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 by way of illustration.
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 the masses of these bodies 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 in daily life, viz, the elastic force which arises when we use 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 natural 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 ( to attain its natural length) 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.
This feature makes gravitation stand apart from other forces in nature, which, like the elastic force disappear once their demands are met. The physicist Hermann Bondi called this tendency of gravitation “dictatorial”. If you give in to the demands of a dictator, he makes further demands. As we will see, this dictatorial tendency leads to the formation of black holes.
Before we come to that aspect let us examine another situation wherein gravitational force behaves strangely. This involves, what scientists call a thought experiment, i. e., an imaginary experiment. Suppose you connect a hot body to a cold one by a heat conducting wire. What will happen? Heat energy will flow from the hot body to a cold body with the result that the hot body will become cooler and the cold body hotter. 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. This in turn raises the thermal ( gravity opposing) forces and in the ensuing readjustment the star’s 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 by our thought experiment.
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. Having grown large in size because of expansion the star is called a giant. As its outer envelope is cooler the star has a reddish appearance. Hence the name “red giant”.
The role of thermal pressures in maintaining stellar equilibrium cannot be overstated. Imagine our Sun suddenly losing all its pressures. With nothing to oppose its gravity the whole mass of hot plasma will collapse and the star would shrink to a point. 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 nuclear fuel. With no resistance to their own gravity such stars would undergo rapid gravitational collapse.
The collapse process leads to a stronger and stronger force of gravity near the surface of the star, so much 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.
The writer, a renowned astrophysicist, is professor emeritus at Inter- University
Centre for Astronomy and Astrophysics, Pune University Campus. He was Cambridge University’s Senior
Wrangler in Maths in 1959.