Do black holes deserve their bad reputation? Explaining a black hole's gravity

It is undeniable that black holes have a reputation for being voracious mass eaters. Rumors are spreading that they are destroying our Universe with their appetite, leaving voids in places where galaxies once thrived. With gravity so strong that nothing can escape, they swallow up everything like giant cosmic hoovers and will persist until the final star has gone. Some even claim the dirty deed has been completed, and we already live inside a black hole, unable to escape. But are they truly that malicious or just the victims of malicious gossip?

Fig. 1. At a distance, the gravitational pull of a black hole is no different from that of a regular star.

Referring to the well-known saying, we can assert that the rumors about black holes are greatly exaggerated. When it comes to gravity, the difference between a black hole and a regular star of equivalent mass is short-range. The strength of a gravitational field is determined by mass, so bodies with similar mass produce similar fields. However, the field above the body's surface follows the inverse square law, whereas the field below the surface follows a linear law. This is where the distinction between a black hole and a star becomes apparent, as the black hole's radius shrinks to a tiny point.

Consider two astronomical bodies, yellow and grey in Fig. 2, which have equal mass but different sizes. The yellow body has a radius of R, while the grey one has a radius of r, where R=6r. The difference in volume results in the grey body's surface being 6 times closer to its center of mass, leading to a 36-fold increase in surface gravity due to the inverse square law. So, if you weighed 100 lb (45 kg) on the yellow body, your weight would increase to 3600 lb (1620 kg) on the grey one.

Fig. 2. The Sun and a black hole pull a planet with equal strength.

This dramatic rise in surface gravity will continue as the body continues to contract. Once it reaches the Schwarzschild radius, it becomes a black hole, with gravity at the event horizon so enormous that it even captures light. However, the Schwarzschild radius is minuscule on a cosmic scale. Away from the event horizon, the black hole's gravity starts decreasing at the same rate. At a distance of r from the black hole's center, its gravity will weaken to equal that at the grey body's surface; at a distance of R, it will equal that at the surface of the yellow body. Beyond R, the gravitational fields of all three bodies become similar, meaning each will pull the Blue Planet with equivalent strength.

 If we replaced the Sun with a black hole of equal mass, the planets would maintain their orbits like nothing happened. The only change would occur in the region between the Schwarzschild radius and the Sun's radius. Since the star's surface gravity is strong enough to trap even tiny particles like electrons, the difference would mainly apply to massless light. Therefore, accusing black holes of a crime against the mass looks to me more like character assassination than justice.

Black holes fascinate us with their invisible yet formidable presence. Like cosmic phantoms, they are shrouded in mystery and fraught with danger. We tend to fear most what we can't see, and fear makes the wolf look bigger. Black holes trap light, which is essential for our vision, making it unlikely that we will ever glimpse what lies inside the event horizon. Nevertheless, they don't trap gravity, allowing us to study their gravitational field freely. In this regard, their dominance over stars is limited to a short range. Beyond this range, their gravitational pull is no stronger than that of any other astronomical body of similar mass.