Related papers: The Schwarzschild metric: It's the coordinates, st…
As is well-known, the Schwarzschild metric cannot be derived based on pre-general-relativistic physics alone, which means using only special relativity, the Einstein equivalence principle and the Newtonian limit. The standard way to derive…
The Schwarzschild metric is derived in a manner that does not require familiarity with the formalism of differential geometry beyond the ability to interpret a general spacetime metric. As such, the derivation is suitable for an…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
Since its first introduction, the Schwarzschild metric has been written in various coordinate systems. This has been done primarily to understand the nature of the coordinate singularity at the event horizon. However, very often, the…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
A strict derivation of the Schwarzschild metric, based solely on Newton's law of free fall and the equivalence principle, is presented. In the light of it, regarding Schwarzschild's coordinates as representing the point of view of a distant…
The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match…
In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate…
Gravity field theory and electromagnetic field theory are well established and confirmed by experiments. The Schwarzschild metric and Kerr Metric of Einstein field equation shows that the spatial differential of time gauge is the gravity…
A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…
Translation by S. Antoci and A. Loinger of the fundamental memoir, that contains the ORIGINAL form of the solution of Schwarzschild's problem. The solution is regular in the whole space-time, with the only exception of the origin of the…