Properties and features of black holes

According to the "No Hair" theorem a black hole has only three independent physical properties: mass, charge and angular momentum. [citation|last=Heusler |first=M. |year=1998 |title=Stationary Black Holes: Uniqueness and Beyond |journal=Living Rev. Relativity |volume=1 |number=6 |url=http://www.livingreviews.org/Articles/Volume1/1998-6heusler/] Any two black holes that share the same values for these properties are indistinguishable. This contrasts with other astrophysical objects such as stars, which have very many—possibly infinitely many—parameters. Consequently, a great deal of information is lost when a star collapses to form a black hole. Since in most physical theories information is preserved (in some sense), this loss of information in black holes is puzzling. Physicists refer to this as the black hole information paradox.

The "No Hair" theorem does make some assumptions about the nature of our universe and the matter it contains. Other assumptions would lead to different conclusions. For example, if nature allows magnetic monopoles to exist—which appears to be theoretically possible, but has never been observed—then it should also be possible for a black hole to have a magnetic charge. If the universe has more than four dimensions (as string theories, a controversial but apparently possible class of theories, would require), or has a global anti-de Sitter structure, the theorem could fail completely, allowing many sorts of "hair". However, in our apparently four-dimensional, very nearly flat universe [citation| author=Hinshaw, G. et al. |title=Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results |year=2008 |url=http://arxiv.org/abs/0803.0732.] , the theorem should hold.

Black hole types

The simplest possible black hole is one that has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.Citation
last=Schwarzschild
first=Karl
author-link=Karl Schwarzschild
title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie
journal=Sitzungsber. Preuss. Akad. D. Wiss.
year=1916
pages=189–196
and Citation
last=Schwarzschild
first=Karl
author-link=Karl Schwarzschild
title=Über das Gravitationsfeld eines Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie
journal=Sitzungsber. Preuss. Akad. D. Wiss.
pages=424–434
year=1916
.] It was the first (non-trivial) exact solution to the Einstein equations to be discovered, and according to Birkhoff's theorem, the only vacuum solution that is spherically symmetric. For real world physics 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—for example a spherical star or planet—once you are in the empty space outside the object. The popular notion of a black hole "sucking in everything" in its surroundings is therefore incorrect; the external gravitational field, far from the event horizon, is essentially like that of ordinary massive bodies.

More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström solution describes a black hole with electric charge, while the Kerr solution yields a rotating black hole. The most general known stationary black hole solution is the Kerr-Newman metric having both charge and angular momentum. All these general solutions share the property that they converge to the Schwarzschild solution at distances that are large compared to the ratio of charge and angular momentum to mass (in natural units).

While the mass of a black hole can take any (positive) value, the other two properties, charge and angular momentum, are constrained by the mass. In natural units , the total charge "Q" and the total angular momentum "J" are expected to satisfy "Q"2+("J"/"M")2 ≤ "M"2 for a black hole of mass "M". Black holes saturating this inequality are called extremal. Solutions of Einstein's equation violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are thus deemed "unphysical". The cosmic censorship hypothesis states that it is impossible for such singularities to form in due to gravitational collapse of generic realistic matter. [For a review see citation |last=wald |first=Robert. M. |author-link=Robert Wald |title=Gravitational Collapse and Cosmic Censorship |year=1997 |url=http://arxiv.org/abs/gr-qc/9710068.] This is supported by numerical simulations. [For a discussion of these numerical simulations see Citation| last=Berger | first=Beverly K. | year=2002 | url=http://www.livingreviews.org/lrr-2002-1 | title=Numerical Approaches to Spacetime Singularities | journal=Living Rev. Relativity | volume=5 |access-date=2007-08-04.]

Black holes forming from the collapse of stars are expected—due to the relatively large strength of electromagnetic force—to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source GRS 1915+105 [citation |first1=Jeffrey E. |last1=McClintock |first2=Rebecca |last2=Shafee |first3=Ramesh |last3=Narayan |first4=Ronald A. |last4=Remillard |first5=Shane W. |last5=Davis |first6=Li-Xin |last6=Li |title=The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105 |journal=Astrophys.J. |volume=652 |year=2006 |pages=518-539 |url=http://arxiv.org/abs/astro-ph/0606076.] appears to have an angular momentum near the maximum allowed value.

izes

Black holes occurring in nature are commonly classified according to their mass, independent of angular momentum "J". The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass M, through r_{sh} approx 3.0, M/M_igodot ;mathrm{km,} where r_{sh}, is the Schwarzschild radius and M_igodot is the mass of the Sun. Thus, size and mass have a simple relationship, which is independent of rotation. According to this mass/size criterion then, black holes are commonly classified as:

* Supermassive black holes that contain hundreds of thousands to billions of solar masses are believed to exist in the center of most galaxies, including our own Milky Way. They are thought to be responsible for active galactic nuclei, and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses. [Citation |last1=Valtonen |first1=M.J. |last2=et. al. |title=A massive binary black-hole system in OJ 287 and atest of general relativity |journal=Nature |year=2008 |volume=452 |doi=10.1038/nature06896 |pages=851]

* Intermediate-mass black holes, whose sizes are measured in thousands of solar masses, probably exist. They have been proposed as a possible power source for the ultra-luminous X ray sources. There is no known mechanism for them to form directly, so they most probably form via collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies. Such creation events should produce intense bursts of gravitational waves, which may be observed in the near- to mid-term. The boundary limit between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present.

