⚛️ general relativity

Galactic microlensing by backreacted massless wormholes

This paper investigates Galactic microlensing by backreacted massless wormholes, demonstrating that electrically charged variants produce distinct observational signatures—specifically dimmer light curves with characteristic "gutters" and vanishing Einstein radii at extreme charge limits—compared to Schwarzschild black holes, suggesting that re-examining past microlensing data could reveal their presence as dark halo objects.

Original authors: G. F. Akhtaryanova, R. Kh. Karimov, R. N. Izmailov, K. K. Nandi

Published 2026-07-01

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CC BY 4.0

Original authors: G. F. Akhtaryanova, R. Kh. Karimov, R. N. Izmailov, K. K. Nandi

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, invisible trampoline. Usually, we think of heavy objects like stars or black holes as bowling balls sitting on this trampoline, creating deep dips that make other things roll toward them. This is gravity.

But what if there were objects that didn't weigh anything at all, yet still had a strange ability to bend the path of light? This is the idea behind wormholes. Think of a wormhole not as a heavy ball, but as a "handle" or a tunnel connecting two distant parts of the trampoline.

This paper explores a specific, theoretical type of wormhole that acts like a cosmic lens. Here is the breakdown of their findings in simple terms:

1. The "Ghost" Lens

The scientists are studying a wormhole proposed by Kim and Lee. The most surprising thing about this wormhole is that it has zero weight (zero mass). In normal physics, if something has no weight, it shouldn't bend light. However, because of its unique shape and the fact that it carries an electric charge (like a static shock, but on a cosmic scale), it does bend light.

Think of it like a ghost in a hallway. You can't see the ghost, and it doesn't have mass, but if you walk past it, you might feel a strange tug or see the air shimmer. This wormhole is that ghost: it has no mass, but its electric charge creates a "shimmer" that bends starlight.

2. The Experiment: Watching Stars Blink

To find these ghostly wormholes, the researchers looked at a phenomenon called microlensing.

The Setup: Imagine a distant star (the source) and a wormhole (the lens) passing in front of it from our perspective on Earth.
The Expectation: Usually, when a heavy object (like a black hole) passes in front of a star, the star gets brighter because the gravity acts like a magnifying glass.
The Wormhole Twist: The paper predicts that a charged wormhole acts differently. Instead of just making the star brighter, it creates a very specific pattern of light and dark.

3. The "Gutter" Effect (The Key Discovery)

This is the most exciting part of the paper. When a normal black hole lenses a star, the light curve (a graph of brightness over time) looks like a smooth hill: it goes up, peaks, and comes down.

The charged wormhole, however, creates a light curve with "gutters."

The Analogy: Imagine driving over a hill. A normal hill (black hole) is smooth. A wormhole is like a hill with a dip in the middle, right before you reach the top, and another dip right after you pass the top.
What happens: As the star moves behind the wormhole, its brightness rises, then suddenly dips (the gutter), then rises to a peak, dips again, and falls.
The "Extreme" Case: If the wormhole has a very high electric charge (approaching a specific limit), these two dips get closer and closer together until they merge. At that point, the "hill" disappears entirely, and the star crosses the wormhole's path instantly without the usual delay.

4. Why This Matters for Finding Them

The paper suggests that if astronomers re-examine old data from surveys that look for stars getting brighter, they might have missed these wormholes.

The Problem: Most surveys are programmed to look for stars that get brighter.
The Solution: The wormhole creates a pattern where the star might actually get dimmer than usual at specific moments (the gutters) before getting bright. The paper argues that by looking for these specific "dips" or "gutters" in the light curves, we could prove these massless, charged wormholes exist.

5. The Odds

The authors did some math to guess how likely it is to find one. They calculated that if these wormholes exist in our galaxy (either stuck in the galaxy's halo or flying freely through space), we should be able to detect them if we monitor enough stars. They suggest that with current technology, we might need to watch about a million stars to catch a glimpse of one, especially if the wormhole is relatively large (in cosmic terms).

Summary

In short, this paper proposes a new way to hunt for wormholes. Instead of looking for heavy objects bending light, we should look for weightless, electrically charged tunnels that create a unique "dip-and-peak" pattern in starlight. If we see a star flicker with these specific "gutters," it might be the first sign that a wormhole is passing right in front of us.

Problem Statement
Gravitational lensing serves as a diagnostic tool to distinguish between compact objects such as black holes, naked singularities, and wormholes. While the microlensing properties of background massless Ellis-Bronnikov wormholes have been previously studied (e.g., by Abe), the specific effects of additional matter distributions surrounding a lens on the resulting spacetime geometry remain an open area of investigation. This paper addresses the application of "backreacted" wormholes—specifically the Kim & Lee charged wormhole models—as lenses in Galactic microlensing scenarios. The authors investigate whether the presence of scalar or electric charges, arising from the backreaction of additional matter, alters the lensing signatures (such as light curves, image positions, and magnification) in a way that distinguishes them from uncharged wormholes and Schwarzschild black holes.

