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Of black holes, naked singularities, and quantum gravity

Modern science has introduced us to many strange ideas on the universe, but one of the strangest is the ultimate fate of massive stars in the Universe that reached the end of their life cycles. Having exhausted the fuel that sustained it for millions of years of shining life in the skies, the star is no longer able to hold itself up under its own weight, and it then shrinks and collapses catastrophically unders its own gravity. Modest stars like the Sun also collapse at the end of their life, but they stabilize at a smaller size. But if a star is massive enough, with tens of times the mass of the Sun, its gravity overwhelms all the forces in nature that might possibly halt the collapse. From a size of millions of kilometers across, the star then crumples to a pinprick size, smaller than even the dot on an “i”.

What would be the final fate of such massive collapsing stars? This is one of the most exciting questions in astrophysics and modern cosmology today. An amazing inter-play of the key forces of nature takes place here, including gravity and quantum forces. This phenomenon may hold the secrets to man’s search for a unified understanding of all forces of nature, with exciting implications for astronomy and high energy astrophysics. Surely, this is an outstanding unresolved mystery that excites physicists and the lay person alike.

The story of massive collapsing stars began some eight decades ago when Subrahmanyan Chandrasekhar probed the question of final fate of stars such as the Sun. He showed that such a star, on exhausting its internal nuclear fuel, would stabilize as a “White Dwarf”, about a thousand kilometers in size. Eminent scientists of the time, in particular Arthur Eddington, refused to accept this, saying how a star can ever become so small. Finally Chandrasekhar left Cambridge to settle in the United States. After many years, the prediction was verified. Later, it also became known that stars which are three to five times the Sun’s mass give rise to what are called Neutron stars, just about ten kilometers in size, after causing a supernova explosion.

But when the star has a mass more than these limits, the force of gravity is supreme and overwhelming. It overtakes all other forces that could resist the implosion, to shrink the star in a continual gravitational collapse. No stable configuration is then possible, and the star which lived millions of years would then catastrophically collapse within seconds. The outcome of this collapse, as predicted by Einstein’s theory of general relativity, is a space-time singularity: an infinitely dense and extreme physical state of matter, ordinarily not encountered in any of our usual experiences of physical world.

Cradle of Stars
Cradle of stars, photo by Scott Cresswell CC-by-2.0 via Flickr

As the star collapses, an ‘event horizon’ of gravity can possibly develop. This is essentially ‘a one way membrane’ that allows entry, but no exits permitted. If the star entered the horizon before it collapsed to singularity, the result is a ‘Black Hole’ that hides the final singularity. It is the permanent graveyard for the collapsing star.

As per our current understanding of physics, it was one such singularity, the ‘Big Bang’, that created our expanding universe we see today. Such singularities will be again produced when massive stars die and collapse. This is the amazing place at boundary of Cosmos, a region of arbitrarily large densities billions of times the Sun’s density.

An enormous creation and destruction of particles takes place in the vicinity of singularity. One could imagine this as ‘cosmic inter-play’ of basic forces of nature coming together in a unified manner. The energies and all physical quantities reach their extreme values, and quantum gravity effects dominate this regime. Thus, the collapsing star may hold secrets vital for man’s search for a unified understanding of forces of nature.

The question then arises: Are such super-ultra-dense regions of collapse visible to faraway observers, or would they always be hidden in a black hole? A visible singularity is sometimes called a ‘Naked Singularity’ or a ‘Quantum Star’. The visibility or otherwise of such super-ultra-dense fireball the star has turned into, is one of the most exciting and important questions in astrophysics and cosmology today, because when visible, the unification of fundamental forces taking place here becomes observable in principle.

A crucial point is, while gravitation theory implies that singularities must form in collapse, we have no proof the horizon must necessarily develop. Therefore, an assumption was made that an event horizon always does form, hiding all singularities of collapse. This is called ‘Cosmic Censorship’ conjecture, which is the foundation of current theory of black holes and their modern astrophysical applications. But if the horizon did not form before the singularity, we then observe the super-dense regions that form in collapsing massive stars, and the quantum gravity effects near the naked singularity would become observable.

“It turns out that the collapse of a massive star will give rise to either a black hole or naked singularity”

In recent years, a series of collapse models have been developed where it was discovered that the horizon failed to form in collapse of a massive star. The mathematical models of collapsing stars and numerical simulations show that such horizons do not always form as the star collapsed. This is an exciting scenario because the singularity being visible to external observers, they can actually see the extreme physics near such ultimate super-dense regions.

It turns out that the collapse of a massive star will give rise to either a black hole or naked singularity, depending on the internal conditions within the star, such as its densities and pressure profiles, and velocities of the collapsing shells.

When a naked singularity happens, small inhomogeneities in matter densities close to singularity could spread out and magnify enormously to create highly energetic shock waves. This, in turn, have connections to extreme high energy astrophysical phenomena, such as cosmic Gamma rays bursts, which we do not understand today.

Also, clues to constructing quantum gravity–a unified theory of forces, may emerge through observing such ultra-high density regions. In fact, the recent science fiction movie Interstellar refers to naked singularities in an exciting manner, and suggests that if they did not exist in the Universe, it would be too difficult then to construct a quantum theory of gravity, as we will have no access to experimental data on the same!

Shall we be able to see this ‘Cosmic Dance’ drama of collapsing stars in the theater of skies? Or will the ‘Black Hole’ curtain always hide and close it forever, even before the cosmic play could barely begin? Only the future observations of massive collapsing stars in the universe would tell!

Recent Comments

  1. Bernard Goetz

    I don’t accept that black holes collapse to a singularity. If the pressure P of ultra relativistic material is given as (rho)(c^2)/3 [where rho is the energy density], the total supporting energy or viral energy of this object would be ∫PdV = (Mc^2)/3. The gravitational binding energy of a star is about 1.1G(M^2)/R. Using the viral equation, if (Mc^2)/3 is equal to 1/2 of 1.1 G(M^2)/R, the radius R of this object equals 1.65GM/(c^2), or 0.82 the Schwarzschild radius.

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