Freely Falling Finite Frames Near a Black Hole

TL;DR

This paper examines the limitations of finite-sized frames near a black hole horizon, showing they cannot remain coherent or meaningful due to differing clock rates and vanishing forces, challenging the assumption of finite observer frames.

Contribution

It introduces the analysis of finite frames near a black hole horizon, revealing their physical inconsistency and the breakdown of their coherence at the horizon.

Findings

Clocks at the front and rear of a finite frame have different time scales at the horizon.

The forces needed to keep a finite frame intact tend to zero near the horizon.

Finite frames become physically meaningless and tend to fall apart at the horizon.

Abstract

It is well-known that the Riemann curvature tensor has no discontinuity at the black hole horizon. It is also well-known that a freely falling observer takes finite time to reach the horizon from an outside point. However, the usual assumption is that such an observer resides in a frame of reference (spaceship) of infinitesimal size. This assumption is justified as long as the coordinates are continuous enough to assume that the observer's frame is small compared to the variations of the metric from a local flat metric. Such an assumption may be invalid when the coordinate system has not only a discontinuity but a singularity like the one at the horizon. Hence, here, the characteristics of a finite frame (a spaceship) near a black hole horizon is discussed. It is shown that clocks placed at the front and rear ends have different time scales even in the limit when they reach the horizon at the same time. This renders such a frame physically meaningless. It is also argued that the forces that are expected to keep a realistic frame (like a spaceship) in one piece tend to zero near the horizon. So, a physical spaceship is expected to fall apart near the horizon.