
	Where results make sense

Topic: Deriving the Schwarzschild solution

Related Topics

Schwarzschild radius

Schwarzschild metric

Martin Schwarzschild

Schwarzschild or static black hole

Schwarzschild coordinates

In the News (Sat 2 Jun 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Schwarzschild metric - Wikipedia, the free encyclopedia
		According to Birkhoff's theorem, the Schwarzschild solution is the most general static, spherically symmetric, vacuum solution of the Einstein field equations.
		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.
	en.wikipedia.org /wiki/Schwarzschild_metric (1336 words)

	Deriving the Schwarzschild solution - Wikipedia, the free encyclopedia
		The Schwarzschild solution is one of the simplest and useful solutions of the Einstein field equations (see general relativity).
		The solution is assumed to be spherically symmetric, static and vacuum.
		In deriving the Schwarzschild metric, it was assumed that the metric was vacuum, spherically symmetric and static.
	en.wikipedia.org /wiki/Deriving_the_Schwarzschild_solution (679 words)

	Schwarzschild metric (Site not responding. Last check: 2007-10-13)
		In the theory of gravity general relativity the Schwarzschild metric is a static spherically symmetric solution Einstein's field equations of the vacuum (empty space).
		Since the Schwarzschild solution is the simplest of the Einstein field equations (see general relativity) it is worthwhile to review a considerations in some detail.
		The Schwarzschild metric leads predictions such as the bending of light the Sun and a change in the of the planet Mercury as compared to result of Kepler's laws of planetary motion.
	www.freeglossary.com /Schwarzschild_metric (2160 words)

	Schwarzschild metric (Site not responding. Last check: 2007-10-13)
		Since the Schwarzschild solution is the simplest solution of the Einstein field equations (see general relativity), it is worthwhile to review a few considerations in some detail.
		Solving the Einstein equations, means deriving the gravitational field (expressed in the form of the metric tensor) for a given mass distribution.
		The Schwarzschild metric leads to predictions such as the bending of light near the Sunand a change in the path of the planet Mercury as compared to the result of Kepler's laws of planetary motion.
	www.therfcc.org /schwarzschild-metric-44008.html (1812 words)

	The Ultimate Schwarzschild metric Dog Breeds Information Guide and Reference
		Schwarzschild discovered the solution only a few months after the publication of Einstein's theory of general relativity.
		Schwarzschild's solution showed how the predictions of general relativity would deviate from the predictions obtained from Newtonian gravity.
		The Schwarzschild radius is clearly proportional to the mass of the gravitating object.
	www.dogluvers.com /dog_breeds/Schwarzschild_metric (972 words)

	Schwarzschild metric - InformationBlast
		Using his solution for the gravitational field of the Earth and the Sun, three classical tests of general relativity have been predicted.
		Schwarzschild realized that his solution was singular (it becomes infinite for radii approaching the Schwarzschild radius).
		The Schwarzschild metric leads to predictions such as the bending of light near the Sun and a change in the path of the planet Mercury as compared to the result of Kepler's laws of planetary motion.
	www.informationblast.com /Schwarzschild_metric.html (1891 words)

	General relativity - QuickSeek Encyclopedia (Site not responding. Last check: 2007-10-13)
		The solutions of the EFE are metrics of spacetime.
		Expansion of the universe: This is predicted by cosmological solutions of the Einstein Field Equations.
		For the Schwarzschild solution (which is the simplest possible spacetime surrounding a massive object), the same acceleration as that which (in Newtonian physics) is created by gravity is obtained when a constant of integration is set equal to 2m (where m=MG/c^2).
	encyclopedia.quickseek.com /index.php/General_relativity (4615 words)

	Force, Curvature, and Uncertainty
		To escape from the static solution, Newtonian mechanics splits the kinematic equation of motion into two parts, coupled together by the dynamical concepts of force and mass.
		It's tempting to imagine that there might be some way of deriving the gravitational constant based on the idea that the initial condition for (1) is determined by the characteristic quantum uncertainty for the separations between massive particles, since, as we've seen, this initial condition fully determines the trajectory of radial gravitational free-fall.
		In a flat manifold the covariant derivative is identical to the partial derivative, which is commutative.
	www.mathpages.com /rr/s4-04/4-04.htm (2072 words)

	Schwarzschild metric: Encyclopedia topic (Site not responding. Last check: 2007-10-13)
		The Schwarzschild metric is derived in the article deriving the Schwarzschild solution (deriving the Schwarzschild solution: more facts about this subject).
		Schwarzschild's solution showed how the predictions of general relativity would deviate from the predictions obtained from Newtonian gravity (Newtonian gravity: the law of universal gravitation states that gravitational force between masses decreases...
		Using his solution for the gravitational field of the Earth and the Sun, the outcome of three classical tests of general relativity (classical tests of general relativity: the classical tests of general relativity are the direct consequences for experimental verification...
	www.absoluteastronomy.com /reference/schwarzschild_metric (1086 words)

