https://en.wikipedia.org/wiki/Gravitational_collapse
29 dec. 2017,
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 a pocket 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.
This mass depends on the temperature and density of the cloud, but is typically thousands to tens of thousands of solar masses.[2]
29 dec, 2017.
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:
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.
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.
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 massive neutron star could exist within its Schwarzschild radius (1.0 SR) and appear like a black hole without having all the mass compressed to a singularity at the center; however, this is probably incorrect.
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 a star smaller than 1.0 SR 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]
Kwok, Sun (2006). Physics and chemistry of the interstellar medium. University Science Books. pp. 435–437. ISBN 1-891389-46-7.
Prialnik, Dina (2000). An Introduction to the Theory of Stellar Structure and Evolution. Cambridge University Press. pp. 198–199. ISBN 0-521-65937-X.
And theoretically Black dwarfs - but: "...no black dwarfs are expected to exist in the universe yet"
Class. Quantum Grav. 13 (1996)p393
"Gravitational collapse and space-time singularities", R. Penrose, Phys. Rev. Let. 14 (1965) p 57
B. Carter, "Axisymmetric black hole has only two degrees of freedom", Phys. Rev. Let. 26 (1971) p331
"Black Holes - Planck Unit? WIP". Physics Forums. Archived from the original on 2008-08-02.
Brill, Dieter (19 January 2012). "Black Hole Horizons and How They Begin". Astronomical Review.
29 dec. 2017,
Contents
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 a pocket 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.
This mass depends on the temperature and density of the cloud, but is typically thousands to tens of thousands of solar masses.[2]
29 dec, 2017.
Stellar remnants
NGC 6745 produces material densities sufficiently extreme to trigger star formation through gravitational collapse
Depending on the mass during its lifetime, these stellar remnants can take one of three forms:
- White dwarfs, in which gravity is opposed by electron degeneracy pressure[3]
- Neutron stars, in which gravity is opposed by neutron degeneracy pressure and short-range repulsive neutron–neutron interactions mediated by the strong force
- Black hole, in which there is no force strong enough to resist gravitational collapse
White dwarf
The collapse of the stellar core 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 the cores of larger stars, and are 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.
Simulated view from outside black hole with thin accretion disc, by J. A. Marck[4]
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]
Theoretical minimum radius for a star
The radii of larger mass neutron stars (about 2.0 solar mass) are estimated to be about 12-km, or approximately 2.0 times their equivalent Schwarzschild radius.It might be thought that a sufficiently massive neutron star could exist within its Schwarzschild radius (1.0 SR) and appear like a black hole without having all the mass compressed to a singularity at the center; however, this is probably incorrect.
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 a star smaller than 1.0 SR 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]
See also
References
- Bedran, ML et al.(1996)."Model for nonspherical collapse and formation of black holes by emission of neutrinos, strings and gravitational waves", Phys. Rev. D 54(6),3826.
External links
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