general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation...

In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical...

In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution...

(2023). DOI 10.1103/PhysRevD.107.044052 Canonical coordinates Hamilton–Jacobi–Einstein equation Peres metric "ADM-50: A Celebration of Current GR Innovation"...

theory Hamiltonian system Hamilton–Jacobi equation Hamilton–Jacobi–Einstein equation Lagrangian mechanics Maxwell's equations Hamiltonian (quantum mechanics)...

universe Hamilton–Jacobi–Einstein equation Higher-dimensional Einstein gravity Kähler–Einstein metric Wiener–Khinchin–Einstein theorem Einstein pseudotensor...

They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric...

relativity. He also introduced the Peres metric and researched the Hamilton–Jacobi–Einstein equation in general relativity. With Mario Feingold, he published work...

gravitational waves and weak-field gravitational lensing. The Einstein field equation (EFE) describing the geometry of spacetime is given as (using natural...

is determined by the Einstein field equations themselves, not by a new law. Accordingly, Einstein proposed that the field equations would determine the...

gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology...

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

electromagnetic wave and, therefore, travelled at speed c. In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame...

→ ∞ of Poincaré transformations yields Galilean transformations. The equations below are only physically valid in a Newtonian framework, and not applicable...

Albert Einstein developed special and general relativity to accommodate the invariant speed of light, a consequence of Maxwell's equations, with the...

within r {\textstyle r} , is discussed below. The equation is derived by solving the Einstein equations for a general time-invariant, spherically symmetric...

slices of constant time. When we do this, Einstein's equations can be decomposed into one set of equations, which must be satisfied on each slice, and...

also true for such classical unified field theories as the Einstein–Maxwell–Dirac equations. The idea can be stated in the form that, due to quantum gravity...

measurement of changes in mass difference, as a check on Einstein's equation itself. Einstein mentions in his 1905 paper that mass–energy equivalence might...

Maxwell equations have the same form in all inertial frames of reference. In the framework of general relativity the Maxwell equations or the Einstein field...

to two. This view of special relativity was first proposed by Albert Einstein's former professor Hermann Minkowski and is known as Minkowski space. The...

gradually corrected. More recently, it has become possible to solve Einstein's field equation using a computer instead of mathematical formulae. As the two...

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

references therein. The Ernst equation is employed in order to produce the exact solutions of the Einstein's equations in the general theory of relativity...

The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation...

observer. The amount of gravitational lensing is described by Albert Einstein's general theory of relativity. If light is treated as corpuscles travelling...

differential equation given initial conditions. In the context of general relativity, it means the problem of finding solutions to Einstein's field equations - a...

Hamilton–Jacobi–Bellman equation Hamilton–Jacobi–Einstein equation Hamilton–Jacobi–Isaacs equation Ivory–Jacobi formula Jacobi–Lie bracket Jacobi–Anger expansion...

particles in cosmological models which are exact dust solutions of the Einstein field equation (provided that these world lines are not twisting about one another...

relativity. According to the special theory of relativity introduced by Albert Einstein, it is impossible to say in an absolute sense that two distinct events...