Mathematical equation used to find exact solutions of equations in the general theory of relativity
Not to be confused with Nernst equation.
In mathematics, the Ernst equation[1] is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst [Wikidata].[2]
^Weisstein, Eric W, Ernst equation, MathWorld--A Wolfram Web.
^"Biography of Frederick J. Ernst". Archived from the original on 2018-01-04. Retrieved 2017-05-09.
mathematics, the Ernstequation is an integrable non-linear partial differential equation, named after the American physicist Frederick J. Ernst [Wikidata]...
field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were...
reduced system of equations is often difficult to solve. For example, the Ernstequation is a nonlinear partial differential equation somewhat resembling...
The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern the expansion of...
Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter. The equation is important...
_{10}p=A-{\frac {B}{T}}} is the August equation, after the German physicist Ernst Ferdinand August (1795–1870). The August equation describes a linear relation between...
defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the...
to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called...
1994, the Alcubierre drive is based on a solution of Einstein's field equations. Since those solutions are metric tensors, the Alcubierre drive is also...
→ ∞ of Poincaré transformations yields Galilean transformations. The equations below are only physically valid in a Newtonian framework, and not applicable...
Newman–Penrose formalism (also known as the spin–coefficient formalism), Ernstequation, or Ellipsoid coordinate transformation. The Kerr metric describes the...
In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames...
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...
theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity...
Analytic Extension of the Symmetry Axis of Kerr's Solution of Einstein's Equations". Phys. Rev. 141 (4): 1242–1247. Bibcode:1966PhRv..141.1242C. doi:10.1103/PhysRev...
The equation t′ = constant defines a "line of simultaneity" in the (x′, t′) coordinate system for the second (moving) observer, just as the equation t =...
Elimination of the variables D and L from these three equations results in: Time dilation equation Δ t ′ = Δ t 1 − v 2 c 2 = γ Δ t {\displaystyle \Delta...
confined to configurations with sufficiently high symmetry for Einstein's equations to be solvable explicitly, and there was doubt about whether such cases...
{\displaystyle d_{p}=\int _{0}^{t_{0}}{\frac {c}{a(t)}}\,dt.} In this equation, a is the scale factor, c is the speed of light, and t0 is the age of the...
around the star onto three-dimensional (3-D) space. The full geodesic equation is d 2 x μ d s 2 + Γ μ α β d x α d s d x β d s = 0 {\displaystyle {d^{2}x^{\mu...
months later, Karl Schwarzschild found a solution to the Einstein field equations that describes the gravitational field of a point mass and a spherical...
In 1929, Weyl proposed an equation, known as the Weyl equation, for use in a replacement to the Dirac equation. This equation describes massless fermions...