat and free of curvature singularities for $L > 0$ .
- Energy Conditions: The authors note that these regularized geometries violate the Null Energy Condition (NEC), implying the presence of exotic matter, which is a known requirement for singularity resolution in classical general relativity.
Geodesic Analysis:
- The study analyzes null geodesics in the equatorial plane to determine the effective potential ( $V_{eff}$ ).
- The authors distinguish between an "exterior photon sphere" (unstable circular orbit at $r > 0$ ) and a "throat light ring" (orbit at the throat $r=0$ ).
- They calculate the critical impact parameters ( $b_{ph}$ ) associated with exterior photon spheres and $b_0$ associated with the throat or singularity.
Shadow and Intensity Modeling:
- A simplified emissivity model is employed, assuming spherically symmetric, radially infalling thin accretion matter emitting monochromatic radiation.
- The observed intensity is calculated by integrating the specific intensity along the photon path, accounting for redshift factors and the proper length element.
- The study focuses on the "shadow boundary" (the edge of the central dark region) and compares it with the "photon ring" (bright halo from lensed photons).

Key Contributions and Results

Shadow Formation Without Exterior Photon Spheres: The primary finding is that regularized null singularity and charged null singularity spacetimes can cast shadow-like dark regions even in the complete absence of an exterior photon sphere. In these configurations, the shadow boundary is determined by the regular core (the throat at $r=0$ ) rather than by an unstable circular orbit at a finite radius.
Role of the Regularization Parameter ( $L$ ):
- For the uncharged regularized null singularity, the shadow size depends on the parameter $x = L/M$ . The exterior photon sphere is absent for all values of $L$ . The shadow radius varies with $L$ , allowing for a range of observational signatures distinct from the Schwarzschild limit.
- For the charged regularized null singularity, the shadow size depends on both $x = L/M$ and the charge parameter $y = q/M$ . The shadow radius decreases monotonically with increasing charge magnitude.
Comparison with Black-Bounce Geometries:
- In the charged black-bounce (SV-Reissner-Nordström) spacetime, the existence of an exterior photon sphere depends on the parameters. When present, it defines a photon ring. However, the authors show that for certain parameter ranges, the shadow boundary is controlled by the regular core ( $b_0$ ) rather than the exterior photon sphere ( $b_{ph}$ ), resulting in a dark region smaller than the photon ring.
Phenomenological Comparison with EHT Data:
- The authors compare the predicted shadow radii ( $R_{sh}/M$ ) of their models with the angular diameter measurements of Sgr A* and M87* provided by the EHT.
- For the neutral regular null geometry, the parameter space compatible with the observed shadow sizes (within $1\sigma$ and $2\sigma$ confidence intervals) is identified.
- The charged models show that increasing charge leads to a modest deviation from the Schwarzschild limit, but specific parameter ranges remain consistent with EHT observations.
- The study demonstrates that the predicted shadow sizes for these regularized objects can closely mimic those of Schwarzschild black holes, despite the fundamental differences in causal structure (e.g., lack of event horizons or exterior photon spheres).

Significance and Claims
The paper claims that the presence of a bright photon ring does not necessarily imply that the shadow boundary is determined by an exterior photon sphere. The results suggest that "shadow-like" images can arise from regularized compact objects (such as traversable wormholes or regular null singularities) that lack event horizons and exterior photon spheres.

The authors emphasize that their findings challenge the assumption that a shadow is an exclusive marker of a black hole with an exterior photon sphere. Instead, the optical appearance of a regularized core can produce observational signatures comparable to those of classical black holes. This implies that distinguishing between classical black holes and alternative compact objects based solely on shadow size or the presence of a photon ring is difficult without additional observables (e.g., brightness distribution, higher-order ring structures, polarization).

The study concludes that while the predicted shadow angular diameters of the proposed geometries are compatible with current EHT measurements, a comprehensive assessment of their observational viability requires more complex modeling, including GRMHD simulations and detailed plasma dynamics, which are beyond the scope of the current work. The regularization parameter $L$ is noted as a potential source of quantum gravitational information that could leave observable imprints on the shadow structure.

More like this