The Relativistically Apparent Black Hole: A Thought Experiment

This thought experiment explores how a massive star, not yet a black hole in its own rest frame but potentially close to its gravitational limit, might appear to a fast-moving observer.

The core idea is that due to the principles of Special Relativity, an observer moving at a significant fraction of the speed of light towards such a star would perceive its properties in a drastically altered way:

1. Increased Relativistic Mass-Energy: From the observer's perspective, the star's total energy (and thus its effective gravitational mass) would appear significantly increased by the Lorentz factor γ (i.e., E_apparent = γM₀c²).

2. Length Contraction: The star would appear flattened along the observer's direction of motion, its radius in that dimension contracted by the same factor γ (i.e., r'_apparent = r₀/γ).

If the observer then naively applies the Schwarzschild radius formula (r_s = 2GM/c²) using these apparent, frame-dependent parameters, a fascinating consequence emerges:

• The apparent Schwarzschild radius (r_s_apparent = 2G(γM₀)/c²) would be larger than the star's rest-frame Schwarzschild radius.

• It's conceivable that for a sufficiently high velocity (large γ), this expanding r_s_apparent could become equal to, or even exceed, the star's contracting apparent physical radius (r'_apparent).

The "Illusion":
When this condition (r_s_apparent ≥ r'_apparent) is met in the observer's frame, the star would partially look like a black hole to that observer. Light emitted from regions of the star now within this apparent event horizon would not be able to reach them. This could manifest visually as the star appearing to develop a "black dot" or a dark region at its center (where it is most flattened and first engulfed by the apparent event horizon), which could grow as the observer's relative velocity increases.

Crucially:
This is an "illusion" or an "appearance" specific to the high-velocity observer's reference frame. The star itself has not undergone further gravitational collapse to become an invariant black hole for all observers. Instead, this thought experiment highlights the profound frame-dependence of perceived physical properties and how relativistic effects can create scenarios where an object partially appears to satisfy the conditions for being a black hole from a particular observational standpoint.