	Schwarzschild metric -
		The Schwarzschild metric is a solution to vacuum field equations, meaning that it is only valid outside the gravitating body.
		The Schwarzschild solution appears to have singularities at $r = 0$ and $r=r_s$ ; some of the metric components blow up at these radii.
		If one asks that the solution be valid for all $r$ one runs into a true physical singularity, or gravitational singularity, at the origin.
	psychcentral.com /psypsych/Schwarzschild_black_hole (1450 words)

	YWWI - Ergosphere (Site not responding. Last check: 2007-10-13)
		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.
		This solution, the metric of spacetime associated with a point mass containing angular momentum and vacuum outside, was obtained by Roy Kerr in 1963 and is called the Kerr metric.
		The solution resembles a wormhole (from the exterior to the interior) in a neighborhood of the horizon, with the horizon as the neck.
	www.infoax.com /en/ergosphere (13454 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Recall that solutions to Maxwell's equation can be classified according to the nature of the eigenvectors of the EM field tensor (the eigenvectors are always null vectors).
		The Petrov classification of vacuum solutions to Einstein's field equation is the analogue of the classification of vacuum solutions to Maxwell's field equation according to whether or not they represent pure radiation fields.
		The Ansatz with which I began in deriving this solution assumes that all the "planes" z = z0 are isometric and that they are filled with "concentric" copies of H^(1,1) nested about the point r = 0.
	math.ucr.edu /home/baez/PUB/exactsolutions (6943 words)

	The world's top schwarzschild metric websites
		A spherical symmetric solution implies that the resulting metric should not depend on cross terms like, because otherwise the lengths of curves in the positive -direction would be different from curves in the negative -direction, violating spherical symmetry.
		where is the gravitational radius (or Schwarzschild radius) and is the mass of the source of the field.
		The geometry of the plane inside the star (using the simplifying assumption for a constant density inside the star) is drawn in the figure.
	www.websbiggest.com /wiki-article-tab.cfm/schwarzschild_metric (1876 words)

	:::► Dictionary of Meaning www.mauspfeil.net ◄:::
		The solutions of the EFE are metric tensor (general relativity) metrics of spacetime.
		The EFE reduce to Newton's law of gravity in the limiting cases of a weak-field approximation weak gravitational field and slow-motion approximation slow speed relative to the speed of light.
		For the Schwarzschild solution (which is the simplest possible spacetime surrounding a massive object), the same acceleration as that of the 'force of gravity' is obtained when constant of integration is set equal to ''2m'' (where ''m=MG/c^2'').
	www.mauspfeil.net /general_relativity.html (4630 words)

	FUNDAMENTAL PLANCK UNITS
		] The Schwarzschild radius appearing in the spheristatic solution of the Einstein equations as the radius of the singular surface determined by the gravitational potential given by the time-time component of the covariant, symmetric, 2nd rank, gravimetric tensor, 1 g
		In the Schwarzschild solution of general relativity as a constant of integration of the differential equations that are the Einstein equations reduced by the imposition of the condition of spheristasis.
		The Schwarzschild diameter for the Planck mass is the Planck length.
	graham.main.nc.us /~bhammel/PHYS/planckunits.html (2410 words)

	A simple derivation of the Schwarzschild solution from the field equations
		A simple method is presented for deriving the Schwarzschild metric in the weak-field limit of the field equations of general relativity.
		The solution is derived in spherical coordinates natural to the problem, but to which standard weak-field theory does not apply.
		The derivation can be used in an undergraduate presentation, where this metric is frequently used to desrcibe the key experimental tests of general relativity, all of which require first-order results.
	stacks.iop.org /0143-0807/18/99 (329 words)

	Schwarzschild solution
		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...
		The first and still the most important rigorous solution of the Einstein field equations was found by Schwarzschild in 1916. Although it's quite difficult to find exact analytical solutions...
		The Schwarzschild solution has a problem at a certain distance, called the Schwarzschild radius or the Event Horizion, at which light cannot escape.
	www.logicjungle.com /wiki/Schwarzschild_solution (337 words)

	[No title]
		The derivative indices, if they are present, are appended as additional arguments to the symbolic function representing the tensor.
		The derivative indices are displayed as subscripts, separated from the covariant indices by a comma (see the example above).
		The derivative of an indexed object will be replaced by the noun form of DIFF taken with respect to OMEGA subscripted by the derivative index.
	www.unf.edu /public/cap4630/kmartin/gradfall94/maxima/tensor/manual.txt (4543 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 ergoregion* and shape of a fl hole are attributes derived** by existence of or absence of angular momentum i.e.
		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=Stars&SubCate=OG04&SubCa... (5984 words)

