The Black Hole Singularity In An SFL-Informed Ontology Of The General Theory Of Relativity

ChRIS said:

So, is the singularity still relevant in this [SFL-informed] model, or is it an artefact of the classical model?

ChatGPT said:

In the model you're working with—where space and time are contracted or expanded in relation to a centre of mass, and the geodesic is what's curved—it seems that the singularity as classically understood may not be relevant in the same way.

Classical Singularity vs. This Model:

In the classical general relativity model, the singularity is typically understood as the point where both space and time are infinitely contracted and dilated, respectively. It's a region where the curvature of spacetime becomes infinite and the usual laws of physics break down, leading to what we often refer to as a gravitational singularity.

However, in your reinterpreted model where:

• Space is contracted (but not curved) relative to the centre of mass.
• Time is either contracted or expanded depending on proximity to the centre of mass, and time itself is viewed as a sequence of intervals rather than the ticking of a clock.
• Curvature applies to the geodesic (the path through space and time, not to space itself).

Under this interpretation, the singularity may no longer serve the same function as in the classical model. Here's why:

1. No Infinite Curvature of Space:

• In classical general relativity, the singularity is tied to infinite curvature of spacetime. In your model, space itself isn’t curved; rather, the geodesic (the path through space-time) is curved. Therefore, there's no infinite curvature at a single point in space, and so the idea of a singularity, where space "ends," may be irrelevant.
• The focus is on space-time intervals and the relative expansion or contraction of space and time, not on an infinite curving of spacetime. Therefore, the concept of a "singularity" where the fabric of space-time breaks down doesn't quite apply.

2. Event Horizon as the Boundary:

• In your model, the event horizon becomes the key boundary, where extreme space contraction and time dilation occur. Beyond this point, information (including light) can't escape to the outside universe, but this doesn't imply a point of infinite space-time curvature.
• This would suggest that rather than a singularity where space and time break down, the event horizon serves as a more practical boundary beyond which the nature of the space-time metrics (intervals) changes drastically. There's no need for a "point" where everything goes infinite, just an asymptotic approach where space-time behaves extremely in a way that becomes essentially non-interactive with the outer universe.

3. Singularity as a Classical Artefact:

• In classical general relativity, the singularity represents the breakdown of the theory itself—essentially where our mathematical model of space-time no longer holds (infinite density, infinite curvature).
• But in your model, since space isn’t curved but instead contracted or expanded relative to the mass centre, the singularity could indeed be viewed as a classical artefact—a theoretical endpoint that emerges from trying to model what happens at a very extreme point of space-time using classical general relativity.

Conclusion:

In your reinterpreted model of General Relativity, the singularity, as traditionally defined (a point of infinite density and curvature), doesn't seem to hold the same significance. The event horizon becomes the important boundary where relativistic effects like space contraction and time dilation reach their extreme limits, and it marks the point where space and time lose their usual relationship to the outside universe. The singularity could be seen as a relic of the classical model, no longer needed in this alternative framework where space and time are seen as relative and processes unfold along geodesics rather than being defined by infinite curvature.

In essence, your model suggests that the singularity, in its classical sense, is unnecessary; what really matters is the event horizon and the extreme relativistic effects it induces.