Do black holes deserve their bad reputation? Beyond the event horizon

It's undeniable that black holes have a reputation for being voracious mass eaters. Rumors have it 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 suck everything in like giant hoovers and won't stop until the last 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. A black hole with an accretion disk. Artistic impression. Source: wallpaperflare

As the famous saying goes, the rumors about black holes' long-reaching hands are greatly exaggerated. When it comes to gravity, the difference between a black hole and a star of similar mass is significant only within a certain distance from its center. The gravitational field generated by a body is determined by its mass, so celestial bodies with similar mass create similar fields. However, the gravitational field behaves differently above and beneath the body's surface. Above the surface, gravity follows the inverse square law, while below, the distribution is linear. This is where the distinction between a black hole and a star becomes evident, as the black hole's surface contracts to nearly zero.

Consider two spherically symmetric celestial bodies, one Yellow and one Grey, as shown in Fig. 2. The bodies have the same mass: M(yellow) = M(grey). However, the mass of the Grey Body is compressed into a much smaller sphere, with a radius of r that is 1/6 of the Yellow Body's radius R, where R = 6r. This size disparity results in the Grey Body's surface being 6 times nearer to its center, leading to a 36-fold increase in surface gravity due to the inverse square law, g(grey) = 36 x g(yellow). Therefore, if you weighed 200 lb (91 kg) on the Yellow Body, your weight would rise to 7200 lb (3276 kg) on the Grey Body. This is the difference you would certainly notice.

Fig. 2. The Yellow and Grey Bodies exert equal force on the Blue Body, because they both have the same mass (M) and their centers are at equal distance (d) from the Blue Body's center.

However, if we position a Blue Body at the same distance, d, from the centers of the Yellow and Blue Bodies, each will exert the same gravitational force on the Blue Body. According to Newton's shell theorem, the gravitational field created by a spherically symmetric mass acts as if all its mass is concentrated at its center. This concept allows us to consider planets and stars as point masses when analyzing their orbits. The formula for determining the gravitational field strength, g(d), produced by mass M at a distance d, does not involve the mass's radius, the only stipulation being that the distance d must be outside the mass or on its surface, d≥R. Therefore, two bodies with equal mass M but different densities (and thus different radii) will exert equal force on a third body, provided that this third body is equidistant from their centers and located outside both.

With all the necessary information at hand, we can now explore how a star transforms into a black hole through gravitational collapse. Gravity is constantly present and always attractive. Without any opposing forces, all matter in the universe would ultimately collapse together. A star maintains its stability as long as the outward pressure from nuclear fusion in its core balances the inward pull of gravity. Once a star exhausts its nuclear fuel, gravity takes over, causing the star to contract rapidly.

Let the Yellow body become a star that has depleted its fuel and undergone gravitational collapse, hypothetically without losing mass. When it reaches the stage where its size shrinks to that of the grey body (Fig. 3), its surface gravity increases 36 times in accordance with the inverse square law, as previously discussed. This dramatic rise in surface gravity will continue as the star contracts further. Once the radius of the collapsing star shrinks to the Schwarzschild radius, the star transforms into a black hole. The Schwarzschild radius marks the spatial boundary where the gravitational field becomes so strong that the escape velocity equals the speed of light, c. Although the star continues to contract, its final state remains unknown. Since nothing can surpass the speed of light, no signal can come back to us after crossing the Schwarzschild boundary to tell the story.

Fig. 3. The Star undergoes gravitational collapse, shrinking first to the size of the grey body, and finally contracting to the black hole.

While the Schwarzschild boundary signifies the point of no return for all known particles, this region is minuscule on a cosmic scale. As one moves away from the event horizon, the gravitational pull of the black hole decreases at the same rate it increased before. At a distance of d=r from the black hole's center, the gravitational field weakens to match the Grey Body surface gravity. At a distance of d=R, the field further weakens to equal the Yellow Body surface gravity, which was the surface gravity of the star before the hypothetical collapse. Outside that distance, the fields of both the star and the black hole become identical, continuing to decrease at the same rate. If we placed the Blue planet (Fig. 4) at an equidistance d>R from the centers of the star and the black hole, they would pull the planet with equal force.

Fig. 4. The Star and the Black hole exert equal force on the Blue planet, because they both have the same mass (M) and their centers are at equal distance (d) from the Blue planet.

Our Sun is too small to form a black hole. Still, if we were to replace the Sun with a hypothetical black hole of identical mass, the planets would continue their orbits as if nothing had changed, with the same distances and periods. Without the Sun's energy, the solar system would go dark and freeze. In terms of gravity, differences would arise only in the region between the Sun's radius of ~700,000 km (~400,000 miles) and the proposed black hole's radius of ~3 km (~2 miles). Surprisingly, these differences would not increase the black hole's ability to capture foreign bodies. In fact, the opposite would happen.

While asteroids and comets already bound to the Sun would continue their paths, interstellar wanderers would significantly decrease their chances of colliding with the black hole due to its tiny surface area.. Instead of plunging into the Sun's expansive photosphere, they would now target a 3-km bullseye to meet their end. Potential prey would also avoid the super gravity. Travelling at high speed, they would need to pass within a few kilometers of the black hole for the trap to work, providing the predator with a narrow opportunity in the vastness of the solar system. All in all, a poor score for a famed mass eater. The Sun is doing a better job than this.

In the event of gravitational collapse, the Sun would lose its magnetic field, which currently protects it from Galactic Cosmic Rays. This field is generated by the movement of hot plasma inside the Sun. As the plasma breaks down, the field disappears, allowing the interstellar nuclei, protons, and electrons to reach the black hole for consumption. Nevertheless, the dramatic decrease in surface area would negate any advantages. In view of all the evidence, we can conclude that accusations brought to black holes for crimes against the masses look more like character assassination than fair justice!

Black holes fascinate us with their invisible yet formidable presence. They evoke visions of colossal cosmic phantoms, shrouded in mystery and fraught with danger. We fear most what remains unseen. Their unique ability to capture light, which is essential for our vision and measuring devices to access data, sets them apart from other celestial bodies and endows them with magical properties they do not actually have.

We may never discover what exists inside black holes, as any signal that passes through the event horizon boundary gets obliterated from our data. Still, the black holes don't trap gravity, allowing us to study their gravitational fields just as we do with other masses. Therefore, we can confidently assert that their gravitational advantage is confined to regions near the event horizons. Outside of these areas, their gravitational pull is no different than that of other celestial bodies with a similar mass.