the Raychaudhuri equation, or Landau–Raychaudhuri equation, is a fundamental result describing the motion of nearby bits of matter. The equation is important...

and cosmology. His most significant contribution is the eponymous Raychaudhuri equation, which demonstrates that singularities arise inevitably in general...

field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were...

in the formulation and proof of the singularity theorems is the Raychaudhuri equation, which describes the divergence θ {\displaystyle \theta } of a congruence...

The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern cosmic expansion...

aeroacoustic equation Landau–Raychaudhuri equation Landau–Zener formula Landau–Lifshitz model Landau–Lifshitz pseudotensor Landau–Lifshitz–Gilbert equation...

Nagasaki in 1945, the equation E = mc2 became directly linked in the public eye with the power and peril of nuclear weapons. The equation was featured on page...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

presence of the Ricci tensor in the Raychaudhuri equation. Partly for this reason, the Einstein field equations propose that spacetime can be described...

of solutions) to Einstein's equations. Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific...

{\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...

solutions. In particular, exact vacuum solutions to the Einstein field equation of general relativity, augmented by the trivial scalar field ϕ = 1 {\displaystyle...

Einstein field equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation Phenomena Black...

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...

Friedmann–Lemaître (FL). When combined with Einstein's field equations the metric gives the Friedmann equation which has been developed into the Standard Model of...

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 =...

confined to configurations with sufficiently high symmetry for Einstein's equations to be solvable explicitly, and there was doubt about whether such cases...

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...

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...

Hamiltonian, and thereby write the equations of motion for general relativity in the form of Hamilton's equations. In addition to the twelve variables...

and frequency of a gravitational wave are related by the equation c = λf, just like the equation for a light wave. For example, the animations shown here...

discussing the physics implied by these equations since 1887. Early in 1889, Oliver Heaviside had shown from Maxwell's equations that the electric field surrounding...

months later, Karl Schwarzschild found a solution to the Einstein field equations that describes the gravitational field of a point mass and a spherical...

arises from special relativity, has been called "the world's most famous equation". He received the 1921 Nobel Prize in Physics for his services to theoretical...

metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions...

In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is...

Analytic Extension of the Symmetry Axis of Kerr's Solution of Einstein's Equations". Physical Review. 141 (4): 1242–1247. Bibcode:1966PhRv..141.1242C. doi:10...

deviations from equivalence to be very small. In classical mechanics, Newton's equation of motion in a gravitational field, written out in full, is: inertial mass...

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...

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...