The existence or non-existence of a theoretical object or phenomenon does not prevent physicists from studying it (theoretical physics), and first, such investigations establish the basis for explaining various known events, and it is conceivable that, if mathematics permits, the universe could exhibit such phenomena. Black holes are a prime example of such objects, and for decades, they remained puzzling oddities, causing puzzles within Einstein’s general theory of relativity, until their discovery in the universe exposed the limitations of the renowned physicist’s theory.
Even before the first black hole –Cygnus X-1– was observed in 1971, a number of theoretical physics scientists had worked diligently on this concept, and among them we find J.Robert Oppenheimerwho played a fundamental role in estimating the density at which an object turns into a black holea calculation with significant implications for some of today’s most groundbreaking observations.
General relativity was published in 1915, and already in 1916 the German physicist Carl Schwarzschild –remembered precisely for having given fundamental contributions to theoretical physics and relativity– found a solution to Einstein’s field equations which led to a particular result. His solution became singular at a certain radius, where the terms of the equation became infinite, and from these early descriptions, we derived the term “singularity” to describe a black hole and the “Schwarzschild radius,” which indicates the event horizon of a black hole.
Subsequently, scientists spent decades debating the “physicality” of this solution, and in all the elaborations of theoretical physics the assumption was that things would not collapse in on themselves, with internal forces resisting them, for example a planet does not implode because the forces between its atoms are sufficient to maintain stability, and a star, although much heavier, balances the effect of gravity with the energy released by nuclear fusion in its core.
However, what happens when a star like the Sun stops merging? It implodes, or rather collapses on itself, yet, at the time, it was not perceived as an unstoppable process. The effects of quantum mechanics would transform the object into a dense sphere made of degenerate matter, with the material inside no longer behaving like a classical plasma, but instead entering a new state in which electrons, protons and neutrons (all kinds of fermions) interact.
Further additions to theoretical black hole physics, to date
Fermions cannot all occupy the same energy state at the same time (this is known as Pauli exclusion principle) and this property creates a pressure that counteracts gravitational collapse, and today we call objects like these “white dwarfs” and the fate of the Sun is to become one, however this quantum pressure was not an absolute limit.
In 1931 Subrahmanyan Chandrasekhar calculated that a white dwarf cannot be indiscriminately large, and a non-rotating object made of electrodegenerated matter with a mass greater than 1.4 times that of the Sun (now known as Chandrasekhar limit) doesn’t have a stable solution, but this turned out to be only partially correct.
The limit is now seen as the amount of material a white dwarf can accrue from a companion star before going supernova, this is known as type Ia supernova and they all have the same brightness, making them excellent standard candles for measuring distances to galaxies. So what is the stable solution that is even denser than a white dwarf? Well, that’s a neutron star.
Still in the “early days” of theoretical physics, while white dwarfs were becoming known to science at the same time these theoretical discussions were taking place, neutron stars had not yet been discovered; it took Jocelyn Bell Burnell in 1967 with the discovery of the first pulsars (pulsating neutron stars) to bring them from theory to reality.
Neutron stars allow for higher masses and densities, and that limit is now known as Tolman-Oppenheimer-Volkoff limit (TOV), named after Oppenheimer and George Volkoff, who elaborated it in 1939, based on the research of Richard Tolman.
For masses below this limit, the short-range neutron repulsion is sufficient to balance gravity but, for larger masses, the neutron star will collapse into a black hole. The limit determines how massive stars that go supernova can transform into neutron stars or black holes, depending on their original mass.
We recently had the opportunity to test the TOV limit using some of the most advanced tools at our disposal: gravitational wave observatories. Historical observations of a neutron star collision (resulting in the formation of a black hole) have allowed us to estimate the limit in a real-life scenario, and while Oppenheimer worked on this theoretical physics problem long before we knew neutron stars and black holes as real objects, their discovery hasn’t solved all the mysteries surrounding them.
The neutron star collision puts the limit between 2.01 and 2.17 solar masses, however the most massive known pulsar is 2.35 times the mass of the Sun, so the path to understanding the densest objects in the universe is probably still long, but some of the most important and brilliant theoretical physics minds of the 20th century have played a crucial role in what we know and understand so far.
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