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ADM formalism

Index ADM formalism

The ADM formalism (named for its authors Richard Arnowitt, Stanley Deser and Charles W. Misner) is a Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity. [1]

51 relations: ADM formalism, Alternatives to general relativity, Canonical commutation relation, Canonical coordinates, Canonical quantum gravity, Charles W. Misner, Christoffel symbols, Coordinate system, Covariant derivative, Determinant, Einstein field equations, Einstein notation, Einstein–Hilbert action, Energy, Exponential growth, Foliation, General relativity, General Relativity and Gravitation, Generalized coordinates, Gibbons–Hawking–York boundary term, Hamilton–Jacobi–Einstein equation, Hamiltonian constraint, Hamiltonian mechanics, Inflation (cosmology), Initial value problem, Lagrange multiplier, Lagrangian (field theory), Lagrangian mechanics, Louis Witten, Metric tensor, Minkowski space, Noether's theorem, Nonlinear system, Numerical relativity, Oxford University Press, Partial derivative, Partial differential equation, Peres metric, Physical cosmology, Physical Review, Quantum gravity, Quantum mechanics, Richard Arnowitt, Scalar curvature, Schrödinger equation, Spacetime, Stanley Deser, Supercomputer, Symmetry, Vacuum energy, ..., Wheeler–DeWitt equation. Expand index (1 more) »

ADM formalism

The ADM formalism (named for its authors Richard Arnowitt, Stanley Deser and Charles W. Misner) is a Hamiltonian formulation of general relativity that plays an important role in canonical quantum gravity and numerical relativity.

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Alternatives to general relativity

Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition to Einstein's theory of general relativity.

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Canonical commutation relation

In quantum mechanics (physics), the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another).

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Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.

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Canonical quantum gravity

In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity).

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Charles W. Misner

Charles W. Misner (born June 13, 1932) is an American physicist and one of the authors of Gravitation.

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Christoffel symbols

In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Covariant derivative

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

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Einstein notation

In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.

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Einstein–Hilbert action

The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the principle of least action.

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Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.

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Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

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Foliation

In mathematics, a foliation is a geometric tool for understanding manifolds.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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General Relativity and Gravitation

General Relativity and Gravitation is a monthly peer-reviewed scientific journal.

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Generalized coordinates

In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration.

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Gibbons–Hawking–York boundary term

In general relativity, the Gibbons–Hawking–York boundary term is a term that needs to be added to the Einstein–Hilbert action when the underlying spacetime manifold has a boundary.

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Hamilton–Jacobi–Einstein equation

In general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation of geometrodynamics in superspace, cast in the "geometrodynamics era" around the 1960s, by Asher Peres in 1962 and others.

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Hamiltonian constraint

The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant.

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Hamiltonian mechanics

Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.

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Inflation (cosmology)

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe.

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Initial value problem

In mathematics, the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.

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Lagrange multiplier

In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).

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Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory.

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Lagrangian mechanics

Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.

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Louis Witten

Louis Witten (born April 13, 1921) is an American theoretical physicist and the father of Edward Witten.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Noether's theorem

Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.

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Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

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Numerical relativity

Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Peres metric

In mathematical physics, the Peres metric is defined by the proper time ^.

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Physical cosmology

Physical cosmology is the study of the largest-scale structures and dynamics of the Universe and is concerned with fundamental questions about its origin, structure, evolution, and ultimate fate.

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Physical Review

Physical Review is an American peer-reviewed scientific journal established in 1893 by Edward Nichols.

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Quantum gravity

Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as near compact astrophysical objects where the effects of gravity are strong.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Richard Arnowitt

Richard Lewis Arnowitt (May 3, 1928 – June 12, 2014) was an American physicist known for his contributions to theoretical particle physics and to general relativity.

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Scalar curvature

In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold.

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Schrödinger equation

In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Stanley Deser

Stanley Deser (born 1931) is an American physicist known for his contributions to general relativity.

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Supercomputer

A supercomputer is a computer with a high level of performance compared to a general-purpose computer.

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Symmetry

Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.

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Vacuum energy

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe.

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Wheeler–DeWitt equation

The Wheeler–DeWitt equation is a field equation.

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ADM Hamiltonian, ADM decomposition, ADM energy, ADM formulation, ADM mass.

References

[1] https://en.wikipedia.org/wiki/ADM_formalism

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