31 relations: Abstract index notation, ADM formalism, Closed-form expression, Continuity equation, Coordinate conditions, Cosmological constant, Dust solution, Einstein field equations, Einstein tensor, Equation of state, Exact solutions in general relativity, Fluid solution, Gauge theory, General relativity, Gravitation (book), Harmonic coordinate condition, Kurt Gödel, Linearized gravity, Metric tensor (general relativity), Non-exact solutions in general relativity, Numerical relativity, Open University, Partial differential equation, Princeton University Press, Pseudo-Riemannian manifold, Ricci calculus, Spacetime, Spacetime symmetries, Stress–energy tensor, Synchronous frame, Vacuum solution (general relativity).
Abstract index notation
Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis.
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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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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Continuity equation
A continuity equation in physics is an equation that describes the transport of some quantity.
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Coordinate conditions
In general relativity, the laws of physics can be expressed in a generally covariant form.
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Cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.
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Dust solution
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure.
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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 tensor
In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold.
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Equation of state
In physics and thermodynamics, an equation of state is a thermodynamic equation relating state variables which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature (PVT), or internal energy.
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Exact solutions in general relativity
In general relativity, an exact solution is a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field.
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Fluid solution
In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid.
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Gauge theory
In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.
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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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Gravitation (book)
Gravitation is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973.
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Harmonic coordinate condition
The harmonic coordinate condition is one of several coordinate conditions in general relativity, which make it possible to solve the Einstein field equations.
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Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
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Linearized gravity
Linearized gravity is an approximation scheme in general relativity in which the nonlinear contributions from the spacetime metric are ignored, simplifying the study of many problems while still producing useful approximate results.
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Metric tensor (general relativity)
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.
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Non-exact solutions in general relativity
Non-exact solutions in general relativity are solutions of Albert Einstein's field equations of general relativity which hold only approximately.
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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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Open University
The Open University (OU) is a public distance learning and research university, and one of the biggest universities in the UK for undergraduate education.
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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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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
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Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields.
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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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Spacetime symmetries
Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry.
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Stress–energy tensor
The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.
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Synchronous frame
In the special theory of relativity, choice of coordinates is limited by the requirement for a special kind of spacetime metric: the Minkowski metric.
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Vacuum solution (general relativity)
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically.
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References
[1] https://en.wikipedia.org/wiki/Solutions_of_the_Einstein_field_equations