LECTURE 7: BLACK HOLES
A black hole is a region of space in which the gravitational field is so powerful that nothing, not even light, can escape its pull after having fallen past its event horizon. The term "Black Hole" comes from the fact that, at a certain point, even electromagnetic radiation (e.g. visible light) is unable to break away from the attraction of these massive objects. This renders the hole's interior invisible or, rather, black like the appearance of space itself.
Despite its interior being invisible, a black hole may reveal its presence through an interaction with matter that lies in orbit outside its event horizon. For example, a black hole may be perceived by tracking the movement of a group of stars that orbit its center. Alternatively, one may observe gas (from a nearby star, for instance) that has been drawn into the black hole. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes.[2][3][4] Such observations have resulted in the general scientific consensus that — barring a breakdown of our understanding nature— black holes do exist in our universe.[5]
While the idea of an object with gravity strong enough to prevent light from escaping was proposed in 1783, by the Reverend John Mitchell, an amateur British astronomer. In 1795, Pierre-Simon Laplace, a French physicist independently came to the same conclusion.[6][7] Black holes, as currently understood, are described by Einstein's general theory of relativity, which he developed in 1916. This theory predicts that when a large enough amount of mass is present in a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, preventing all matter and radiation within it from escaping.
While general relativity describes a black hole as a region of empty space with a pointlike singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation.[8][9][10] However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.
Popular accounts commonly try to explain the black hole phenomenon by using the concept of escape velocity, the speed needed for a vessel starting at the surface of a massive object to completely clear the object's gravitational field. Using Newton's law of gravity it is straight forward to show that if you take a sufficiently dense object its escape velocity will equal or even exceed the speed of light. Citing that nothing can exceed the speed of light they then infer that nothing would be able escape such a dense object. Of course, this argument has a flaw in that it doesn't explain why light would even be affected by a gravitating body, let alone why it wouldn't be able to escape. Some argue that in general relativity light is affected by gravity and that indeed the energy required to escape a black hole is infinite. This makes the argument for the attraction of light stronger but still leaves needed explanation.
Two concepts introduced by Albert Einstein help us understand this situation. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, spacetime. This continuum has some special properties. An object is not free to move around spacetime at will, instead it must always move forwards in time. In fact, not only must an object move forwards in time, it also cannot change its position faster than the speed of light. This is the main result of the theory of special relativity.
The second lesson is the main message of general relativity, mass deforms the structure of spacetime. Loosely speaking, the effect of a mass on spacetime is to slightly tilt the direction of time towards the mass. As a result, objects tend to move towards masses; we experience this as gravity. As you get closer to a mass this tilting effect becomes stronger. At some point close to the mass this effect becomes so strong that all the possible paths an object can take lead towards the mass. That is, you can no longer get further away from the black hole no matter how much you try; you are trapped. This is precisely what happens at the event horizon of a black hole.
So, to put it succinctly, the reason you cannot escape a black hole is because you cannot move backwards in time (or faster than the speed of light).
An object in any very strong gravitational field feels a tidal force stretching it in the direction of the object generating the gravitational field. This is because the inverse square law causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it, even atoms or composite nucleons; this is called spaghettification. The process of spaghettification is as follows. First, the object that is falling into the black hole splits in two. Then the two pieces each split themselves, rendering a total of four pieces. Then the four pieces split to form eight. This process of bifurcation continues up to and past the point in which the split-up pieces of the original object are at the order of magnitude of the constituents of atoms. At the end of the spaghettification process, the object is a string of elementary particles.
The strength of the tidal force of a black hole depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.
An object in a gravitational field experiences a slowing down of time, called gravitational time dilation, relative to observers outside the field. The outside observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity.
From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer, as well as redder.
From the viewpoint of the falling object, distant objects generally appear blue-shifted due the gravitational field of the black hole. This effect may be partly (or even entirely) negated by the red shift caused by the velocity of the infalling object with respect to the object in the distance.
From the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, the Earth could be passing through an event horizon at just this moment without us ever noticing. An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon.
The object reaches the singularity at the center within a finite amount of proper time, as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory. Objects closer to the singularity aren't seen, as all paths light could take from objects farther in point inwards towards the singularity.
The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A paper in 2007 examined the effect of firing a rocket pack with the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicious burst of the rocket can extend the lifetime of the faller, but overdoing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.[16]
As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; it is believed that a theory of quantum gravity is needed to accurately describe events near it. Regardless, as soon as an object passes within the hole's event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole's mass, charge, and angular momentum change slightly, to reflect the addition of the infalling object's matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study.
According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center. The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble and ground-based telescopes in Hawaii were used in a large survey of galaxies.
For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission.[26][27] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[26][27] The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.[27]
Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, and the Sombrero Galaxy.[28]
Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:
- A star called S2 (star) follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
- The first estimates indicated that the central object contains 2.6M (2.6 million) solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
- Further observations[29] strengthened the case for a black hole, by showing that the central object's mass is about 3.7M solar masses and its radius no more than 6.25 light-hours.
In 2002, the Hubble Space Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes.[30][31] This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.
In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.[32][33] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.
In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 400 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.[34]
Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses.[35][36] The most distant stellar-mass black hole ever observed is a member of a binary system located in the Messier 33 galaxy.[37]
In theory there is no smallest size for a black hole. Once created, it has the properties of a black hole. Stephen Hawking theorized that primordial black holes could evaporate and become even tinier, i.e. micro black holes. Searches for evaporating primordial black holes are proposed for the GLAST satellite to be launched in 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate.
The formation of black hole analogs on Earth in particle accelerators has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.[38]
They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at the Relativistic Heavy Ion Collider [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic Large Hadron Collider [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested.
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