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Topic: Schwarzschild radius

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Schwarzschild black hole

Black hole

Supermassive black hole

Ping Pong Ball Theory

Gravitational redshift

Schwarzschild metric

Timeline of black hole physics

Karl Schwarzschild

Compton length

Planck mass

RADIUS

Chandrasekhar limit

Planck length

Gravitational constant

Event horizon

	Schwarzschild radius - Wikipedia, the free encyclopedia
		The Schwarzschild radius is proportional to the mass.
		The Schwarzschild radius of a sphere with a uniform density equal to the critical density is equal to the radius of the visible universe.
		The Schwarzschild radius is proportional to the mass, with a proportionality constant involving the gravitational constant and the speed of light.
	en.wikipedia.org /wiki/Schwarzschild_radius (680 words)

	Schwarzschild metric - Wikipedia, the free encyclopedia
		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.
		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.
		For example, the radius of the Sun is approximately 700,000 km, while its Schwarzschild radius is only 3 km.
	en.wikipedia.org /wiki/Schwarzschild_metric (1336 words)

	Schwarzschild radius: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-22)
		Radius (remote authentication dial in user service) is an authentication, authorization and accounting (aaa) protocol for applications such as network...
		In einsteins theory of general relativity, the schwarzschild metric is the most general static, rotation groupspherically symmetric solution of the vacuum...
		A schwarzschild fl hole or static fl hole is a fl hole fully defined by its only parameter, the mass m....
	www.absoluteastronomy.com /encyclopedia/s/sc/schwarzschild_radius.htm (1914 words)

	Very Strong Gravity (Site not responding. Last check: 2007-10-22)
		This is a radius where, if all of the mass of the object were squeezed interior to, would cause the object to become a fl hole.
		At the Schwarzschild radius the escape velocity is the speed of light.
		For the Earth the Schwarzschild radius is 9 millimeters.
	www.geocities.com /CapeCanaveral/Hall/5803/grav.html (458 words)

	Schwarzschild Geometry
		Curiously, the Schwarzschild radius had already been derived (with the correct result, but an incorrect theory) by John Michell in 1783 (this reference is from Erk's Relativity Pages) in the context of Newtonian gravity and the corpuscular theory of light.
		The Schwarzschild surface, the sphere at 1 Schwarzschild radius, is also called the horizon of a fl hole, since an outside observer, even one just outside the Schwarzschild surface, can see nothing beyond the horizon.
		Inside the Schwarzschild radius, proper radial distances and proper times appear to become imaginary (that is, the square root of a negative number).
	casa.colorado.edu /~ajsh/schwp.html (2298 words)

	sciforums.com - The swarzchild radius (Site not responding. Last check: 2007-10-22)
		The Schwarzschild radius is the radius of the event horizon of a fl hole.
		Within the Schwarzschild radius, the escape velocity from the fl hole is greater than the speed of light.
		The size of the Schwarzschild radius may be proportional to the mass of the fl hole.
	www.sciforums.com /showthread.php?t=10755 (604 words)

	Extended Definitions: Schwarzschild radius
		The term Schwarzschild Radius honors the mathematician Karl Schwarzschild, who was the first to calculate the necessary density of matter which would be required to boost the escape velocity from that same mass to the speed of light.
		The Schwarzschild radius is defined as the radius at which the outer boundaries of the Black-Hole would start.
		The Schwarzschild radius is also the radius (from the center ofthe Black-Hole's mass) at which the escape velocity first and exactly equals the speed of light.
	www.geocities.com /recycling_universe/ed_schwarzschildradius.htm (804 words)

	Black Holes
		The Schwarzschild radius is the radius at which the escape velocity from the star is equal to the speed of light.
		Therefore, any material that approaches nearer than the Schwarzschild radius, of a collapsed object, would be trapped forever because to escape the material would have to travel at a speed greater than that of light, which, according to relativity theory, is impossible.
		The Schwarzschild radius defines a one-way boundary (a membrane) that separates the inside of the fl hole from the rest of the universe.
	www.physics.fsu.edu /courses/spring99/ast1002h/blackholes/black.htm (1185 words)

	[No title]
		To be able to see this much deflection of light at the surface of the sun, the Schwarzschild radius (or equivalently the mass of the Sun) would have to be about 700000 ÷ 200 = 3500 times greater than it actually is. Which makes it 3500210^30 kg = 7*10^33 kg.
		The numbers on the vertical axis is in the units of Rs, the Schwarzschild radius, which is the radius of the fl circle at the origin.
		This ring is called the Einstein ring and the angular radius of the ring, the Einstein radius, after his report in 1936 [3] on the possibility of this situation.
	physics.csufresno.edu /akira/GR/Modeling.html (1233 words)

