On the impossibility of observational confirmation of black holes

This paper argues that despite the remarkable agreement between observational data from collaborations like LIGO-Virgo-KAGRA and the Event Horizon Telescope and Kerr black hole predictions, general relativity fundamentally imposes limits that prevent any observational data from conclusively confirming the existence of black holes, leaving them only as candidates rather than proven entities.

The Gist

Imagine you are a detective trying to solve a mystery: Do black holes actually exist, or are we just seeing very convincing look-alikes?

According to this paper by Thiago T. Bergamaschi, the answer is a bit surprising. While we have amazing new tools to look at the universe, the author argues that we have never actually proven a black hole exists. We have only found "black hole candidates" that act exactly like the theory says they should.

Here is the breakdown of the argument using simple analogies:

1. The "Black Swan" Problem

The paper starts with a logic puzzle. Imagine you want to prove that "all swans are white." You can go out and see a million white swans, and you will never be 100% sure that a black swan doesn't exist somewhere you haven't looked yet. However, if you see just one black swan, you instantly know your theory is wrong.

The author says our current observations are like seeing a million white swans. We see objects that behave exactly like black holes, but we haven't found the "smoking gun" that proves they are black holes and not something else that just looks the same.

2. The "Cosmic Imposter" (The Event Horizon vs. The Surface)

In General Relativity, a true black hole has an event horizon—a point of no return where nothing, not even light, can escape. It's like a bottomless pit.

However, there could be "imposters": ultra-dense objects that have a tiny, hard surface just a hair's breadth away from where the horizon should be. Let's call this tiny gap the "epsilon" (ε).

• The Analogy: Imagine a black hole is a bottomless well. An imposter is a well with a very thin, invisible trampoline at the very bottom.
• The Problem: If that trampoline is close enough to the bottom, and you are standing far away looking in, you can't tell the difference. The light and waves bouncing off the trampoline look exactly the same as light falling into the bottomless well, within the time we have to watch.

The paper argues that no matter how good our telescopes get, if we only watch for a finite amount of time (which we always do), we can never rule out the possibility that there is a tiny surface there. We can only say, "It's very close to being a black hole," but we can never say, "It is a black hole."

3. The "Echo" That Never Comes

Scientists look for "ringing" sounds (gravitational waves) after two massive objects crash together.

• The Theory: If they crash into a true black hole, the sound should fade away smoothly (like a bell ringing and dying out).
• The Hope: If they crash into an imposter with a surface, the sound should bounce back and create an "echo."

The author points out that while we haven't heard echoes yet, that doesn't prove there is no surface. It just means the surface is so close to the "bottom" that the echo is too faint or too late for our current instruments to hear. It's like trying to hear a whisper in a noisy room; just because you don't hear it doesn't mean no one is whispering.

4. The "Shadow" Photo

You may have seen the famous "first photo of a black hole" from the Event Horizon Telescope. It looks like a dark circle surrounded by a ring of light.

• The Reality: The paper says this isn't a photo of a black hole. It's a photo of a shadow.
• The Analogy: Think of a streetlamp shining on a wall. If you put a solid ball in front of it, you get a shadow. If you put a "black hole" in front of it, you get a shadow. But you could also get that same shadow if you put a very dense, dark ball that isn't a black hole in front of the light.
• The photo proves there is something massive and compact there, but it doesn't prove that thing has an event horizon. It just proves it has a "light ring" (a place where light orbits), which many different types of objects can have.

5. The "Hawking Radiation" Trap

There is a famous theory that black holes glow with a specific type of radiation (Hawking radiation). The author notes that even if we detect this glow, it wouldn't prove a black hole exists.

• The Analogy: Imagine you smell smoke. You might think, "Aha! A fire!" But you could also be smelling a very hot piece of metal that isn't on fire. Many different hot, dense objects can produce similar "smoke" (radiation). Detecting the smoke tells us the object is hot and dense, but not that it is a true black hole.

The Bottom Line

The author is not saying black holes don't exist. He is saying that science is being too confident in its language.

• What we have: Overwhelming evidence that there are objects behaving exactly like the math predicts black holes should.
• What we don't have: A way to observationally prove that these objects are not just "ultra-compact imposters" with a tiny surface.

The paper is a call for scientific humility. It asks us to stop saying "We have found black holes" and start saying "We have found the best candidates for black holes, and General Relativity describes them perfectly." It's a reminder that in science, being consistent with the theory is not the same thing as proving the theory's reality.