* Stellar-mass black holes have masses ranging from a lower limit of about 1.5–3.0 solar masses (the Tolman-Oppenheimer-Volkoff limit for the maximum mass of neutron stars) up to perhaps 15–20 solar masses, and are created by the collapse of individual stars, or by the coalescence (inevitable, due to gravitational radiation) of binary neutron stars. Stars may form with initial masses up to ≈100 solar masses, or possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the red giant, AGB, and Wolf-Rayet stages, or expelled in supernova explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form white dwarfs.

* Micro black holes (also mini black holes) have masses much less than that of a star. At these sizes, the effects of quantum mechanics are expected to come into play. There is no known mechanism for them to form via normal processes of stellar evolution, but certain inflationary scenarios predicted their production during the early stages of the evolution of the universe. According to some theories of quantum gravity they may also be produced in the highly energetic reaction produced by cosmic rays hitting the atmosphere or even in particle accelerators such as the Large Hadron Collider. The theory of Hawking radiation predicts that such black holes will evaporate in bright flashes of gamma radiation. NASA's Fermi Gamma-ray Space Telescope satellite (formerly GLAST), launched in 2008, will search for such flashes as one of its scientific objectives.

Features

Event horizon

The defining feature of a black hole, the event horizon, is a surface in spacetime that marks a point of no return. Once an object has crossed this surface there is no way that it can return to the other side. Consequently, anything inside this surface is completely hidden from observers outside. Other than this the event horizon is a completely normal part of space, with no special features that would allow someone falling into the a black hole to know when he would cross the horizon. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation that is traveling towards the region within the event horizon.

Outside of the event horizon, the gravitational field is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely, provided they stay outside the photon sphere (described below), and also ignoring the effects of gravitational radiation, which causes orbiting objects to lose energy, similar to the effect of electromagnetic radiation.

ingularity

According to general relativity, there is a space-time "singularity" at a center of a spherical black hole, which means an infinite space-time curvature. It means that from a point of view of an observer which falls into a black hole, in a finite time (at the end of his fall) a black hole's mass becomes entirely compressed into a region with zero volume, so its density becomes infinite. This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.

The singularity in a non-rotating black hole is a point, in other words it has zero length, width, and height. The singularity of a rotating black hole is smeared out to form a ring shape lying in the plane of rotation. The ring still has no thickness and hence no volume.

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown is not unexpected, as it occurs in a situation where quantum mechanical effects should become important, since densities are high and particle interactions should thus play a role. Unfortunately, to date it has not been possible to combine quantum and gravitation effects in a single theory. It is however quite generally expected that a theory of quantum gravity will feature black holes without singularities.

Note, however, that formation of the singularity takes finite (and very short) time only from the point of view of an observer which resides in collapsing object. From the point of view of distant observer, it takes infinite time to do so due to gravitational time dilation.

Photon sphere

The photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are dynamically unstable, hence any small perturbation (maybe caused by some infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing the event horizon.

While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.

Other compact objects, such as neutron stars, can also have photon spheres. [citation |first=Robert J. |last=Nemiroff |title=Visual distortions near a neutron star and black hole |journal= American Journal of Physics |volume=61 |pages=619 |year=1993] This follows from the fact gravitation field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will in fact have a photon sphere.

Ergosphere

Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole this effect becomes so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still.

The ergosphere of black hole is bounded by
* on the outside, an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, spacetime is "dragged around at the speed of light."
* on the inside, the (outer) event horizon.

Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in "orbit" within the ergosphere without falling to the center. But they cannot hover (remain stationary, as seen by an external observer), because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also "escape" from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.

Hawking radiation

In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.Citation|last=Hawking |first=S.W. |title=Black hole explosions? |journal=nature |year=1974 |volume=248 |pages=30–31 |url=http://www.nature.com/nature/journal/v248/n5443/abs/248030a0.html |doi=10.1038/248030a0] He got this result by applying quantum field theory in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect black body spectrum. This effect has become known as Hawking radiation. Since Hawking's result many others have verified the effect through various methods. [Citation|last=Page |first=Ron N.|title=Hawking Radiation and Black Hole Thermodynamics |year=2005 |journal=New.J.Phys. |volume=7 |number=203 |url=http://arxiv.org/abs/hep-th/0409024 |doi=10.1088/1367-2630/7/1/203|pages=203]

The temperature of the emitted black body spectrum is proportional to the surface gravity of the black hole. For a Schwarzschild black hole this is inversely proportional to the mass. Consequently, large black holes are very cold and emit very little radiation. A stellar black hole of 10 solar masses, for example, would have a Hawking temperature of several nanokelvin, much less than the 2.7K produced by the Cosmic Microwave Background. Micro black holes on the other hand could be quite bright producing high energy gamma rays.

Due to low Hawking temperature of stellar black holes, Hawking radiation has never been observed at any of the black hole candidates.

Effects of falling into a black hole

This section describes what happens when something falls into a Schwarzschild (i.e. non-rotating and uncharged) black hole. Rotating and charged black holes have some additional complications when falling into them, which are not treated here.

paghettification

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.

Before the falling object crosses 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. Its time would appear to be stopped.

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 to 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.

As the object passes through the event horizon

From the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, there is no (local) way for him to find out whether he has passed the horizon or not. 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.

Inside the event 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 within 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. [cite journal
url=http://adsabs.harvard.edu/abs/2007PASA...24...46L
author=Lewis, G. F. and Kwan, J.
year=2007
title=No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon
journal=Publications of the Astronomical Society of Australia
volume=24
issue=2
pages=46-52
]

Hitting the singularity

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. -- commented out since nothing "passes within the hole's event horizon and lost to the outside universe" in finite time as outside universe sees it. For outside universe, a rock thrown into the hole one million years ago is still outside of the horizon and, theoretically, can be retrieved.

References


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