D-brane - Black Holes

Black Holes

Another important use of D-branes has been in the study of black holes. Since the 1970s, scientists have debated the problem of black holes having entropy. Consider, as a thought experiment, dropping an amount of hot gas into a black hole. Since the gas cannot escape from the hole's gravitational pull, its entropy would seem to have vanished from the universe. In order to maintain the second law of thermodynamics, one must postulate that the black hole gained whatever entropy the infalling gas originally had. Attempting to apply quantum mechanics to the study of black holes, Stephen Hawking discovered that a hole should emit energy with the characteristic spectrum of thermal radiation. The characteristic temperature of this Hawking radiation is given by


where G is Newton's gravitational constant, M is the black hole's mass and kB is Boltzmann's constant.

Using this expression for the Hawking temperature, and assuming that a zero-mass black hole has zero entropy, one can use thermodynamic arguments to derive the "Bekenstein entropy":

The Bekenstein entropy is proportional to the black hole mass squared; because the Schwarzschild radius is proportional to the mass, the Bekenstein entropy is proportional to the black hole's surface area. In fact,

where is the Planck length.

The concept of black hole entropy poses some interesting conundra. In an ordinary situation, a system has entropy when a large number of different "microstates" can satisfy the same macroscopic condition. For example, given a box full of gas, many different arrangements of the gas atoms can have the same total energy. However, a black hole was believed to be a featureless object (in John Wheeler's catchphrase, "Black holes have no hair"). What, then, are the "degrees of freedom" which can give rise to black hole entropy?

String theorists have constructed models in which a black hole is a very long (and hence very massive) string. This model gives rough agreement with the expected entropy of a Schwarzschild black hole, but an exact proof has yet to be found one way or the other. The chief difficulty is that it is relatively easy to count the degrees of freedom quantum strings possess if they do not interact with one another. This is analogous to the ideal gas studied in introductory thermodynamics: the easiest situation to model is when the gas atoms do not have interactions among themselves. Developing the kinetic theory of gases in the case where the gas atoms or molecules experience inter-particle forces (like the van der Waals force) is more difficult. However, a world without interactions is an uninteresting place: most significantly for the black hole problem, gravity is an interaction, and so if the "string coupling" is turned off, no black hole could ever arise. Therefore, calculating black hole entropy requires working in a regime where string interactions exist.

Extending the simpler case of non-interacting strings to the regime where a black hole could exist requires supersymmetry. In certain cases, the entropy calculation done for zero string coupling remains valid when the strings interact. The challenge for a string theorist is to devise a situation in which a black hole can exist which does not "break" supersymmetry. In recent years, this has been done by building black holes out of D-branes. Calculating the entropies of these hypothetical holes gives results which agree with the expected Bekenstein entropy. Unfortunately, the cases studied so far all involve higher-dimensional spaces — D5-branes in nine-dimensional space, for example. They do not directly apply to the familiar case, the Schwarzschild black holes observed in our own universe.

Read more about this topic:  D-brane

Other articles related to "black holes, black hole, black":

Safety Of Particle Collisions At The Large Hadron Collider - Large Hadron Collider - Specific Concerns - Concerns Not Meeting Peer Review
... University of Tübingen, argues that micro black holes created in the LHC could grow exponentially ... the potential catastrophic threat from microscopic black holes, including the possible danger from Hawking radiation emitted by black holes ... the authors of the research paper "Astrophysical implications of hypothetical stable TeV-scale black holes", responded to Plaga's concerns ...
Sandip Chakrabarti
... then asked him to solve the Dirac Equation in Kerr black hole geometry ... Subsequently, he concentrated on black hole astrophysics, received his Ph.D ... Major work in this period includes nucleosynthesis around black holes with Prof ...
Science Writing Award - Past Winners: Scientist
2003 Ray Jayawardhana Astronomy Magazine "Beyond Black" 1999 John Wheeler and Kenneth Ford W.W ... Norton Geons, Black Holes Quantum Foam 1998 Leonard Susskind Scientific American Magazine Black Holes and the Information Paradox 1996 Mitchell Begelman Martin Rees W.H ... Gravity's Fatal Attraction Black Holes in the Universe 1994 Kip S ...
M-sigma Relation - Importance
... Before the M–σ relation was discovered in 2000, a large discrepancy existed between black hole masses derived using three techniques ... based on the motion of stars or gas near the black hole seemed to give masses that averaged ~1% of the bulge mass (the Magorrian relation) ... and the Soltan argument, which computes the cosmological density in black holes needed to explain the quasar light—both gave a mean value of M/Mbulge that was a factor ~10 smaller than implied ...
Black Holes In Fiction - Games
... video games Super Mario Galaxy and Super Mario Galaxy 2, black holes are the equivalent of bottomless pits in which if Mario (or Luigi) falls or slips off an edge with a black ... end of the game, when Mario defeats Bowser, his galaxy collapses into a supermassive black hole and starts consuming the universe ... Only the Lumas were able to neutralize the black hole ...

Famous quotes containing the words holes and/or black:

    A person taking stock in middle age is like an artist or composer looking at an unfinished work; but whereas the composer and the painter can erase some of their past efforts, we cannot. We are stuck with what we have lived through. The trick is to finish it with a sense of design and a flourish rather than to patch up the holes or merely to add new patches to it.
    Harry S. Broudy (b. 1905)

    He hangs in the hall by his black cravat,
    The ladies faint, and the children holler:
    Only my Daddy could look like that,
    And I love my Daddy like he loves his Dollar.
    William Jay Smith (b. 1918)