Space-time Curvature, Gravity, and the Black Hole Threshold: A New Geometric Perspective

In astrophysics, the concept of escape velocity defines how fast an object must move to break free from a celestial body's gravitational pull. For Earth, it's around 11.2 km/s. But for a black hole, escape velocity exceeds the speed of light — which is why not even light can escape once it crosses the event horizon. This led me to wonder: what if the escape velocity of any body is directly related to the curvature angle of the spacetime fabric around it?

The Hypothesis

The greater a celestial body’s gravity, the more it bends spacetime. I propose that as mass increases, the spacetime curvature around it steepens — and the angle of curvature from a central reference point correlates with the escape velocity.

When this curvature becomes extremely steep — approaching a 90° geometric threshold — it marks the formation of a black hole. At this point, the "slope" of spacetime becomes so vertical that the escape velocity equals the speed of light. Anything beyond this point, including photons, becomes trapped.

However, this 90° curvature is not literal but metaphorical — representing a shift where spacetime bends so drastically that it redirects all geodesic paths inward.

Why Light Still Falls In?

A common question arises: If spacetime is curved so sharply at the event horizon, how does light even get in? The answer lies in the nature of curved spacetime itself. According to general relativity, spacetime around a black hole behaves like a river flowing inward. Light and matter, like boats on this river, are swept along geodesics — the straightest possible paths in a curved geometry. Outside the event horizon, light can still resist the current. But at the horizon, the inward flow of spacetime exceeds the speed of light itself. Light doesn’t “enter” the black hole — it’s carried in with spacetime.

Two Possibilities Beyond the Horizon

This model opens up two imaginative possibilities for what happens inside the black hole:

1. Spacetime Wrapping: The fabric of spacetime bends so dramatically that it loops around itself. Light and matter follow these loops endlessly inward, never to return — possibly spiraling toward a singularity.

2. Dimensional Tunneling: Rather than endlessly falling inward, the extreme curvature acts as a tunnel, ejecting energy or information into another region or dimension — possibly explaining theories like white holes or parallel universes.

Conclusion

This hypothesis invites us to reconsider how geometry, gravity, and energy interact on cosmic scales. By thinking of black holes not just as gravitational traps but as thresholds in the geometry of spacetime itself, we edge closer to a deeper understanding of their true nature — and perhaps, of the universe beyond.

                                                                                                                        Author:

                                                                                                                        Nagarjuna Reddy W