The strange behaviour of gravity

When the falling apple supposedly inspired Isaac Newton to discover the law of gravity, he did not imagine that he had opened a Pandora’s box. For the journey from the falling apple has led to several strange consequences, like black holes. We will look at some.

The law of gravity as enunciated by Newton says that there is a force of attraction between any two bodies in the universe. The force is in direct proportion to their masses and in inverse proportion to the distance separating them. To understand the full implications of this statement we will compare it with another force which is familiar to us viz, the elastic force in a rubber band.

Tie up two bodies to the ends of a rubber band and stretch it. The natural tendency of the rubber band is to contract to its original unstretched size. The two bodies that were tied to its ends will therefore feel a force of attraction because of the band’s tendency to shrink. Is this not like Newton’s gravitation which also causes the two bodies to attract each other?

This may appear to be the case, but in reality, there is a world of difference between the two cases. As we saw with the rubber band, it tends to contract when stretched, but this force of contraction disappears as soon as the band is allowed to shrink to its natural length.

Thus, as its demands are met, the force disappears. Not so with gravitation! If we yield to it and allow the two bodies to approach each other, the force does not disappear. Rather, because of the inverse square law, it gets stronger. Physicist Hermann Bondi called this tendency of gravitation “dictatorial”. As we will see, this tendency leads to the formation of black holes.

Before we come to that aspect let us examine another situation where gravity behaves strangely. This involves an imaginary experiment. Suppose you connect a hot body to a cold one by a wire. What will happen? Heat energy will flow from the hot body to a cold body.

This process will go on till both bodies have the same temperature. But now imagine that you are connecting two stars A and B of which A is considerably hotter than B. As before heat will flow out of the hotter star A to B. Because A has lost energy, its internal equilibrium is upset.

Normally in a star like the Sun, two internal forces are at play. The force of gravity tends to highlight the force of attraction between its different parts with the result that the star as a whole tends to contract. The star is, however, able to maintain a fixed size because the gravitational force is balanced by a thermal force arising from the fact that the star is made of hot plasma.

In our thought experiment, this exact balance is upset. Since star A has lost heat, it finds its interior deficient in strength, especially in balancing gravity. So it contracts and goes on doing so and in the process its internal temperature rises.

What happens to star B? Recall that it receives energy from star A which results in the strengthening of its thermal forces. This results in an expansion of the second star. Because by expansion, hot gas and plasma cool down, the overall temperature of the colder star B will be lowered. So what is the bottomline?

The experiment results in the hot star getting hotter and the cool star getting cooler! This counter-intuitive result arises because gravity is at play. In reality, we may have such a situation with a somewhat different scenario when a star becomes a red giant, The interior of such a star has a hot core surrounded by a cooler mantle. The conditions of equilibrium have to accommodate this reality.

So what happens? The core emits heat and contracts but this process raises its temperature. The mantle receives that heat which makes it expand. As expansion of a gas or plasma leads to its cooling, the envelope cools down. Thus, we have a large star which is cooler at its outer boundary but hotter at the centre of its core.

The role of thermal pressures in maintaining equilibrium cannot be overstated. Imagine our Sun suddenly losing all its pressures. With nothing to oppose its gravity the hot plasma will collapse and the star would shrink. How long will it take to shrink to a point? A mere 29 minutes!

Not our Sun, but more massive stars may find themselves at such a stage when they have exhausted their fuel. The collapse process leads to stronger gravity near the surface of the star, so that eventually its strong gravity will pull back even light. That is when we say that the star has become a black hole. In a sense, a black hole is the outcome of unrestricted contraction induced by gravity.