	Black Holes
		Any mass can become a fl hole if it collapses down to the Schwarzschild radius - but if a mass is over some critical value between 2 and 3 solar masses and has no fusion process to keep it from collapsing, then gravitational forces alone make the collapse to a fl hole inevitable.
		One of the terms used with fl holes is "photon sphere", the radius of the orbit of light around the fl hole.
		The event horizon radius is also called the Schwarzschild radius.
	hyperphysics.phy-astr.gsu.edu /hbase/astro/blkhol.html (286 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The Schwarzschild radius need not be the radius of the body that is producing the gravity.
		The Schwarzschild radius can be derived from the equation for escape velocity which is the same as nether velocity downward for any given location within a gravity funnel.
		The Schwarzschild radius was placed here to show how fl hole radii can be found within certain limits (these radii will always be equal to or less than their corresponding Schwarzschild radii) - and for some other calculations to be shown regarding the electron.
	www.softcom.net /users/greebo/black.htm (651 words)

	FAQ to SCI.PHYSICS on Black Holes by Matt McIrvin (Site not responding. Last check: 2007-10-22)
		Schwarzschild expressed his metric in terms of coordinates which, at large distances from the object, resembled spherical coordinates with an extra coordinate t for time.
		Therefore the fatal r goes as the cube root of the mass, whereas the Schwarzschild radius of the fl hole is proportional to the mass.
		If you start timing from the moment the you see the object half a Schwarzschild radius away from the event horizon, the light will dim exponentially from that point on with a characteristic time of about 0.2 milliseconds, and the time of the last photon is about a hundredth of a second later.
	antwrp.gsfc.nasa.gov /htmltest/gifcity/bh_pub_faq.html (3321 words)

	Introduction
		Schwarzschild Radius is the distance from the center of a fl hole to its event horizon.
		The "radius" is essentially the distance from the center of the fl hole, singularity, to the edge of the fl hole, the event horizon.
		Where m equals the mass of the fl hole, G equals the universal constant, and r is the Schwarzschild radius.
	www.hepguru.com /blackholes/characteristics_frame.htm (909 words)

	Schwarzschild radius (Site not responding. Last check: 2007-10-22)
		Schwarzschild radius is the radius below which the gravitational attraction between the particles of a body must cause it to undergo irreversible gravitational collapse.
		The gravitational radius (R) of an object of mass M is given by the following formula, in which G is the universal gravitational constant and c is the speed of light: R = 2GM/c
		For a mass as small as a human being, the gravitational radius is of the order of 10
	abyss.uoregon.edu /~js/glossary/schwarzschild_radius.html (114 words)

	Lecture 18 - White Dwarfs & Neutron Stars (3/23/99)
		This radius is called the Schwarzschild Radius for the astrophysicist Karl Schwarzschild who calculated it soon after the publication of Einstein's theory in 1916.
		The effective radius of a fl hole, the Schwarzschild radius, depends only on the mass itself, not on the actual density the the mass has (beyond the fact that it must be within its own Schwarzschild radius.
		However, the Schwarzschild radius for 1 Msun is 3 km, and thus for 3 Msun it is 9km.
	www.aoc.nrao.edu /~smyers/courses/astro12/L18.html (1605 words)

	Black Holes
		Another way of defining a fl hole is that for a given mass, there is a radius where if all the mass is compress within this radius the curvature of spacetime becomes infinite and the object is surrounded by an event horizon.
		Schwarzschild radius and varys with the mass of the object (large mass objects have large Schwarzschild radii, small mass objects have small Schwarzschild radii).
		It is simply the radius where a test particle of mass m must move at the speed of light to exceed the gravitational energy of the primary object.
	zebu.uoregon.edu /~js/ast122/lectures/lec21.html (686 words)

	Halfbakery: Schwarzschild radius warning labels
		The circle in question would be quite tiny (and might get distorted to even smaller size should the product be crushed at all), but this warning should suffice to absolve your company of liability in the case of consumer fl hole mishaps.
		I guess it would have to take into account the increased gravitational pull as the object is squished further, so the circle is probably bigger than you would first imagine, maybe even a few micrometres in size.
		In fact, if you had your thumb one penny radius away from the fl hole, you'd experience the same graviational pull as said penny at that distance.
	www.halfbakery.com /idea/Schwarzschild_20radius_20warning_20labels (1364 words)

