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Exact solutions in general relativity and General relativity

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

Difference between Exact solutions in general relativity and General relativity

Exact solutions in general relativity vs. 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. 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.

Similarities between Exact solutions in general relativity and General relativity

Exact solutions in general relativity and General relativity have 35 things in common (in Unionpedia): Alcubierre drive, Binary pulsar, Closed timelike curve, Cosmological constant, Covariant derivative, Curvature form, Dark energy, Einstein field equations, Einstein tensor, Energy condition, Friedmann–Lemaître–Robertson–Walker metric, Gödel metric, General relativity, Gravitational constant, Gravitational wave, Integrable system, Lagrangian (field theory), Local spacetime structure, Metric tensor (general relativity), Minkowski space, Nonlinear system, Partial differential equation, Perturbation theory, Post-Newtonian expansion, Pseudo-Riemannian manifold, Ricci curvature, Riemann curvature tensor, Roger Penrose, Scalar field, Solutions of the Einstein field equations, ..., Spacetime topology, Speed of light, Stationary spacetime, Stress–energy tensor, Tensor. Expand index (5 more) »

Alcubierre drive

The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Alcubierre drive and Exact solutions in general relativity · Alcubierre drive and General relativity · See more »

Binary pulsar

A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star.

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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.

Closed timelike curve and Exact solutions in general relativity · Closed timelike curve and 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.

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Covariant derivative

In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.

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Curvature form

In differential geometry, the curvature form describes the curvature of a connection on a principal bundle.

Curvature form and Exact solutions in general relativity · Curvature form and General relativity · See more »

Dark energy

In physical cosmology and astronomy, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe.

Dark energy and Exact solutions in general relativity · Dark energy and General relativity · 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.

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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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Energy condition

In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is one of various alternative conditions which can be applied to the matter content of the theory, when it is either not possible or desirable to specify this content explicitly.

Energy condition and Exact solutions in general relativity · Energy condition and General relativity · 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 General relativity · See more »

Gödel metric

The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution).

Exact solutions in general relativity and Gödel metric · Gödel metric and General relativity · 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 General relativity · See more »

Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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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.

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

Integrable system

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

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Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory.

Exact solutions in general relativity and Lagrangian (field theory) · General relativity and Lagrangian (field theory) · See more »

Local spacetime structure

Local spacetime structure refers to the structure of spacetime on a local level, i.e. only considering those points in an open region of a point.

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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.

Exact solutions in general relativity and Metric tensor (general relativity) · General relativity and Metric tensor (general relativity) · See more »

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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Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

Exact solutions in general relativity and Nonlinear system · General relativity and Nonlinear system · See more »

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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Perturbation theory

Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.

Exact solutions in general relativity and Perturbation theory · General relativity and Perturbation theory · See more »

Post-Newtonian expansion

Post-Newtonian expansions in general relativity are used for finding an approximate solution of the Einstein field equations for the metric tensor.

Exact solutions in general relativity and Post-Newtonian expansion · General relativity and Post-Newtonian expansion · 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 · General relativity 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 · General relativity and Ricci curvature · 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.

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Roger Penrose

Sir Roger Penrose (born 8 August 1931) is an English mathematical physicist, mathematician and philosopher of science.

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Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.

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Solutions of the Einstein field equations

Solutions of the Einstein field equations are spacetimes that result from solving the Einstein field equations (EFE) of general relativity.

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Spacetime topology

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity.

Exact solutions in general relativity and Spacetime topology · General relativity and Spacetime topology · See more »

Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

Exact solutions in general relativity and Speed of light · General relativity and Speed of light · See more »

Stationary spacetime

In general relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike.

Exact solutions in general relativity and Stationary spacetime · General relativity and Stationary 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.

Exact solutions in general relativity and Stress–energy tensor · General relativity 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 · General relativity and Tensor · See more »

The list above answers the following questions

Exact solutions in general relativity and General relativity Comparison

Exact solutions in general relativity has 89 relations, while General relativity has 366. As they have in common 35, the Jaccard index is 7.69% = 35 / (89 + 366).

References

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