Black Holes and Neutron Stars
A black hole is a region of spacetime from which gravity prevents anything, including light, from escaping.[1] The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole, there is a mathematically defined surface called an event horizon that marks the point of no return. The hole is called "black" because it absorbs all the light that hits the horizon, reflecting nothing, just like a perfect black body in thermodynamics.[2][3] Quantum field theory in curved spacetime predicts that event horizons emit radiation like a black body with a finite temperature. This temperature is inversely proportional to the mass of the black hole, making it difficult to observe this radiation for black holes of stellar mass or greater.
Objects whose gravity fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.
Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies.
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as light. Matter falling onto a black hole can form an accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location. These data can be used to exclude possible alternatives (such as neutron stars). In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the core of our Milky Way galaxy contains a supermassive black hole of about 4.3 million solar masses.
The no-hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum.[27] Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical (i.e. non-quantum) mechanics.
These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.[33] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.[34] This is different from other field theories like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox.[35][36]
Physical properties The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.[8] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[37] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[38]
Solutions describing more general black holes also exist. Charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.[39]
While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy
for a black hole of mass M. Black holes saturating this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.[40] This is supported by numerical simulations.[41]
Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects. The black-hole candidate binary X-ray source GRS 1915+105[42] appears to have an angular momentum near the maximum allowed value.
Black holes are commonly classified according to their mass, independent of angular momentum J or electric charge Q. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass M through... where rsh is the Schwarzschild radius and MSun is the mass of the Sun.[43] This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
Singularity Main article: Gravitational singularity At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[54] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity lying in the plane of rotation.[55] In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[56] The singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity, once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a point; after attaining a certain ideal velocity, it is best to free fall the rest of the way.[57] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".[58]
In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole.[59] The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility.[60] It also appears to be possible to follow closed timelike curves (going back to one's own past) around the Kerr singularity, which lead to problems with causality like the grandfather paradox.[61] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.[62]
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[63] This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.[64][65]
http://en.wikipedia.org/wiki/Black_hole
Objects whose gravity fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Long considered a mathematical curiosity, it was during the 1960s that theoretical work showed black holes were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.
Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies.
Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as light. Matter falling onto a black hole can form an accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location. These data can be used to exclude possible alternatives (such as neutron stars). In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the core of our Milky Way galaxy contains a supermassive black hole of about 4.3 million solar masses.
The no-hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum.[27] Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical (i.e. non-quantum) mechanics.
These properties are special because they are visible from outside a black hole. For example, a charged black hole repels other like charges just like any other charged object. Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.[33] Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.
When an object falls into a black hole, any information about the shape of the object or distribution of charge on it is evenly distributed along the horizon of the black hole, and is lost to outside observers. The behavior of the horizon in this situation is a dissipative system that is closely analogous to that of a conductive stretchy membrane with friction and electrical resistance—the membrane paradigm.[34] This is different from other field theories like electromagnetism, which do not have any friction or resistivity at the microscopic level, because they are time-reversible. Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in. The information that is lost includes every quantity that cannot be measured far away from the black hole horizon, including approximately conserved quantum numbers such as the total baryon number and lepton number. This behavior is so puzzling that it has been called the black hole information loss paradox.[35][36]
Physical properties The simplest black holes have mass but neither electric charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after Karl Schwarzschild who discovered this solution in 1916.[8] According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.[37] This means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass. The popular notion of a black hole "sucking in everything" in its surroundings is therefore only correct near a black hole's horizon; far away, the external gravitational field is identical to that of any other body of the same mass.[38]
Solutions describing more general black holes also exist. Charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum.[39]
While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy
for a black hole of mass M. Black holes saturating this inequality are called extremal. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These solutions have so-called naked singularities that can be observed from the outside, and hence are deemed unphysical. The cosmic censorship hypothesis rules out the formation of such singularities, when they are created through the gravitational collapse of realistic matter.[40] This is supported by numerical simulations.[41]
Due to the relatively large strength of the electromagnetic force, black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects. The black-hole candidate binary X-ray source GRS 1915+105[42] appears to have an angular momentum near the maximum allowed value.
Black holes are commonly classified according to their mass, independent of angular momentum J or electric charge Q. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is roughly proportional to the mass M through... where rsh is the Schwarzschild radius and MSun is the mass of the Sun.[43] This relation is exact only for black holes with zero charge and angular momentum; for more general black holes it can differ up to a factor of 2.
Singularity Main article: Gravitational singularity At the center of a black hole as described by general relativity lies a gravitational singularity, a region where the spacetime curvature becomes infinite.[54] For a non-rotating black hole, this region takes the shape of a single point and for a rotating black hole, it is smeared out to form a ring singularity lying in the plane of rotation.[55] In both cases, the singular region has zero volume. It can also be shown that the singular region contains all the mass of the black hole solution.[56] The singular region can thus be thought of as having infinite density.
Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity, once they cross the event horizon. They can prolong the experience by accelerating away to slow their descent, but only up to a point; after attaining a certain ideal velocity, it is best to free fall the rest of the way.[57] When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces in a process sometimes referred to as spaghettification or the "noodle effect".[58]
In the case of a charged (Reissner–Nordström) or rotating (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different spacetime with the black hole acting as a wormhole.[59] The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility.[60] It also appears to be possible to follow closed timelike curves (going back to one's own past) around the Kerr singularity, which lead to problems with causality like the grandfather paradox.[61] It is expected that none of these peculiar effects would survive in a proper quantum treatment of rotating and charged black holes.[62]
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory.[63] This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.[64][65]
http://en.wikipedia.org/wiki/Black_hole
Neutron Stars
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Neutron stars are the densest and tiniest stars known to exist in the universe. Neutron stars are the end points of stars whose mass after nuclear burning is greater than the Chandrasekhar Limit for white dwarfs, but whose mass is not great enough to overcome the neutron degeneracy pressure to become black holes. Such stars are composed almost entirely of neutrons, which are subatomic particles without net electrical charge and with slightly larger mass than protons. Neutron stars are very hot and are supported against further collapse by quantum degeneracy pressure due to the phenomenon described by the Pauli exclusion principle. This principle states that no two neutrons (or any other fermionic particles) can occupy the same place and quantum state simultaneously.
Any star with an initial main-sequence mass of around 10 solar masses or above has the potential to become a neutron star. As the star evolves away from the main sequence, subsequent nuclear burning produces an iron-rich core. When all nuclear fuel in the core has been exhausted, the core must be supported by degeneracy pressure alone. Further deposits of material from shell burning cause the core to exceed the Chandrasekhar limit. Electron degeneracy pressure is overcome and the core collapses further, sending temperatures soaring to over 5 billion Kelvin. At these temperatures, photodisintegration (the breaking up of iron nuclei into alpha particles by high- energy gamma rays) occurs. As the temperature climbs even higher, electrons and protons combine to form neutrons, releasing a flood of neutrinos. When densities reach nuclear density of 4 x 1017 kilograms per cubic meter, neutron degeneracy pressure halts the contraction. The infalling outer atmosphere of the star is flung outwards, becoming a Type II or Type Ib supernova. The remnant left is a neutron star. If it has a mass greater than about 2-3 solar masses, it collapses further to become a black hole. Other neutron stars are formed within close binaries.
As the core of a massive star is compressed during a supernova, and collapses into a neutron star, it retains most of its angular momentum. Since it has only a tiny fraction of its parent's radius (and therefore its moment of inertia is sharply reduced), a neutron star is formed with very high rotation speed, and then gradually slows down. Neutron stars are known to have rotation periods from about 1.4 ms to 30 seconds. The neutron star's density also gives it very high surface gravity, up to 7×1012 m/s2 with typical values of a few ×1012 m/s2 (that is more than 1011 times of that of Earth). One measure of such immense gravity is the fact that neutron stars have an escape velocity of around 100,000 km/s, about a third of the speed of light. Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.
The surface of the neutron star is made of iron. In the presence of a strong magnetic field the atoms of iron polymerize. The polymers pack to form a lattice with density about ten thousand times that of terrestrial iron and strength a million times that of steel. It has excellent electrical conductivity along the direction of the magnetic field, but is a good insulator perpendicular to this direction. Immediately beneath this surface the neutron star is still solid, but its composition is changing. Larger nuclei, particularly rich in neutrons, are formed, and materials that on Earth would be radioactive are stable in this environment, such as nickel-62. With increasing depth, the density rises. When its density reaches 400 billion times that of water, the nuclei can get no larger and neutrons start ‘dripping’ out. As the density goes up further, the nuclei dissolve in a sea of neutrons. The neutron fluid is a superfluid – it has no viscosity and no resistance to flow or movement. Within a few kilometres of the surface the density has reached the density of the atomic nucleus. Up to this point the properties of matter are reasonably well understood, but beyond it understanding becomes increasingly sketchy. The composition of the core of the star is particularly uncertain: it may be liquid or solid; it may consist of other nuclear particles (pions, for example, or hyperons); and there may be another phase change, where quarks start ‘dripping’ out of the neutrons, forming another liquid.
