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Topic: Schwarzschild black hole

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	black hole
		Black holes began to take on their modern form in 1916 when the German astronomer Karl Schwarzschild (1873-1916) used Einstein's general theory of relativity to find out what would happen if all the mass of an object were squeezed down to a dimensionless point – a singularity.
		Supermassive fl holes are known almost certainly to exist at the center of many large galaxies, and to be the ultimate source of the energy behind the phenomenon of the active galactic nucleus.
		For a non-rotating fl hole, the event horizon is a spherical surface, with a radius equal to the Schwarzschild radius, centered on the singularity at the fl hole's heart.
	www.daviddarling.info /encyclopedia/B/blackhole.html (1208 words)

	Black Hole
		However, a fl hole could be detected by the effect of its gravitational field on nearby objects (e.g., if it is orbited by a visible star), during the collapse while it was forming, or by the X rays and radio frequency signals emitted by rapidly swirling matter being pulled into the fl hole.
		Black holes require the general relativistic concept of a curved spacetime: their most striking properties rely on a distortion of the geometry of the space surrounding them.
		Using the first law of fl hole mechanics, it follows that the entropy of a fl hole is one quarter of the area of the horizon.
	www.juliantrubin.com /encyclopedia/astronomy/blackhole.html (5554 words)

	Black Holes (Site not responding. Last check: 2007-10-17)
		Black holes are the densest, most massive singular objects in the universe.
		A second way for fl holes to form is that, in some rare instances, two neutron stars will be locked in a binary relationship.
		The matter is funneled into a disk-shaped torus by the hole's spin and magnetic fields, but in the very narrow regions over the fl hole's poles, matter can be energized to extremely high temperatures and speeds, escaping the fl hole in the form of high-speed jets.
	filer.case.edu /~sjr16/advanced/stars_blackhole.html (1527 words)

	Schwarzschild metric - Wikipedia, the free encyclopedia
		In Einstein's theory of general relativity, the Schwarzschild solution (or the Schwarzschild vacuum) describes the gravitational field outside a spherical, non-rotating mass such as a (non-rotating) star, planet, or fl hole.
		A Schwarzschild fl hole or static fl hole is a fl hole that has no charge or angular momentum.
		The Schwarzschild solution is named in honour of its discoverer Karl Schwarzschild who found the solution in 1916, only a few months after the publication of Einstein's theory of general relativity.
	en.wikipedia.org /wiki/Schwarzschild_metric (1391 words)

	black hole Comparison Table (Site not responding. Last check: 2007-10-17)
		Black hole endowed with the maximal amount of force charge possible for a given total mass.
		Utilized in a theoretical model for quasars and active galactic nuclei, according to which the energy source is due to infall (and resultant heating) of gas and stars onto a supermassive central fl hole.
		In string theory, a particular kind of fl hole that may have large mass initially, but that becomes ever lighter as a piece of the Calabi-Yau portion of space shrinks.
	www.site.uottawa.ca:4321 /astronomy/blackhole_table.html (313 words)

	Rotating black hole - Wikipedia, the free encyclopedia
		A rotating fl hole (Kerr fl hole or Kerr-Newman fl hole) is a fl hole that possesses angular momentum.
		Rotating fl holes are thought to be formed in the gravitational collapse of a massive rotating star or from the collapse of a collection of stars with an average non-zero angular momentum.
		A fl hole in general is surrounded by a spherical surface, the event horizon situated at the Schwarzschild radius, where the escape velocity is equal to the velocity of light.
	en.wikipedia.org /wiki/Rotating_black_hole (1156 words)

	Schwarzschild black hole
		A Schwarzschild fl hole or static fl hole is a fl hole fully defined by its only parameter, the mass M.
		The Schwarzschild fl hole is characterized by a surrounding area, called the event horizon which is situated at the Schwarzschild radius, often called the radius of a fl hole.
		The static fl hole is represented by the Schwarzschild metric, a solution to the Einstein field equations for a point mass in empty space (vacuum), found by Karl Schwarzschild in 1916.
	publicliterature.org /en/wikipedia/s/sc/schwarzschild_black_hole.html (243 words)