Methodology
The study employs the Kim & Lee formalism, which considers the backreaction of additional matter fields (scalar or electric) on a background massless Ellis-Bronnikov wormhole spacetime. The authors focus on the specific case where the background equation of state parameter is $\gamma = -1$ .

Metric Derivation: The authors analyze two backreacted metrics: one with a scalar charge ( $\alpha$ ) and one with an electric charge ( $Q$ ). They demonstrate that while the scalar charge merely shifts the shape function, the electric charge introduces a non-trivial redshift function ( $\Phi \neq 0$ ) and alters the throat radius, yet the resulting spacetime remains massless (zero ADM mass).
Light Deflection: Using the Keeton-Petters Post-Post-Newtonian (PPN) expansion method, the authors calculate the light deflection angle up to the 4th order. They derive the PPN coefficients ( $A_1$ through $A_4$ ) for the electrically charged metric.
Lensing Observables: Based on the deflection angle, the authors compute standard microlensing observables: image positions, magnification, centroid shifts, and differential time delays. They utilize a cubic equation approach (following Abe) to solve for image positions and construct Paczyński light curves.
Probabilistic Analysis: The paper calculates the optical depth ( $\tau$ ) and event rate ( $\dot{\Gamma}$ ) for microlensing events. These calculations assume the wormhole lens is either bound to the Galaxy (with transverse velocity $v_T = 220$ km/s) or unbound ( $v_T = 5000$ km/s), considering source stars in the Galactic Bulge and the Large Magellanic Cloud (LMC).

Key Contributions and Results

Massless Nature and Charge Constraints: The study confirms that both the backreacted scalar and electrically charged wormholes possess zero ADM mass, consistent with the background Ellis-Bronnikov solution. However, the electric charge $Q$ introduces a non-trivial redshift function. A critical finding is the constraint on the charge-to-throat ratio: for the Einstein radius ( $R_E$ ) to be real, the condition $Q/r_{th} < 1/\sqrt{2}$ must hold.
Deflection Angle: The leading-order light deflection angle for the charged wormhole is found to be of order $O(1/r^2)$ , distinct from the $O(1/r)$ behavior of massive black holes. The presence of charge $Q$ reduces the deflection angle compared to the uncharged background. Notably, the deflection angle becomes zero at $Q^2 = b_0^2/3$ and negative for higher charges within the physical throat constraint.
Image Positions and Magnification:
- The zeroth-order image position is independent of the charge $Q$ and coincides with the source position.
- Corrections to the image position and magnification depend on $Q$ . As $Q$ increases, the magnitude of these corrections decreases. In the extreme limit ( $Q/r_{th} = 1/\sqrt{2}$ ), all corrections vanish, rendering the images indistinguishable from the source.
- The total magnification and centroid shifts show similar dependencies, with the first-order corrections often vanishing or being zero, leaving second-order terms as the primary indicators of charge.
Paczyński Light Curves: The most distinctive qualitative prediction is the behavior of the light curves. Compared to Schwarzschild black holes, the light curves of charged wormholes are significantly dimmer.
- Gutters: The curves exhibit characteristic "gutters" (dips in brightness below the baseline) when the source enters and exits the Einstein ring.
- Charge Effect: As $Q$ approaches the extreme limit ( $r_{th}/\sqrt{2}$ ), these gutters move closer to the peak. At the extreme limit, the Einstein radius vanishes, and the source crosses the ring instantly, causing the gutters to merge.
- Brightness: For impact parameters $\hat{\beta}_0 > 1$ , the source does not brighten; instead, it appears dimmer than the baseline illumination, a feature absent in standard black hole lensing.
Probabilistic Estimates: The calculated optical depths and event rates suggest that detecting wormholes with throat radii $r_{th} \geq 10^4$ km is theoretically possible in Galactic Bulge surveys, provided the lens is bound to the Galaxy. The event rates are generally low, requiring the monitoring of a large number of stars ( $\sim 10^6$ ) to expect a detection.

Significance
The paper claims that re-analyzing past Galactic microlensing data could potentially betray the presence of charged wormholes. The primary significance lies in the identification of unique signatures—specifically the "dimmer" light curves with characteristic gutters and the specific dependence of these features on the charge parameter $Q$ —that differentiate backreacted wormholes from both uncharged wormholes and black holes. The authors posit that while the detection is challenging due to low magnification and the need to identify brightness decreases rather than increases, the specific qualitative features of the light curves offer a viable, albeit difficult, pathway for observational verification. The work represents a novel application of backreacted metrics to lensing, providing a framework to estimate the influence of additional matter distributions on lensing scenarios.