schwarzschild solution sentence in Hindi
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- In the 1970s, when the thermal nature of black hole physics was discovered, the wormhole property of the Schwarzschild solution turned out to be an important ingredient.
- Kruskal ( in parallel with George Szekeres ) discovered the maximal analytic continuation of the Schwarzschild solution, which he exhibited elegantly using what are now called Kruskal Szekeres coordinates.
- However, be careful, because the Schwarzschild radius is the radius of the singularity around a spherically symmetrical system, and the Schwarzschild solution only applies in empty space.
- In a maximally extended external Schwarzschild solution, that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go.
- To describe the gravitational field both inside and outside the gravitating body the Schwarzschild solution must be matched with some suitable interior solution at, such as the interior Schwarzschild solution.
- To describe the gravitational field both inside and outside the gravitating body the Schwarzschild solution must be matched with some suitable interior solution at, such as the interior Schwarzschild solution.
- In the nonrotating, Schwarzschild solution, with ? = 0, the inner and outer photon spheres degenerate, so that all the photons sphere occur at the same radius.
- Furthermore, he was in 1919 invited to Uppsala by Oseen and it was there he started his work on general relativity and in particular his generalization of the Schwarzschild solution.
- Thus, the Kerr solution provides an example of a stationary spacetime that is "'not "'static; the non-rotating Schwarzschild solution is an example that is static.
- As one examines suitable model spacetimes ( either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion ), several effects of gravity on light propagation emerge.
- The Schwarzschild solution, which makes use of Schwarzschild coordinates and the Schwarzschild metric, leads to a derivation of the Schwarzschild radius, which is the size of the event horizon of a non-rotating black hole.
- In only a few years of work ( by 1916 he had died from a chronic illness ) he had made fundamental contributions in astrophysics and to Schwarzschild solution " and which is of fundamental importance for the theory of black holes.
- 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 " 2MG / c 2 " ).
- The theory shows some promise for the treatment of black holes, as its form of the Schwarzschild solution does not break down at singularities; most of the results of general relativity have been mathematically reproduced, and the relativistic formulation of classical electrodynamics has been extended to quantum mechanics and the Dirac equation.
- The Schwarzschild solution is the simplest spherically symmetric solution of the Einstein equations with zero cosmological constant, and it describes a black hole event horizon in otherwise empty space . de Sitter Schwarzschild is a combination of the two, and describes a black hole horizon spherically centered in an otherwise de Sitter universe.
- For example, the Schwarzschild solution has a Killing algebra of dimension 4 ( 3 spatial rotational vector fields and a time translation ), whereas the Friedmann-Lema�tre-Robertson-Walker ( FLRW ) metric ( excluding the Einstein static subcase ) has a Killing algebra of dimension 6 ( 3 translations and 3 rotations ).
- In other words, the Schwarzschild solution can be applied, provided that the " M " + " m " is used in place of " M " in the formulae for the Schwarzschild radius " r " " s " and the precession angle per revolution ??.
- In the Schwarzschild solution, it is assumed that the larger mass " M " is stationary and it alone determines the gravitational field ( i . e ., the geometry of space-time ) and, hence, the lesser mass " m " follows a geodesic path through that fixed space-time.
- In Einstein's theory of general relativity, the "'Schwarzschild metric "'( also known as the "'Schwarzschild vacuum "'or "'Schwarzschild solution "') is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.
- For the Schwarzschild solution, we take k ^ a to be the time translation Killing vector k ^ a \ partial _ a = \ frac { \ partial } { \ partial t }, and more generally for the Kerr-Newman solution we take k ^ a \ partial _ a = \ frac { \ partial } { \ partial t } + \ Omega \ frac { \ partial } { \ partial \ phi }, the linear combination of the time translation and axisymmetry Killing vectors which is null at the horizon, where \ Omega is the angular velocity.
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