Appendix 8 — Tidal Forces
The lines of the gravitational field, produced by a mass, are not parallel but are directed radially toward the center of that mass. The magnitude of gravity decreases with the square of the distance from the center:
\[ |\vec{g}(r)| = \frac{GM}{r^{2}}. \]
When an extended body (here represented as a gray object) is placed in this field, it does not experience the same force everywhere. The gravitational forces can be decomposed into:
- horizontal components — these compress the body,
- vertical components — these stretch the body in the direction of the mass.
This occurs because the gravitational field becomes stronger closer to the mass. The difference in force between the near and far sides of the body produces a tidal force.
Because the field lines are radially directed, the forces at different points of the body do not point in the same direction. This leads to deformation: compression in the transverse direction and stretching in the radial direction.
Tidal forces in extreme conditions
In the case of a black hole, tidal forces become extremely large. The radial component of gravity increases so strongly that a body that approaches too closely is stretched into a long, thin structure.
This phenomenon is known as:
\[ \text{“spaghettification”}. \]
It is a direct consequence of the enormous gradient of the gravitational field near the singularity.