Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

Exact solutions in general relativity and Petrov classification

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Exact solutions in general relativity and Petrov classification

Exact solutions in general relativity vs. Petrov classification

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. In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.

Similarities between Exact solutions in general relativity and Petrov classification

Exact solutions in general relativity and Petrov classification have 21 things in common (in Unionpedia): Cambridge University Press, Classical field theory, Eigenvalues and eigenvectors, Einstein field equations, Electromagnetic field, Electrovacuum solution, Friedmann–Lemaître–Robertson–Walker metric, General relativity, Gravitational wave, Integrable system, Linear map, Newman–Penrose formalism, Null dust solution, Oxford University Press, Pseudo-Riemannian manifold, Ricci curvature, Rotation around a fixed axis, Segre classification, Stress–energy tensor, Tensor, Weyl tensor.

Cambridge University Press

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

Cambridge University Press and Exact solutions in general relativity · Cambridge University Press and Petrov classification · See more »

Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations.

Classical field theory and Exact solutions in general relativity · Classical field theory and Petrov classification · See more »

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

Eigenvalues and eigenvectors and Exact solutions in general relativity · Eigenvalues and eigenvectors and Petrov classification · See more »

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.

Einstein field equations and Exact solutions in general relativity · Einstein field equations and Petrov classification · See more »

Electromagnetic field

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.

Electromagnetic field and Exact solutions in general relativity · Electromagnetic field and Petrov classification · See more »

Electrovacuum solution

In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass-energy present is the field energy of an electromagnetic field, which must satisfy the (curved-spacetime) source-free Maxwell equations appropriate to the given geometry.

Electrovacuum solution and Exact solutions in general relativity · Electrovacuum solution and Petrov classification · See more »

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.

Exact solutions in general relativity and Friedmann–Lemaître–Robertson–Walker metric · Friedmann–Lemaître–Robertson–Walker metric and Petrov classification · See more »

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.

Exact solutions in general relativity and General relativity · General relativity and Petrov classification · See more »

Gravitational wave

Gravitational waves are the disturbance in the fabric ("curvature") of spacetime generated by accelerated masses and propagate as waves outward from their source at the speed of light.

Exact solutions in general relativity and Gravitational wave · Gravitational wave and Petrov classification · See more »

Integrable system

In the context of differential equations to integrate an equation means to solve it from initial conditions.

Exact solutions in general relativity and Integrable system · Integrable system and Petrov classification · See more »

Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

Exact solutions in general relativity and Linear map · Linear map and Petrov classification · See more »

Newman–Penrose formalism

The Newman–Penrose (NP) formalism The original paper by Newman and Penrose, which introduces the formalism, and uses it to derive example results.

Exact solutions in general relativity and Newman–Penrose formalism · Newman–Penrose formalism and Petrov classification · See more »

Null dust solution

In mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null.

Exact solutions in general relativity and Null dust solution · Null dust solution and Petrov classification · See more »

Oxford University Press

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

Exact solutions in general relativity and Oxford University Press · Oxford University Press and Petrov classification · See more »

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.

Exact solutions in general relativity and Pseudo-Riemannian manifold · Petrov classification and Pseudo-Riemannian manifold · See more »

Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

Exact solutions in general relativity and Ricci curvature · Petrov classification and Ricci curvature · See more »

Rotation around a fixed axis

Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion.

Exact solutions in general relativity and Rotation around a fixed axis · Petrov classification and Rotation around a fixed axis · See more »

Segre classification

The Segre classification is an algebraic classification of rank two symmetric tensors.

Exact solutions in general relativity and Segre classification · Petrov classification and Segre classification · See more »

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.

Exact solutions in general relativity and Stress–energy tensor · Petrov classification and Stress–energy tensor · See more »

Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

Exact solutions in general relativity and Tensor · Petrov classification and Tensor · See more »

Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold.

Exact solutions in general relativity and Weyl tensor · Petrov classification and Weyl tensor · See more »

The list above answers the following questions

Exact solutions in general relativity and Petrov classification Comparison

Exact solutions in general relativity has 89 relations, while Petrov classification has 59. As they have in common 21, the Jaccard index is 14.19% = 21 / (89 + 59).

References

This article shows the relationship between Exact solutions in general relativity and Petrov classification. To access each article from which the information was extracted, please visit:

Hey! We are on Facebook now! »