June 15, 2024

How Oppenheimer Worked on Black Holes Before We Knew They Existed

Physicists do not stop studying it if a theoretical object or phenomenon exists or not. First, it builds the foundation to explain various known events and because mathematics allows it, so does the universe. Black holes are such things. For years, they were just oddballs causing problems in Einstein’s general relativity until they were discovered in the universe, showing that the famous theory of gravity has its limits.

Many physicists worked on them long before the first one was observed – Cygnus X-1, in 1971. Among them was J Robert Oppenheimer, who played an important role in estimating how close an object can be before it turns into a black hole – a calculation that has major implications in some of the most innovative observations today.

General relativity was published in 1915 and by 1916, German physicist Karl Schwarzschild found a solution to Einstein’s field equations that broke things apart. Its solution became singular at a certain radius, meaning that the terms of the equation were infinite. Now, from those first descriptions, we get the term singularity to describe the black hole and also the Schwarzschild radius, where the black hole’s exit horizon is located.

In later years scientists debated how “physical” this solution was. The assumption was that things don’t just fall apart by themselves, that internal forces would push back. A planet only collapses because the forces between atoms are sufficient to keep it stable. A star can be much heavier but the energy released by nuclear fusion in its core balances the effect of gravity.

But what happens when a star like the Sun is no longer fusing? it collapses. Still, it was not thought at the time that this was unstoppable. Quantum mechanical effects would turn the object into a dense sphere made of electron-degenerate matter. The internal matter is no longer in a classical plasma but in a new state where electrons, protons, and neutrons (which are types of fermions) interact.

Fermions cannot all be in the same energy state at the same time (this is called the Pauli exclusion principle) and it is this property that creates a pressure that counteracts the gravitational pull towards collapse. We call objects like these white dwarfs, and the Sun is destined to be one. This quantum pressure was not a hard limit though.

Back in 1931, Subrahmanyan Chandrasekhar calculated that you cannot have a white dwarf without differentiation. A non-rotating object made of electron-depleted matter with a mass greater than 1.4 times that of the Sun (now known as the Chandrasekhar limit) does not have a stable solution. This is only partially correct.

The limit is now how much material thieving white dwarfs can steal from a companion before going supernova. These are called Type Ia (pronounced single-A) supernovae and they all have the same luminosity, making them a great standard candle for measuring how far away galaxies are. So what is the stable solution that is closer to a white dwarf? Well, that’s a neutron star!

Although white dwarfs were known to science at the same time as these theoretical discussions were taking place, neutron stars had not yet been discovered. We will need Joycelyn Bell Burnell in 1967 when the first pulsars (pulsating neutron stars) were discovered to bring them from theory to reality.

Neutron stars allow greater masses and densities, and that limit is now known as the Tolman-Oppenheimer-Volkoff limit named after Oppenheimer and George Volkoff who worked it out in 1939, thanks to Richard Tolman’s research.

For masses lower than that limit, the short-range repulsion between neutrons is sufficient to balance the center of gravity. But for higher masses, the neutron star will fall into a black hole. The limit tells how massive stars going supernova can turn into neutron stars or black holes, depending on their original mass.

But recently, we’ve also had a way to test the Tolman-Oppenheimer-Volkoff limit with some of our most advanced experiments: gravitational wave observatories. The first historical observations of a collision between neutron stars (with both objects spinning into a black hole) allowed us to estimate the limit in a real setting.

Although Oppenheimer worked on this theoretical problem long before we knew that neutron stars and black holes were real objects, he did not solve all the mysteries surrounding them if we knew they existed. The neutron star collision limits between 2.01 and 2.17 solar masses. And yet the largest known pulsar is 2.35 times the mass of the Sun.

The road to understanding the most dense objects in the universe is probably still long, but some of the most famous physicists of the 20th century played a role in what we know and understand so far.

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