Derivation of the Schwarzschild solution information

The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some...

Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations...

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...

The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds...

In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass M , {\textstyle...

true for perfect fluids. The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric...

which makes exact solutions very difficult to find. The Kerr metric is a generalization to a rotating body of the Schwarzschild metric, discovered by...

formulas. Shapiro's original formulation was derived from the Schwarzschild solution and included terms to the first order in solar mass ( M {\displaystyle...

of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution. Manifolds with a vanishing Ricci tensor, Rμν = 0,...

of a point or observer). The first type of wormhole solution discovered was the Schwarzschild wormhole, which would be present in the Schwarzschild metric...

coordinates) Yusuke Hagihara (Schwarzschild geodesics), Mustafa Halilsoy Nutku-Halil solution for colliding waves, On the Nutku—Halil solution for colliding impulsive...

relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point...

we describe how to derive these analogies between the Schwarzschild and FLRW spacetimes from the McVittie metric. In the case of a flat 3-space, with...

Einstein's field equation. Three members in the renowned Kerr–Newman family solutions, namely the Schwarzschild, nonextremal Reissner–Nordström and extremal...

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...

theorem, the Schwarzschild metric is the most general spherically symmetric, vacuum solution of the Einstein field equations. A Schwarzschild black hole...

suggested by the scaling laws of strings approaching the event horizon, suggesting that in the Schwarzschild chart they stretch to cover the horizon and...

rediscovered by Nordström, and is called the Reissner–Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein...

coordinates. The equation can also be used to derive the shape of the orbit for a given force law, but this usually involves the solution to a second order...

and solves for a as a function of time. To make the solutions more explicit, we can derive the full relationships from the first Friedmann equation: H 2...

symmetric solutions of the Einstein field equation, at large distances, the isotropic and Schwarzschild charts become increasingly similar to the usual polar...

has presented a derivation of the geodesic equation of motion directly from the equivalence principle. The first step in such a derivation is to suppose...