Gravitational collapse

Gravitational collapse in astronomy is the sudden inward fall of a massive body under the influence of the force of gravity. It occurs when all other forces fail to supply a sufficiently high pressure to counterbalance gravity and keep the massive body in (dynamical) equilibrium. Gravitational collapse is at the heart of the structure formation in the universe. An initial smooth distribution of matter will eventually collapse and cause the hierarchy of structures, such as clusters of galaxies, stellar groups, stars and planets. For example, a star is born through the gravitational collapse of a cloud of interstellar matter. The compression caused by the collapse raises the temperature until nuclear fuel ignites in the center of the star and the collapse comes to a halt. The thermal pressure gradient (leading to expansion) compensates the gravity (leading to compression) and a star is the dynamical equilibrium between these two forces.

More specifically the term gravitational collapse refers to the gravitational collapse of a star at the end of its life time, also called the death of the star. When all stellar energy sources are exhausted, the interior of a star will undergo a gravitational collapse. In this sense a star is a "temporary" equilibrium state between a gravitational collapse at stellar birth and a gravitational collapse at stellar death. The end states are called compact stars, either white dwarfs or neutron stars. Very massive stars cannot find a new dynamical equilibrium; they keep contracting. They are said to undergo a continued gravitational collapse or catastrophic gravitational collapse. With increasing speed the stellar density increases beyond any bound to infinite densities and the stars shrinks in a time much less than a second to a pointlike object. This is a physical singularity, a problem unsolved in present day physics. At the final stage the density of matter is so high that current gravitational theories do not apply. Before the singular state is reached, however, the condensed matter has the properties of a black hole and the ultimate fate cannot be observed, in principle.

The gravitational collapse of the interior of a star releases so much energy that the outer layers are blown away in an explosion. The remnants of explosions leading to the formation of white dwarfs are observed as planetary nebulae. Larger explosions, leading to the formation of a neutron star or black hole, are observed as supernovae, of which remnants can be observed. When the outer layers of a star are already removed (through a stellar wind for example), a catastrophic gravitational collapse can be seen as a gamma ray burst, a short flash of gamma rays lasting only seconds to minutes (see also gamma-ray astronomy). Each gamma ray burst marks the birth of a black hole, usually in a very distant galaxy.

Catastrophic gravitational collapse toward a black hole

A general relativistic description of catastrophic gravitational collapse has two points of view: as seen by a comoving observer and as seen by a distant (stationary) observer.

Viewed by a comoving observer

An observer standing on a star in catastrophic gravitational collapse towards the black hole state undergoes a free fall (that is: in a comoving frame he does not feel gravity to first order). He only feels the tidal force (difference between the gravity on his head and his feet). This force increases beyond bounds as the star shrinks to a smaller radius. In the transverse direction the comoving observer during the catastrophic gravitational collapse will be squashed by the combination of the tidal force and the increasing curvature of space.

This free fall will end in a finite proper time, with an infinite length and with thickness zero, while in the limit volume zero is reached and the density is increased to infinity.

The comoving observer does not feel any particular force when he passes the Schwarzschild radius (the radius of a black hole, also called the event horizon). In other words, this radius is not a physical singularity. If the black hole is large, perhaps a supermassive black hole at the center of a galaxy, the tidal forces may not even be strong at this radius. However, his observations of the outside world change dramatically. During the fall he will see the horizon on the surface rising upward through the gravitational deflection of light. Just below the horizon he will see more and more light coming from the back of the star until he can see the entire stellar surface. At the same time the part of the sky above him is becoming a smaller and smaller region around his zenith. When he passes the Schwarzschild radius, nothing is left of the outside world and he can't see any stars in the sky. Instead he sees the (shrinking) stellar surface in every direction. "Direction" becomes meaningless, or, rather, all directions become down.

Before the free falling observer passes the Schwarzschild radius, a call for help signal can in principle reach the distant Earth or a spaceship. After passing this radius, all the signals he sends out will fall along with him in the gravitational collapse and never reach the outside world (hence the name event horizon).

Viewed by a distant (stationary) observer

A stationary observer at Earth or in a distant orbit will have an entirely different view on the catastrophic gravitational collapse. A clock of the free falling observer is in a stronger part of the gravitational field and when viewed from a distance appears to tick slower (gravitational time dilation). Also radiation is seen to tick slower and thus is observed at a longer wavelength (gravitational redshift). As the free falling observer (in his time) falls faster and faster toward the Schwarzschild radius, the stationary observer sees him progressing slower and slower towards the Schwarzschild radius and will never see him passing that stage. Instead the stationary observer will see collapse progessively dimmer and redder, until the entire star plus comoving observer disappears in much less than a second. The last photon the stationary observer will receive, comes from a stage of the collapsing star just outside the Schwarzschild radius.

See also Scientific wager.

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