Stellar Collapse and the Formation of Black Holes

Key Insight

A star forms when a large quantity of gas, primarily hydrogen, collapses under its own gravitational pull. This contraction causes the gas atoms to collide with increasing frequency and speed, leading to heating. Eventually, the gas becomes hot enough for hydrogen atoms to fuse into helium, a nuclear reaction akin to a controlled hydrogen bomb. The energy released by this fusion process generates heat, which increases the gas pressure, balancing the gravitational attraction and stabilizing the star. Stars remain stable for extended periods, but they ultimately exhaust their hydrogen and other nuclear fuels. More massive stars consume their fuel faster due to higher temperatures needed to counteract their stronger gravity; for instance, the Sun has approximately five thousand million years of fuel remaining, while more massive stars can deplete theirs in as little as one hundred million years.

When a star runs out of fuel, it cools and begins to contract. In 1928, Subrahmanyan Chandrasekhar calculated how large a star could be and still resist its own gravity after fuel exhaustion. His theory posited that as a star shrinks, matter particles become extremely close, and due to the Pauli exclusion principle, they must have distinct velocities, generating a repulsive force that could balance gravity. However, the theory of relativity limits the maximum difference in particle velocities to the speed of light. This means that if a star becomes sufficiently dense, the repulsion from the exclusion principle becomes insufficient to counterbalance gravitational attraction. Chandrasekhar determined that a cold star exceeding about 1.5 times the mass of the Sun could not support itself against its own gravity; this value is now known as the Chandrasekhar limit. Lev Davidovich Landau independently made a similar discovery around the same time.

For stars below the Chandrasekhar limit, contraction can eventually cease, leading to a stable final state as a 'white dwarf' with a radius of a few thousand miles and a density of hundreds of tons per cubic inch, supported by electron exclusion. Another potential final state is a 'neutron star,' with a radius of only ten miles and a density of hundreds of millions of tons per cubic inch, supported by neutron and proton exclusion. However, stars with masses above the Chandrasekhar limit face an inevitable gravitational collapse when their fuel is exhausted. While some may explode or shed mass, an unstoppable collapse to extreme densities is the predicted outcome. Robert Oppenheimer's 1939 work, using general relativity, showed that as such a star contracts, its gravitational field intensely bends light cones inward. Upon shrinking to a critical radius, the gravitational field at the surface becomes so strong that light, and by extension nothing else, can escape, forming a black hole. From a distant observer's perspective, the star would dim, redden, and eventually vanish, leaving behind an object defined by its event horizon.