59 relations: Aleksei Zinovyevich Petrov, Bivector, Cambridge University Press, Cartan formalism (physics), Classical field theory, Classification of electromagnetic fields, Conformally flat manifold, Congruence (general relativity), Coulomb, Differential geometry, Eigenvalues and eigenvectors, Einstein field equations, Electrogravitic tensor, Electromagnetic field, Electrovacuum solution, Energy, Exact solutions in general relativity, Felix Pirani, Friedmann–Lemaître–Robertson–Walker metric, General relativity, Gravitational potential, Gravitational wave, Gravitoelectromagnetism, Gyroscope, Integrable system, Kerr metric, LIGO, Linear map, Linearized gravity, Longitudinal wave, Lorentz transformation, Metric (mathematics), Multilinear algebra, Multiplicity (mathematics), Multipole expansion, Newman–Penrose formalism, Newton's law of universal gravitation, Null dust solution, Null vector, Oxford University Press, Peeling theorem, Plebanski tensor, Pp-wave spacetime, Pseudo-Riemannian manifold, Quartic function, Ricci curvature, Rotation around a fixed axis, Segre classification, Shear stress, Spherically symmetric spacetime, ..., Spinor, Stress–energy tensor, Symmetry, Tensor, Theoretical physics, Transversality (mathematics), Wave vector, Weyl scalar, Weyl tensor. Expand index (9 more) »
Aleksei Zinovyevich Petrov
Aleksei Zinovyevich Petrov (Алексе́й Зино́вьевич Петро́в; 28 October (15 October, Old Style) 1910, Koshki, Samara Governorate, Russian Empire – 9 May 1972, Kiev, Soviet Union) was a mathematician noted for his work on the classification of Einstein spaces, today called Petrov classification.
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Bivector
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cartan formalism (physics)
The vierbein or tetrad theory much used in theoretical physics is a special case of the application of Cartan connection in four-dimensional manifolds.
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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.
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Classification of electromagnetic fields
In differential geometry and theoretical physics, the classification of electromagnetic fields is a pointwise classification of bivectors at each point of a Lorentzian manifold.
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Conformally flat manifold
A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation.
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Congruence (general relativity)
In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime.
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Coulomb
The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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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.
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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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Electrogravitic tensor
In general relativity, the gravitoelectric tensor or tidal tensor is one of the pieces in the Bel decomposition of the Riemann tensor.
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Electromagnetic field
An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.
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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.
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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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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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Felix Pirani
Felix Arnold Edward Pirani (2 February 1928 – 31 December 2015) was a British theoretical physicist specialising in gravitational physics and general relativity.
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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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Gravitational potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.
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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.
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Gravitoelectromagnetism
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.
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Gyroscope
A gyroscope (from Ancient Greek γῦρος gûros, "circle" and σκοπέω skopéō, "to look") is a device used for measuring or maintaining orientation and angular velocity.
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Integrable system
In the context of differential equations to integrate an equation means to solve it from initial conditions.
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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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LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool.
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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.
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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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Longitudinal wave
Longitudinal waves are waves in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave.
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Lorentz transformation
In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.
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Metric (mathematics)
In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.
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Multilinear algebra
In mathematics, multilinear algebra extends the methods of linear algebra.
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Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
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Multipole expansion
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere.
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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.
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Newton's law of universal gravitation
Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
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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.
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Null vector
In mathematics, given a vector space X with an associated quadratic form q, written, a null vector or isotropic vector is a non-zero element x of X for which.
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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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Peeling theorem
In general relativity, the peeling theorem describes the asymptotic behavior of the Weyl tensor as one goes to.
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Plebanski tensor
The Plebanski tensor is a order 4 tensor in general relativity constructed from the trace-free Ricci tensor.
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Pp-wave spacetime
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation.
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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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Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
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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.
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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.
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Segre classification
The Segre classification is an algebraic classification of rank two symmetric tensors.
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Shear stress
A shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section.
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Spherically symmetric spacetime
A spherically symmetric spacetime is a spacetime whose isometry group contains a subgroup which is isomorphic to the rotation group SO(3) and the orbits of this group are 2-spheres (ordinary 2-dimensional spheres in 3-dimensional Euclidean space).
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Spinor
In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space.
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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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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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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Transversality (mathematics)
In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position.
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Wave vector
In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave.
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Weyl scalar
In the Newman–Penrose (NP) formalism of general relativity, Weyl scalars refer to a set of five complex scalars \ which encode the ten independent components of the Weyl tensors of a four-dimensional spacetime.
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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.
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Algebraically special, Petrov Type, Petrov type, Petrov type D.
References
[1] https://en.wikipedia.org/wiki/Petrov_classification