	Einstein's field equation - All About All (Site not responding. Last check: 2007-10-13)
		The solutions of the Einstein field equations are metrics of spacetime.
		For example, there is no known complete solution for a spacetime with two massive bodies in it (which is a theoretical model of a binary star system, for example).
		The study of exact solutions of Einstein's field equations is one of the activities of cosmology.
	www.answers-zone.com /article/Einstein%27s_field_equation (1114 words)

	Re: Schwartzchild solution
		Then, inside this finite radius you don't have the Schwarzschild solution but something different, but outside the Schwarzschild solution.
		For example a general solution like get.ilja-schmelzer.net/BHharm.gif with m=m(r,t) as the mass inside the radius r.
		Then the vacuum solution would not > have a fixed mass as a parameter, but a mass decreasing as r decreases, > because of the mass of the in situ field escaping from the total mass.
	www.lns.cornell.edu /spr/2001-03/msg0031482.html (521 words)

	[No title]
		Indicial tensor manipulation is implemented by representing tensors as functions of their covariant, contravariant and derivative indices.
		COVDIFF(exp,v1,v2,...) yields the covariant derivative of exp with respect to the variables vi in terms of the Christoffel symbols of the second kind (CHR2).
		GEODESIC(exp,name) enables the user to cause undifferentiated Christoffel symbols and first derivatives of the metric tensor vanish in exp. The name in the GEODESIC function refers to the metric name (if it appears in exp) while the connection coefficients must be called with the names CHR1 and/or CHR2.
	www.unf.edu /public/cap4630/kmartin/gradfall94/maxima/tensor/tensor.doc (4926 words)

	ON QUANTUM THEORETICAL ORIGINS OF NEWTONIAN TIME
		In QM, the integrated Heisenberg solution for an observable O where the Hamiltonian is functionally independent of time is determined in [Section VIII, theorem 8.21] and [Section VIII, theorem 8.22].
		A solution to the equations fails to have the full symmetry of the equations, but this is the usual situation of a spontaneously broken symmetry.
		Thus, there is derived a natural ontology of Newtonian time uniformity which is the same everywhere that the fundamental theory is operative, and one might conclude throughout space.
	graham.main.nc.us /~bhammel/PHYS/newtqtime.html (15514 words)

	Philosophy Forum -> Gravity of Black Holes (Site not responding. Last check: 2007-10-13)
		This time dilation factor tends to zero as r approaches the Schwarzschild radius rs, which means that someone at the Schwarzschild radius will appear to freeze to a stop, as seen by anyone outside the Schwarzschild radius.
		The distortion of the fabric of space-time within the Schwarzschild radius is such that the set of possible "straight" lines (which light follows) does not include any path leading out of the gravity well.
		You need to examine the Kerr solution, which determined that the energy involved, while large, is not infinite.
	forum.darwinawards.com /index.php?showtopic=1160 (5409 words)

	Derivative Definition / Derivative Research (Site not responding. Last check: 2007-10-13)
		One reason is that mathematical knowledge is revised and updated in a different way; though arguably founded on experiment in some manner, it is not comparable to the natural sciences in this respect.
		[click for more], the derivative of a function is one of the two central concepts of calculusCalculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas.
		It permits velocity, acceleration, and the slope of a curve at a given point all to be discussed on a common conceptual basis....
	www.elresearch.com /Derivative (361 words)

	A Nonsymmetric Metric
		The behavior of light rays in the Schwarzschild gravitational solution can be represented by a refractive index model [4].
		The solution is only valid from the perspective of a distant observer, which corresponds to the perspective of a potential theory.
		Further, the cosmological term in these solutions appears to represent the weak gravitational field.
	www.s-4.com /tensor (536 words)

	Black Hole
		The remarkable feature of GR is that its contribution is automatically taken care of by the curvature of space and hence remains generally hidden in the usual considerations.
		For instance, while deriving the Schwarzschild solution we ultimately solve the Laplace equation instead of the Poisson equation with the field energy density on the right.
		Since collapse is driven by the field energy, which in contrast to the Schwarzschild case, vanishes for an extremal hole and hence it cannot be formed of gravitational collapse.
	www.ias.ac.in /currsci/mar25/articles27.htm (1473 words)

	Tensors (Site not responding. Last check: 2007-10-13)
		is restricted to sums of tensor products in which no derivatives are present.
		that have a derivative index identical to a contravariant index.
		The derivative indices will be displayed as subscripts, separated from the covariant indices by a comma.
	starship.python.net /crew/mike/maxima/html/macref/node108.html (1789 words)

	Citebase - Generalized pseudo-Riemannian geometry (Site not responding. Last check: 2007-10-13)
		In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian metric, generalized connection and generalized curvature tensor.
		Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions.
		A solution concept for these equations based on embedding the distributional metric into the Colombeau algebra of generalized functions is p...
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0107057 (1190 words)

Try your search on: Qwika (all wikis)