Technical Summary

Problem
The paper addresses a fundamental epistemological issue in modern gravitational physics: the distinction between observational evidence for "black hole candidates" and the conclusive confirmation of the existence of black holes as defined by General Relativity (GR). While recent data from the LIGO-Virgo-KAGRA (gravitational waves), Event Horizon Telescope (EHT), and GRAVITY collaborations are frequently interpreted as definitive proof of black holes, the author argues that this interpretation is scientifically imprecise. The core problem is that GR itself imposes intrinsic limits on what can be observationally established. Specifically, the definition of a black hole relies on global spacetime properties (causal disconnection from infinity), which are teleological and inaccessible to local, finite-time observations. Consequently, current data can only rule out specific alternative models of ultracompact objects but cannot positively confirm the existence of an event horizon.

Methodology
The paper employs a conceptual and theoretical analysis rather than new experimental data or numerical simulations. The methodology involves:

1. Epistemological Analysis: Applying the philosophy of science (referencing Popper's black swan analogy) to distinguish between falsifying specific models and confirming a general existence.
2. Theoretical Comparison: Comparing the observational signatures predicted for Kerr black holes against those of "ultracompact horizonless objects" (exotic compact objects).
3. Review of Existing Literature: Analyzing claims made in key publications from the LIGO-Virgo-KAGRA, EHT, and GRAVITY collaborations to identify linguistic overreach (e.g., the use of "demonstrate" vs. "consistent with").
4. Parameterization of Closeness: Utilizing the "closeness parameter" ($\epsilon$), where the radius of an ultracompact object is defined as $r = r_+(1 + \epsilon)$. The analysis demonstrates that as $\epsilon \to 0$, the observational differences between a black hole and a horizonless object become inaccessible within any finite observation window.

Key Contributions

• The Impossibility of Confirmation: The paper establishes that no finite-time observational data is sufficient to confirm the existence of black holes. Even with infinite precision, an observer cannot distinguish between a true event horizon and an ultracompact object with an arbitrarily small cutoff parameter ($\epsilon$).
• Reinterpretation of Gravitational Wave Ringdown: The author argues that the detection of ringdown signals (quasinormal modes) consistent with the Kerr metric confirms the existence of "light rings" (unstable circular photon orbits) and the validity of GR's predictive power, but does not confirm the presence of an event horizon. The absence of "echoes" in the waveform only sets an upper bound on $\epsilon$, rather than proving $\epsilon = 0$.
• Reinterpretation of Electromagnetic Shadows: Similarly, the "shadows" observed by the EHT are identified as evidence of extreme gravitational lensing around compact objects with unstable photon orbits. The paper notes that any sufficiently compact object with these orbits produces a similar shadow, meaning the images depict candidates, not confirmed black holes.
• Hawking Radiation Limitations: The paper extends this argument to Hawking radiation, noting that similar thermal spectra can be produced by collapsing objects that do not form black holes. Therefore, detecting such radiation would only set a lower bound on compactness, not verify the existence of a horizon.

Results
The analysis yields the following conclusions regarding current and future observations:

• Gravitational Waves: While data (e.g., GW150914, GW170104) is strikingly consistent with the merger of Kerr black holes, it cannot rule out all horizonless models. The data serves as a test of GR's predictive power regarding the dynamics of compact binaries, not a proof of the final state's identity as a black hole.
• Electromagnetic Observations: EHT images and GRAVITY data are consistent with GR predictions for black holes but are equally consistent with specific models of ultracompact objects. The term "consistent" is scientifically accurate, whereas "demonstrate" or "confirm" is not.
• Fundamental Constraint: The inability to confirm black holes is not merely a technological limitation (e.g., insufficient sensitivity) but an intrinsic constraint imposed by the nature of General Relativity and the definition of the event horizon.

Significance
The paper claims its significance lies in correcting the "illusion of certainty" in contemporary astrophysical discourse. It argues that while black holes serve as a vital conceptual laboratory for theoretical physics, conflating theoretical consistency with empirical confirmation undermines scientific rigor. The author advocates for a disciplined language that distinguishes between the success of a mathematical model (the Kerr metric) and the verified physical reality of the object. The paper concludes that while future increases in sensitivity will allow for "precision black hole astrophysics" and tighter bounds on $\epsilon$, they will never provide conclusive proof of the existence of black holes. The work serves as a call to maintain epistemological humility, acknowledging that we have accumulated compelling evidence for "black hole candidates," but have not proven the existence of black holes themselves.