A neutron star has a mass comparable to that of the Sun, but as it is only about 10 km (6 mi) in radius, it has an average density 1 quadrillion times that of water. Such a large mass in such a small volume produces an intense gravitational force: objects weigh a 100 billion times more on the surface of a neutron star than on the surface of the Earth. The intense gravitational field affects light and other electromagnetic radiation emitted by the star, producing significant redshift (z approximately equal to 0.2). The strong gravitational attraction allows neutron stars to spin rapidly (hundreds of revolutions per second) without disintegrating. Such spin rates are expected if the core of the original star collapses without loss of angular momentum - if the original star has a magnetic field, then this too may be conserved and concentrated in the collapse to a neutron star. Pulsars, gamma-ray burst sources, and the neutron stars in some X-ray binaries are believed to have magnetic fields with a strength of about 100 million Tesla (roughly a million million times the strength of the Earth’s magnetic field).
The gravitational field at the star's surface is about 2×1011 times stronger than on Earth. Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible.[8]
http://en.wikipedia.org/wiki/Neutron_star
Any star with an initial main-sequence mass of around 10 solar masses or above has the potential to become a neutron star. As the star evolves away from the main sequence, subsequent nuclear burning produces an iron-rich core. When all nuclear fuel in the core has been exhausted, the core must be supported by degeneracy pressure alone. Further deposits of material from shell burning cause the core to exceed the Chandrasekhar limit. Electron degeneracy pressure is overcome and the core collapses further, sending temperatures soaring to over 5 billion Kelvin. At these temperatures, photodisintegration (the breaking up of iron nuclei into alpha particles by high- energy gamma rays) occurs. As the temperature climbs even higher, electrons and protons combine to form neutrons, releasing a flood of neutrinos. When densities reach nuclear density of 4 x 1017 kilograms per cubic meter, neutron degeneracy pressure halts the contraction. The infalling outer atmosphere of the star is flung outwards, becoming a Type II or Type Ib supernova. The remnant left is a neutron star. If it has a mass greater than about 2-3 solar masses, it collapses further to become a black hole. Other neutron stars are formed within close binaries.
As the core of a massive star is compressed during a supernova, and collapses into a neutron star, it retains most of its angular momentum. Since it has only a tiny fraction of its parent's radius (and therefore its moment of inertia is sharply reduced), a neutron star is formed with very high rotation speed, and then gradually slows down. Neutron stars are known to have rotation periods from about 1.4 ms to 30 seconds. The neutron star's density also gives it very high surface gravity, up to 7×1012 m/s2 with typical values of a few ×1012 m/s2 (that is more than 1011 times of that of Earth). One measure of such immense gravity is the fact that neutron stars have an escape velocity of around 100,000 km/s, about a third of the speed of light. Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.
The surface of the neutron star is made of iron. In the presence of a strong magnetic field the atoms of iron polymerize. The polymers pack to form a lattice with density about ten thousand times that of terrestrial iron and strength a million times that of steel. It has excellent electrical conductivity along the direction of the magnetic field, but is a good insulator perpendicular to this direction. Immediately beneath this surface the neutron star is still solid, but its composition is changing. Larger nuclei, particularly rich in neutrons, are formed, and materials that on Earth would be radioactive are stable in this environment, such as nickel-62. With increasing depth, the density rises. When its density reaches 400 billion times that of water, the nuclei can get no larger and neutrons start ‘dripping’ out. As the density goes up further, the nuclei dissolve in a sea of neutrons. The neutron fluid is a superfluid – it has no viscosity and no resistance to flow or movement. Within a few kilometres of the surface the density has reached the density of the atomic nucleus. Up to this point the properties of matter are reasonably well understood, but beyond it understanding becomes increasingly sketchy. The composition of the core of the star is particularly uncertain: it may be liquid or solid; it may consist of other nuclear particles (pions, for example, or hyperons); and there may be another phase change, where quarks start ‘dripping’ out of the neutrons, forming another liquid.
A neutron star has a mass comparable to that of the Sun, but as it is only about 10 km (6 mi) in radius, it has an average density 1 quadrillion times that of water. Such a large mass in such a small volume produces an intense gravitational force: objects weigh a 100 billion times more on the surface of a neutron star than on the surface of the Earth. The intense gravitational field affects light and other electromagnetic radiation emitted by the star, producing significant redshift (z approximately equal to 0.2). The strong gravitational attraction allows neutron stars to spin rapidly (hundreds of revolutions per second) without disintegrating. Such spin rates are expected if the core of the original star collapses without loss of angular momentum - if the original star has a magnetic field, then this too may be conserved and concentrated in the collapse to a neutron star. Pulsars, gamma-ray burst sources, and the neutron stars in some X-ray binaries are believed to have magnetic fields with a strength of about 100 million Tesla (roughly a million million times the strength of the Earth’s magnetic field).
The gravitational field at the star's surface is about 2×1011 times stronger than on Earth. Such a strong gravitational field acts as a gravitational lens and bends the radiation emitted by the star such that parts of the normally invisible rear surface become visible.[8]
http://en.wikipedia.org/wiki/Neutron_star