	Gothos: Jillian's Guide to Black Holes
		Why you see the galaxy at all, when the fl hole is between you and it, and why it appears as a ring is from the bending of light due to the strong force of gravity of the fl hole.
		Black holes have escape velocities just like anything else, it's just that the numbers are orders of magnitude bigger than the escape velocities of planets.
		Accept this: the singularity of a static fl hole is described as a point at which spacetime is infinitely curved.
	www.gothosenterprises.com /black_holes/static_black_holes.html (1938 words)

	Kerr black hole
		A type of fl hole that possesses only mass and angular momentum (but not electrical charge – the third possible proerty of a fl hole).
		Kerr fl holes are probably the commonest in nature, since the massive stars from which they typically form possess rotation (but no overall charge) before they collapse at the end of their lives.
		On leaving the fl hole you would find yourself either in a region of "negative space," the physical meaning of which is unclear, or in an entirely different universe.
	www.daviddarling.info /encyclopedia/K/Kerr_black_hole.html (522 words)

	Schwarzschild Black Hole -- from Eric Weisstein's World of Physics
		A fl hole with zero charge Q = 0 and no angular momentum J = 0.
		The exterior solution for such a fl hole is known as the Schwarzschild solution (or Schwarzschild metric), and is an exact unique solution to the Einstein field equations of general relativity for the general static isotropic metric (i.e., the most general metric tensor that can represent a static isotropic gravitational field),
		Here, M is the mass of the fl hole, G is the gravitational constant, and c is the speed of light.
	scienceworld.wolfram.com /physics/SchwarzschildBlackHole.html (372 words)

	Anatomy of A Black Hole
		By definition a fl hole is a region where matter collapses to infinite density, and where, as a result, the curvature of spacetime is extreme.
		For a fl hole whose mass equals 10 suns, this radius is about 30 kilometers or 19 miles, which translates into a critical circumference of 189 kilometers or 118 miles.
		At the center of a fl hole lies the singularity, where matter is crushed to infinite density, the pull of gravity is infinitely strong, and spacetime has infinite curvature.
	archive.ncsa.uiuc.edu /Cyberia/NumRel/BlackHoleAnat.html (649 words)

	SPACE.com -- Voyage into the Vortex: Survival Tips for Black Hole Travelers
		That's the advice of Lior Burko, a University of Utah physicist whose new research shows that travel through a fl hole is not theoretically impossible, despite the violent nature of the beasts and the assumption by most theorists that a spacecraft would be pulverized.
		At the center of a fl hole is a point called a singularity, where matter is crushed to infinite density.
		Stellar fl holes, the variety created by the collapse of a star, are no good.
	www.space.com /scienceastronomy/blackhole_travel_030404.html (751 words)

	Schwarzschild Modern Relativity modernrelativity special general black hole mass energy Einstein wormhole time modern ...
		The Schwarzschild solution is the solution for the case of a non-rotating uncharged fl hole.
		From this we see that the coordinate speed of light near a fl hole depends on the direction in which it travels.
		The photon sphere of a Schwarzschild fl hole is a sphere given by a radius at which a photon can make a complete closed orbit around the fl hole.
	www.geocities.com /zcphysicsms/chap10.htm (1869 words)

	Howstuffworks "HowStuffWorks - Black Holes - Types of Black Holes"
		The Kerr fl hole, which is probably the most common form in nature, rotates because the star from which it was formed was rotating.
		Artist concept of a fl hole and its surroundings: The flened circle is the event horizon and the egg-shaped region is the ergosphere.
		If a fl hole has a companion (another star or disk of material), it is possible to measure the radius of rotation or speed of orbit of the material around the unseen fl hole.
	science.howstuffworks.com /black-hole2.htm (353 words)

