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Fluid solution

Index 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. [1]

34 relations: Algebraic independence, Astrophysics, Cambridge University Press, Characteristic polynomial, Dust solution, Einstein field equations, Equation of state, Equivalence principle, Exact solutions in general relativity, Fluid, Four-velocity, Frame fields in general relativity, Friedmann–Lemaître–Robertson–Walker metric, General relativity, Gröbner basis, Group action, Kerr metric, Linear independence, Lorentz group, Minkowski space, Newton's identities, Perfect fluid, Physical cosmology, Pseudo-Riemannian manifold, Relativistic disk, Scalar curvature, Schwarzschild metric, Spacetime, Static spherically symmetric perfect fluid, Stress–energy tensor, Symmetric matrix, Trace (linear algebra), Vector field, Wahlquist fluid.

Algebraic independence

In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set is algebraically independent over K if and only if α is transcendental over K. In general, all the elements of an algebraically independent set S over K are by necessity transcendental over K, and over all of the field extensions over K generated by the remaining elements of S.

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Astrophysics

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the astronomical objects, rather than their positions or motions in space".

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Characteristic polynomial

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.

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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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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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Equivalence principle

In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

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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

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress.

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Four-velocity

In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetimeTechnically, the four-vector should be thought of as residing in the tangent space of a point in spacetime, spacetime itself being modeled as a smooth manifold.

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Frame fields in general relativity

In general relativity, a frame field (also called a tetrad or vierbein) is a set of four orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime.

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Friedmann–Lemaître–Robertson–Walker metric

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding or contracting universe that is path connected, but not necessarily simply connected.

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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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Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field.

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Group action

In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.

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Kerr metric

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon.

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.

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Lorentz group

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (nongravitational) physical phenomena.

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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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Newton's identities

In mathematics, Newton's identities, also known as the Newton–Girard formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials.

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Perfect fluid

In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m; and isotropic pressure p. Real fluids are "sticky" and contain (and conduct) heat.

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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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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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Relativistic disk

In general relativity, the relativistic disk expression refers to a class of axi-symmetric self-consistent solutions to Einstein's field equations corresponding to the gravitational field generated by axi-symmetric isolated sources.

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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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Schwarzschild metric

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.

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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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Static spherically symmetric perfect fluid

In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure.

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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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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Wahlquist fluid

In general relativity, the Wahlquist fluid is an exact rotating perfect fluid solution to Einstein's equation with equation of state corresponding to constant gravitational mass density.

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References

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

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