Collapsed stars


When a star has burnt up all of its nuclear fuel, it collapses under its own gravitational field. The received wisdom is that no other force of nature is strong enough to resist the gravitational attraction, so, if the total mass of the collapsing star exceeds three solar masses, it ends up with a radius of zero, as a “black hole”. However, the property that the field itself has energy, and therefore a gravitational mass (with negative sign), allows an alternative solution. Even when we neglect all the other forces of nature, the gravity field  itself becomes repulsive, giving solutions where most of the original stellar material concentrates in a thin surface shell. The   concept of the propagating field is fundamental to Einstein's theory of gravity, particularly in the article of 1918, dealing with gravitational waves. Armed with it I have been able to analyse in detail the trajectories of all the material points of an idealized cold star, known as a dust ball. No matter how massive the ball, it collapses into a shell rather than a black hole. I have shown that the catchphrase ‘Matter tells space how to bend and space tells matter how to move.’ (see Wikipedia) is quite misleading. See my article Fields tell matter how to move.

Gravitational energy gravitates

The idea that gravitational energy itself gravitates may be found in articles by Albert Einstein in the four years preceding his article on General Relativity (GR) in 1915. The same idea formed part of David Hilbert’s analysis; this was also published in 1915, and the resulting equation, relating the derivatives of the field to the density of stellar material should properly be called the Hilbert-Einstein equation. To Hilbert we should accord the credit for recognizing, during the decade following 1915, that this energy leads, in the strong-field situation, to repulsion rather than attraction. Hilbert also recognized that, in the collapse process, causality must be preserved. I am afraid that received ‘wisdom’ has ignored this fundamental requirement. The infinitely concentrated mass at the centre of a black hole causes the peculiar object known as an “event horizon” to form at precisely the radius where the field description of Hilbert places the surface shell. For the collapsed object thought to occupy the centre of our galaxy (mass of four million Suns), this radius is about sixteen solar radii. The large concentration of stellar material - rather than an event horizon - at this radius means that Hilbert causality is upheld. The bizarre “spaghettification” of observers passing through the event horizon, which black-hole theory predicts through space and time effectively changing places, does not occur.


Of course, much happened in the theory of gravity between 1924 and 2011. Between 1911 and 1917, I see Einstein as establishing two contradictory theories of gravity. The better known one, called General Relativity (GR), maintained that gravity is geometry and nothing but geometry. This point of view has led us to bizarre conclusions, such as time travel through wormholes and spaghettification. But Einstein never abandoned his other theory, according to which gravity is a field, like electromagnetism. In particular this theory led him to predict, in 1917, the phenomenon of gravitational waves, and also, in 1939, to criticize the notions of the black hole and the event horizon. We can now appreciate that, at these two moments, his physical intuition prevailed over the blinding insight of GR and claiming the ‘principle of equivalence’ misguidedly as “the happiest thought of my life”. Indeed, at these two moments Einstein was speaking out, not only for Hilbert’s causality, but also for his own ‘Special Relativity’ of 1905. In retrospect we ought to call the latter simply Relativity, since there is no ‘general’ relativity.


The contradictory nature of these two theories of gravity caused deep confusion in the gravitational community. Sociologically, we may say that Einstein’s two big issues were resolved in favour of his critics in the late 1960s (in respect of black holes), and in his favour in the late 1970s (in respect of gravitational waves). But, I submit, we do not have to follow the laws of sociology! It was inevitable that the waves were going to be observed, albeit indirectly, because that is the only way interactions can propagate. In the seventy years that the scholars were debating whether the world is geometric or causal, all sorts of misconceptions about the nature of gravitational energy crept in; in particular it became customary to claim that this energy, in contrast with its electromagnetic equivalent, could not be localized.


Actually the field theory of gravity did undergo some development, starting indeed with two close associates of Einstein, Theodore de Donder and Cornelius Lanczos in the 1920s, and continuing with Vladimir Fock and Lev Landau in the 1940s. Landau developed an expression for the localized energy of the gravitational field, but unfortunately the isolation of Soviet science, in the World War and subsequent Cold War, resulted in both his and Fock’s contributions being largely ignored. However, with the publication of Steven Weinberg's textbook Gravitation and Cosmology in 1971, and encouraged by the indirect observation of gravitational waves through the inspiralling orbits of binary neutron stars, we now have been provided with the tools necessary to understand gravitational collapse properly.