	Comments on Problem Set #9 (Site not responding. Last check: 2007-10-22)
		We want to find the radius of the planet such that the escape velocity is the velocity of light c.
		The Schwarzschild radius emerges from a solution to the Einstein field equations for a spherical mass of radius R.
		A fl hole is a star or stars that have collapsed into a point (where the radius of the star had at some point become smaller than the Schwarzschild radius).
	www.physics.nyu.edu /courses/V85.0020/node93.html (751 words)

	Proper Time In Circular Orbits
		That's because 3m is the radius of the orbit of light.
		This suggests that even if something prevented a massive object from collapsing within its Schwarzschild radius 2m, it would still be a very remarkable object if it was just within 3m, because then it could (theoretically) support circular light orbits, although I don't believe such orbits would be stable (even neglecting interference from infalling matter).
		Not surprisingly, the ratio goes to infinity as r drops to 3, because the proper time for a circular orbit of radius 3m is zero.
	www.mathpages.com /rr/s6-05/6-05.htm (1344 words)

	Stellar Evolution - Black Holes
		This definition is known as the Schwarzschild radius (Freedman and Kaufmann 2002), and is also the definition of the critical radius referred to earlier in the introduction.
		The structural properties of a fl hole, as described by the Schwarzschild radius and the event horizon were further extended in 1965 by Roger Penrose, who proved the Singularity Theorem (Weisstein 2004).
		These characteristics also affect the structure of a fl hole such as the length of the Schwarzschild radius which is the distance of the event horizon from the singularity (Freedman and Kauffman 2002).
	astronomyonline.org /Stars/BlackHole.asp?Cate=Stars&SubCate=OG04&SubCa... (5984 words)

	Lecture 32 - Black Holes and Relativity (4/5/96)
		This is known as the Schwarzschild Radius for the astrophysicist Karl Schwarzschild.
		A 3 Msun neutron star has a radius of about 9 km, and a Schwarzschild radius of 9km, so it is a fl hole.
		The angle of bending just depends upon the distance the light ray passes a mass in ratio to the Schwarzschild radius.
	www.aoc.nrao.edu /~smyers/courses/astro01/L32.html (2885 words)

	Falling to the Singularity of the Black Hole
		The white dot is actually a line which extends from us to the Schwarzschild surface still ahead, though we only ever see it as a dot, not as a line.
		The tide at 1 Schwarzschild radius would be less than 1g if the fl hole exceeded 30,000 solar masses.
		If we see someone enter the Schwarzschild bubble through the upper (white) surface, then the moment of passage marks the instant when we see them pass inside the horizon of the fl hole.
	casa.colorado.edu /~ajsh/singularity.html (1766 words)

	Stellar Evolution - Black Holes
		Using Einstein’s field equations, Schwarzschild found for a mass concentrated inside a critical radius, which is defined as the distance from the centre of the mass, no object within this radius can pass to the outside, not even light.
		The calculation of the Schwarzschild radius has only a single variable that affects it, which is the object’s mass (Hamilton 1999).
		Schwarzschild and Reissner-Nordstron fl holes are circular and don’t have an ergoregion, whilst Kerr and Kerr-Newman fl holes are oblate spheroids and have an ergoregion.
	astronomyonline.org /Stars/BlackHole.asp?Cate=Home&SubCate=OG04&... (5984 words)

	Intro to Stars (Lab 7) Black Holes
		The radius at which this occurs is called the Schwarzschild Radius.
		For a fl hole having the same mass as the Sun the Schwarzschild radius is about 3 kms.
		The fact that the motion of light is dramatically affected by the presence of the fl hole leads to some unusual effects.
	www.unm.edu /~astro1/101lab/lab7/lab7_F_2.html (448 words)

	Black Holes
		At this radius, the escape speed is equal to the speed of light, and once light passes through, even it cannot escape.
		If the sun was replaced with a fl hole that had the same mass as the sun, the Schwarzschild radius would be 3 km (compared to the sun's radius of nearly 700,000 km).
		The X-rays are sent off into space before the matter crosses the Schwarzschild radius and crashes into the singularity.
	imagine.gsfc.nasa.gov /docs/science/know_l2/black_holes.html (1378 words)

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