	Black Hole -- from Eric Weisstein's World of Physics
		The gravitational forces are so strong in a fl hole that they overcome neutron degeneracy pressure and, roughly speaking, collapse to a point (known as a singularity).
		The fl hole no hair theorem shows that mass, charge, and angular momentum are the only properties which a fl hole can possess.
		In 1973, S. Hawking showed that fl holes radiate as if they have a temperature proportional to their surface gravity, and therefore evaporate over time.
	scienceworld.wolfram.com /physics/BlackHole.html (691 words)

	3.1 Schwarzschild Black Holes
		Finally, for a study of tails in the presence of a cosmological constant refer to [49], while for a recent study, using analytic methods, of the late-time tails of linear scalar fields outside Schwarzschild and Kerr fl holes refer to [36, 37].
		The existence of ``algebraically special'' solutions for perturbations of Schwarzschild, Reissner-Nordström and Kerr fl holes were first pointed out by Chandrasekhar [57].
		The perturbations of Reissner-Nordström fl holes, due to the spherical symmetry of the solution, follow the footsteps of the analysis that we have presented in this section.
	relativity.livingreviews.org /Articles/lrr-1999-2/node4.html (1436 words)

	Welcome to Rob's Black Hole page
		Black holes are thought to have come from dead stars, and as most stars are spinning then a non-spinning fl hole is rare.
		Black holes come in all sizes, from the super massive said to be at the centre of each galaxy, to atom sizes mini fl holes that are as massive as a mountain!
		Black holes are basically made up of a singularity, an event horizon and a Schwarzschild radius.
	elektro.cmhnet.org /~robert/science.html (1758 words)

	Visualization of the inner accretion disk around a Schwarzschild black hole
		Animation showing the predicted appearance of a turbulent disk around a Schwarzschild fl hole as viewed by a distant observer at an inclination angle of 80 degrees - ie almost edge-on.
		The main goal of the simulations is to investigate the predicted variability of accreting fl holes.
		The variability of accretion onto Schwarzschild fl holes from turbulent magnetized disks, Philip J. Armitage and Christopher S. Reynolds, MNRAS, 341, 1041 (2003).
	jilawww.colorado.edu /~pja/black_hole.html (497 words)

	White Holes and Wormholes
		The trapped region between the two horizons is the Schwarzschild bubble encountered on the trip into the fl hole.
		We are at 0.35 Schwarzschild radii from the central singularity.
		This movie is the same as the Falling to the singularity of the fl hole movie, but now with another Universe, visible but unreachable, on the other side of the horizon.
	casa.colorado.edu /~ajsh/schww.html (1197 words)

	Building Blocks of Code
		Although Karl Schwarzschild analytically solved Einstein's equations for a spherically symmetric, stationary fl hole in 1917, his solution demanded a very special choice of space and time coordinates.
		Although the Schwarzschild fl hole is the simplest model, it's more than just a stepping stone to more complex systems: theory predicts that non-rotating fl holes eventually settle down into Schwarzschild fl holes, just as a gong struck with a mallet gradually stops vibrating.
		In the "real world," fl holes are unlikely to be perfectly spherical: after all, the events surrounding their formation, evolution and interactions with each other or other large objects are likely to be very violent.
	archive.ncsa.uiuc.edu /Cyberia/NumRel/BuildingBlocks.html (524 words)

	Inside a black hole
		Three parameters are enough to fully describe a fl hole : its mass, its electrical charge, and its rotation speed (actually, its angular momentum, but it's quite the same).
		The opposite of a fl hole, one is only able to go out of it, due to the fact that we can't travel back in time.
		In this case, the fl hole is no longer eternal, it only appears when the star collapses.
	nrumiano.free.fr /Estars/int_bh.html (1532 words)

