73 relations: Anti-de Sitter space, Ashtekar variables, Batalin–Vilkovisky formalism, Big Bang, Biquaternion, Black hole, Black hole thermodynamics, Cauchy horizon, Charged black hole, Chronology protection conjecture, Closed timelike curve, Conjugate diameters, Cosmic censorship hypothesis, Cosmic microwave background, Cosmic variance, Cosmological constant, Dark energy, Dark matter, De Sitter space, Einstein field equations, Einstein–Cartan theory, Faster-than-light, Four-acceleration, Four-force, Four-gradient, Four-momentum, Four-vector, Four-velocity, Friedmann–Lemaître–Robertson–Walker metric, General relativity, Geodesic, Gravitational redshift, Hawking radiation, Horizon problem, Hyperbolic orthogonality, Hyperboloid model, Immirzi parameter, Inflation (cosmology), Length contraction, Lorentz covariance, Lorentz group, Lorentz transformation, Mass in special relativity, Micro black hole, Minkowski diagram, Minkowski space, No-hair theorem, Observable universe, Penrose–Hawking singularity theorems, Physical cosmology, ..., Poincaré group, Principle of relativity, Proper length, Proper time, Pseudo-Riemannian manifold, Randall–Sundrum model, Rapidity, Reissner–Nordström metric, Relativistic wave equations, Rotating black hole, Schwarzschild metric, Schwarzschild radius, Spacetime, Special relativity, Speed of light, Split-complex number, Stress–energy tensor, Theory of relativity, Unit hyperbola, Warped geometry, Weyl curvature hypothesis, World line, Wormhole. Expand index (23 more) »

## Anti-de Sitter space

In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.

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## Ashtekar variables

In the ADM formulation of general relativity, spacetime is split into spatial slices and a time axis.

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## Batalin–Vilkovisky formalism

In theoretical physics, the Batalin–Vilkovisky (BV) formalism (named for Igor Batalin and Grigori Vilkovisky) was developed as a method for determining the ghost structure for Lagrangian gauge theories, such as gravity and supergravity, whose corresponding Hamiltonian formulation has constraints not related to a Lie algebra (i.e., the role of Lie algebra structure constants are played by more general structure functions).

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## Big Bang

The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution.

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## Biquaternion

In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group.

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## Black hole

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it.

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## Black hole thermodynamics

In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black-hole event horizons.

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## Cauchy horizon

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations).

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## Charged black hole

A charged black hole is a black hole that possesses electric charge.

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## Chronology protection conjecture

The chronology protection conjecture is a conjecture first proposed by Stephen Hawking which hypothesizes that the laws of physics are such as to prevent time travel on all but submicroscopic scales.

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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.

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## Conjugate diameters

In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter.

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## Cosmic censorship hypothesis

The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity.

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## Cosmic microwave background

The cosmic microwave background (CMB, CMBR) is electromagnetic radiation as a remnant from an early stage of the universe in Big Bang cosmology.

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## Cosmic variance

The term cosmic variance is the statistical uncertainty inherent in observations of the universe at extreme distances.

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## 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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## 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.

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## Dark matter

Dark matter is a theorized form of matter that is thought to account for approximately 80% of the matter in the universe, and about a quarter of its total energy density.

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## De Sitter space

In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary Euclidean space.

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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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## Einstein–Cartan theory

In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity.

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## Faster-than-light

Faster-than-light (also superluminal or FTL) communication and travel are the conjectural propagation of information or matter faster than the speed of light.

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## Four-acceleration

In the theory of relativity, four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see three-acceleration in special relativity).

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## Four-force

In the special theory of relativity, four-force is a four-vector that replaces the classical force.

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## Four-gradient

In differential geometry, the four-gradient (or 4-gradient) \mathbf is the four-vector analogue of the gradient \vec from Gibbs–Heaviside vector calculus.

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## Four-momentum

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime.

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## Four-vector

In special relativity, a four-vector (also known as a 4-vector) is an object with four components, which transform in a specific way under Lorentz transformation.

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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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## 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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## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

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## Gravitational redshift

In astrophysics, gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that is in a gravitational field is reduced in frequency, or redshifted, when observed in a region at a higher gravitational potential.

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## Hawking radiation

Hawking radiation is blackbody radiation that is predicted to be released by black holes, due to quantum effects near the event horizon.

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## Horizon problem

The horizon problem (also known as the homogeneity problem) is a cosmological fine-tuning problem within the Big Bang model of the universe.

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## Hyperbolic orthogonality

In plane geometry, two lines are hyperbolic orthogonal when they are reflections of each other over the asymptote of a given hyperbola.

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## Hyperboloid model

In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+.

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## Immirzi parameter

The Immirzi parameter (also known as the Barbero–Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative theory of quantum gravity.

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## Inflation (cosmology)

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe.

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## Length contraction

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.

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## 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.

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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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## 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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## Mass in special relativity

Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence.

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## Micro black hole

Micro black holes, also called quantum mechanical black holes or mini black holes, are hypothetical tiny black holes, for which quantum mechanical effects play an important role.

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## Minkowski diagram

The Minkowski diagram, also known as a spacetime diagram, was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity.

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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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## No-hair theorem

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.

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## Observable universe

The observable universe is a spherical region of the Universe comprising all matter that can be observed from Earth at the present time, because electromagnetic radiation from these objects has had time to reach Earth since the beginning of the cosmological expansion.

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## Penrose–Hawking singularity theorems

The Penrose–Hawking singularity theorems are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities.

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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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## Poincaré group

The Poincaré group, named after Henri Poincaré (1906), was first defined by Minkowski (1908) as the group of Minkowski spacetime isometries.

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## Principle of relativity

In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.

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## Proper length

Proper length or rest length refers to the length of an object in the object's rest frame.

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## Proper time

In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line.

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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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## Randall–Sundrum model

In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-dimensional brane or branes.

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## Rapidity

In relativity, rapidity is commonly used as a measure for relativistic velocity.

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## Reissner–Nordström metric

In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The metric was discovered by Hans Reissner, Hermann Weyl, Gunnar Nordström and G. B. Jeffery.

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## Relativistic wave equations

In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light.

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## Rotating black hole

A rotating black hole is a black hole that possesses angular momentum.

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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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## Schwarzschild radius

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a physical parameter that shows up in the Schwarzschild solution to Einstein's field equations, corresponding to the radius defining the event horizon of a Schwarzschild black hole.

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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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## Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

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## Speed of light

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

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## Split-complex number

In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z.

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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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## Theory of relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.

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## Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.

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## Warped geometry

In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in form The geometry almost decomposes into a Cartesian product of the y geometry and the x geometry – except that the x part is warped, i.e. it is rescaled by a scalar function of the other coordinates y. For this reason, the metric of a warped geometry is often called a warped product metric.

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## Weyl curvature hypothesis

The Weyl curvature hypothesis, which arises in the application of Albert Einstein's general theory of relativity to physical cosmology, was introduced by the British mathematician and theoretical physicist Sir Roger Penrose in an article in 1979 in an attempt to provide explanations for two of the most fundamental issues in physics.

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## World line

The world line (or worldline) of an object is the path that object traces in -dimensional spacetime.

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## Wormhole

A wormhole is a concept that represents a solution of the Einstein field equations: a non-trivial resolution of the Ehrenfest paradox structure linking separate points in spacetime.

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## Redirects here:

Outline of mathematical topics in relativity.

## References

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