50 relations: Abelian group, Atlas (topology), Bel decomposition, Bivector, Cartesian product, Cauchy surface, Causal structure, Characteristic polynomial, Closed timelike curve, Congruence (general relativity), Cosmological constant, Dust solution, Eigenvalues and eigenvectors, Einstein field equations, Einstein tensor, Eternalism (philosophy of time), Exact solutions in general relativity, Fermi–Walker transport, Frame fields in general relativity, Gödel's incompleteness theorems, Globally hyperbolic manifold, Group action, Homeomorphism, Hubble's law, Isometry (Riemannian geometry), Killing vector field, Kretschmann scalar, Kurt Gödel, Lambdavacuum solution, Lie algebra, Light cone, Line element, Linear map, Lorentz covariance, Mach's principle, Metric tensor, Perfect fluid, Petrov classification, Philosophical presentism, Reviews of Modern Physics, Riemann curvature tensor, Signature, SL2(R), Spacetime, Stress–energy tensor, Tangent vector, Time translation symmetry, Time travel, Van Stockum dust, Weyl tensor.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
New!!: Gödel metric and Abelian group · See more »
Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
New!!: Gödel metric and Atlas (topology) · See more »
Bel decomposition
In semi-Riemannian geometry, the Bel decomposition, taken with respect to a specific timelike congruence, is a way of breaking up the Riemann tensor of a pseudo-Riemannian manifold into lower order tensors with properties similar to the electric field and magnetic field.
New!!: Gödel metric and Bel decomposition · See more »
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.
New!!: Gödel metric and Bivector · See more »
Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
New!!: Gödel metric and Cartesian product · See more »
Cauchy surface
Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time; its significance is that giving the initial conditions on this plane determines the future (and the past) uniquely.
New!!: Gödel metric and Cauchy surface · See more »
Causal structure
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
New!!: Gödel metric and Causal structure · See more »
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.
New!!: Gödel metric and Characteristic polynomial · See more »
Closed timelike curve
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point.
New!!: Gödel metric and Closed timelike curve · See more »
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.
New!!: Gödel metric and Congruence (general relativity) · See more »
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.
New!!: Gödel metric and Cosmological constant · See more »
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.
New!!: Gödel metric and Dust solution · 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.
New!!: Gödel metric and Eigenvalues and eigenvectors · 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.
New!!: Gödel metric and Einstein field equations · See more »
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.
New!!: Gödel metric and Einstein tensor · See more »
Eternalism (philosophy of time)
Eternalism is a philosophical approach to the ontological nature of time, which takes the view that all existence in time is equally real, as opposed to presentism or the growing block universe theory of time, in which at least the future is not the same as any other time.
New!!: Gödel metric and Eternalism (philosophy of time) · See more »
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.
New!!: Gödel metric and Exact solutions in general relativity · See more »
Fermi–Walker transport
Fermi–Walker transport is a process in general relativity used to define a coordinate system or reference frame such that all curvature in the frame is due to the presence of mass/energy density and not to arbitrary spin or rotation of the frame.
New!!: Gödel metric and Fermi–Walker transport · See more »
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.
New!!: Gödel metric and Frame fields in general relativity · See more »
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
New!!: Gödel metric and Gödel's incompleteness theorems · See more »
Globally hyperbolic manifold
In mathematical physics, global hyperbolicity is a certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold).
New!!: Gödel metric and Globally hyperbolic manifold · See more »
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.
New!!: Gödel metric and Group action · See more »
Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
New!!: Gödel metric and Homeomorphism · See more »
Hubble's law
Hubble's law is the name for the observation in physical cosmology that.
New!!: Gödel metric and Hubble's law · See more »
Isometry (Riemannian geometry)
In mathematics, an isometry of a manifold is any (smooth) mapping of that manifold into itself, or into another manifold that preserves the notion of distance between points.
New!!: Gödel metric and Isometry (Riemannian geometry) · See more »
Killing vector field
In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.
New!!: Gödel metric and Killing vector field · See more »
Kretschmann scalar
In the theory of Lorentzian manifolds, particularly in the context of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant.
New!!: Gödel metric and Kretschmann scalar · See more »
Kurt Gödel
Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
New!!: Gödel metric and Kurt Gödel · See more »
Lambdavacuum solution
In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term.
New!!: Gödel metric and Lambdavacuum solution · See more »
Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
New!!: Gödel metric and Lie algebra · See more »
Light cone
In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.
New!!: Gödel metric and Light cone · See more »
Line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space.
New!!: Gödel metric and Line element · 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.
New!!: Gödel metric and Linear map · See more »
Lorentz covariance
In relativistic physics, Lorentz symmetry, named for Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame.
New!!: Gödel metric and Lorentz covariance · See more »
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach.
New!!: Gödel metric and Mach's principle · See more »
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.
New!!: Gödel metric and Metric tensor · See more »
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.
New!!: Gödel metric and Perfect fluid · See more »
Petrov classification
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.
New!!: Gödel metric and Petrov classification · See more »
Philosophical presentism
Philosophical presentism is the view that neither the future nor the past exist.
New!!: Gödel metric and Philosophical presentism · See more »
Reviews of Modern Physics
Reviews of Modern Physics is a quarterly peer-reviewed scientific journal published by the American Physical Society.
New!!: Gödel metric and Reviews of Modern Physics · See more »
Riemann curvature tensor
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.
New!!: Gödel metric and Riemann curvature tensor · See more »
Signature
A signature (from signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent.
New!!: Gödel metric and Signature · See more »
SL2(R)
In mathematics, the special linear group SL(2,R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: a & b \\ c & d \end \right): a,b,c,d\in\mathbf\mboxad-bc.
New!!: Gödel metric and SL2(R) · See more »
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.
New!!: Gödel metric and Spacetime · 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.
New!!: Gödel metric and Stress–energy tensor · See more »
Tangent vector
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point.
New!!: Gödel metric and Tangent vector · See more »
Time translation symmetry
Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval.
New!!: Gödel metric and Time translation symmetry · See more »
Time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically using a hypothetical device known as a time machine.
New!!: Gödel metric and Time travel · See more »
Van Stockum dust
In general relativity, the van Stockum dust is an exact solution of the Einstein field equation in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry.
New!!: Gödel metric and Van Stockum dust · 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.
New!!: Gödel metric and Weyl tensor · See more »
Redirects here:
Godel metric, Godel solution, Godel spacetime, Godel universe, Goedel metric, Goedel solution, Goedel spacetime, Gödel dust, Gödel solution, Gödel spacetime, Gödel universe.
References
[1] https://en.wikipedia.org/wiki/Gödel_metric