	Re: Mass loss rate of a Schwarzschild black hole (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-17)
		The r-coordinate in Schwarzschild spacetime is defined such that for r > 2M, the proper surface area of a sphere of constant r is given by A = 4 pi r^2.
		However, both W2 and W3 say that the effective radius of a radiating fl hole is, due to light bending, 3^(3/2) M. Clearly, this reduces the age and increases dM/dt in your your calculation by a factor of 27/4.
		The inverse relationship between temperature and mass can be explained by saying that since the spacetime curvature goes from (essentially) flat to infinite "faster" for smaller mass fl holes, their tidal effects on the quantum vacuum is greater.
	www.lns.cornell.edu.cob-web.org:8888 /spr/2001-09/msg0035293.html (550 words)

	Wave Scattering and Absorption by a Schwarzschild Black Hole
		M is the mass of the fl hole.
		The product ME may be thought of as the ratio of the fl hole horizon to the wavelength of the quantum particle.
		This plot shows the log of the scattering cross section as a function of angle for a range of fl hole masses.
	www.mrao.cam.ac.uk /~srd24/scattering/index.html (397 words)

	Center of Black Hole
		However, it is true that the Schwarzschild "R" coordinate (the radius) becomes timelike inside the event horizon of a Schwarzschild fl hole - while the Schwarzschild 't' coordinate becomes spacelike.
		Note that in spite of the switch of the roles of the Schwarzschild r and t coordinates, there are still three space and one time coordinates inside a fl hole, just as there are three space and one time coordiante outside a fl hole.
		Havent heard of something like that but I guess I will like to tell you that near a fl hole, space-time coordinates reverse themselves.Like you cannot avoid next thursday in spacetime real universe, near a fl hole, you cannot avoid hitting singularity, that is r-----> 0.
	www.physicsforums.com /showthread.php?t=80310 (774 words)

	Schwarzschild black hole (via CobWeb/3.1 planetlab1.netlab.uky.edu) (Site not responding. Last check: 2007-10-17)
		The simplest kind of fl hole in theory but one that could never occur in the real universe.
		An event horizon: effectively, the outer surface of the fl hole; its distance from the singularity is the Schwarzschild radius
		Compare with Kerr fl hole and Reissner-Nordstrom fl hole.
	www.daviddarling.info.cob-web.org:8888 /encyclopedia/S/Schwarzschild_black_hole.html (183 words)

	Chapter 18. Black Holes
		In this chapter, we present Bekenstein and Hawking's equation for the entropy of a Black Hole in terms of both SI and SG units of measure.
		The SG equation for the density of a Black Hole with a Schwarzschild radius is:
		The equation for the density of a Black Hole that is as dense as water is:
	www.writword.com /unituniv/c18.htm (602 words)

	The Light Cone: The Schwarzschild Black Hole
		That is, using Einstein's equation, Schwarzschild had determined how spacetime is curved due to the presence of a nonrotating spherical mass.
		The spacetime of a fl hole is curved in such a way as to cause the future light cones to tip inward.
		Here is a nice VRML visualization Geometry Around Black Holes: Curvature and Lightcones of the geometry of the Schwarzschild fl hole.
	www.phy.syr.edu /courses/modules/LIGHTCONE/schwarzschild.html (604 words)

	The Anatomy of Black Holes - Page 3
		However, the concept of a fl hole has been around for over 200 years.
		The event horizon can be said to mark the surface of the fl hole, although in truth the fl hole is the singularity in the center of the event horizon sphere.
		Ignoring the differences introduced by rotation, we can say that to be inevitably drawn into a fl hole, one has to cross inside the Schwarzschild radius.
	imagine.gsfc.nasa.gov /docs/teachers/blackholes/imagine/page3.html (547 words)

	INI : Abstracts : GMR : Decay and the conformal energy of waves around the Schwarzschild black hole (Site not responding. Last check: 2007-10-17)
		We provide decay estimates for solutions to the decoupled, inhomogeneous wave equation around a Schwarzschild fl hole.
		In Euclidean space, the conformal charge is a conserved quantity which is used to prove the decay of the local energy.
		The analogue around a Schwarzschild fl hole can grow because of trapping near the photon sphere at r=3M.
	www.newton.cam.ac.uk /programmes/GMR/blue.html (180 words)

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