Gravitational collapse

Gravitational collapse

Gravitational collapse of a star

Gravitational collapse is the inward fall of an astronomical object due to the influence of its own gravity which tends to draw the object toward its center of mass.

Gravitational collapse is at the heart of structure formation in the universe. An initial smooth distribution of matter will eventually collapse and cause a hierarchy of structures, such as clusters of galaxies, stellar groups, stars and planets.

A star is born through the gradual 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 due to the outward thermal pressure balances the gravitational forces and the star is in dynamic equilibrium. And, when all its energy sources are exhausted, a star will again collapse until it reaches a new equilibrium state.

Contents

• Star formation 1
• Stellar remnants 2
• White dwarf 2.1
• Neutron star 2.2
• Black holes 2.3
• References 4

Star formation

An interstellar cloud of gas will remain in hydrostatic equilibrium as long as the kinetic energy of the gas pressure is in balance with the potential energy of the internal gravitational force. Mathematically this is expressed using the virial theorem, which states that, to maintain equilibrium, the gravitational potential energy must equal twice the internal thermal energy.[1] If an interstellar cloud of gas is massive enough that the gas pressure is insufficient to support it, the cloud will undergo gravitational collapse. The mass above which a cloud will undergo such collapse is called the Jeans mass. The Jeans mass depends on the temperature and density of the cloud, but is typically thousands to tens of thousands of solar masses.[2]

Stellar remnants

NGC 6745 produces material densities sufficiently extreme to trigger star formation through gravitational collapse

At what is called the death of the star when a star has burned out its fuel supply, it will undergo a contraction that can be halted only if it reaches a new state of equilibrium. Depending on the mass during its lifetime, these stellar remnants can take one of three forms:

White dwarf

The collapse to a white dwarf takes place over tens of thousands of years, while the star blows off its outer envelope to form a planetary nebula. If it has a companion star, a white dwarf-sized object can accrete matter from the companion star until it reaches the Chandrasekhar limit (about one and a half times the mass of our Sun) at which point gravitational collapse takes over again. While it might seem that the white dwarf might collapse to the next stage (neutron star), they instead undergo runaway carbon fusion, blowing completely apart in a Type Ia supernova.

Neutron star

Neutron stars are formed by gravitational collapse of larger stars, the remnant of other types of supernova. They are so compact that a Newtonian description is inadequate for an accurate treatment, which requires the use of Einstein's general relativity.

Black holes

Logarithmic plot of Mass against mean Density (with solar values as origin) showing possible kinds of stellar equilibrium state. For a configuration in the shaded region, beyond the black hole limit line, no equilibrium is possible, so runaway collapse will be inevitable.

According to Einstein's theory, for even larger stars, above the Landau-Oppenheimer-Volkoff limit, also known as the Tolman–Oppenheimer–Volkoff limit (roughly double the mass of our Sun) no known form of cold matter can provide the force needed to oppose gravity in a new dynamical equilibrium. Hence, the collapse continues with nothing to stop it.

Simulated view from outside black hole with thin accretion disc by J.A.Marck[4]

Once a body collapses to within its Schwarzschild radius it forms what is called a black hole, meaning a space-time region from which not even light can escape. It follows from a theorem of Roger Penrose[5] that the subsequent formation of some kind of singularity is inevitable. Nevertheless, according to Penrose's cosmic censorship hypothesis, the singularity will be confined within the event horizon bounding the black hole, so the space-time region outside will still have a well behaved geometry, with strong but finite curvature, that is expected[6] to evolve towards a rather simple form describable by the historic Schwarzschild metric in the spherical limit and by the more recently discovered Kerr metric if angular momentum is present.

On the other hand, the nature of the kind of singularity to be expected inside a black hole remains rather controversial. According to some theories, at a later stage, the collapsing object will reach the maximum possible energy density for a certain volume of space or the Planck density (as there is nothing that can stop it). This is when the known laws of gravity cease to be valid.[7]There are competing theories as to what occurs at this point, but it can no longer really be considered gravitational collapse at that stage.[8]

It might be thought that a sufficiently large neutron star could exist inside its Schwarzschild radius and appear like a black hole without having all the mass compressed to a singularity at the center; however, this is a misconception. Within the event horizon, matter would have to move outward faster than the speed of light in order to remain stable and avoid collapsing to the center. No physical force therefore can prevent the star from collapsing to a singularity (at least within the currently accepted framework of general relativity; this doesn’t hold for the Einstein–Yang–Mills–Dirac system). A model for nonspherical collapse in general relativity with emission of matter and gravitational waves has been presented.[9]