Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Androidâ„¢ device!
Install
Faster access than browser!
 

List of mathematical topics in relativity

Index List of mathematical topics in relativity

This is a list of mathematical topics in relativity, by Wikipedia page. [1]

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.

New!!: List of mathematical topics in relativity and Anti-de Sitter space · See more »

Ashtekar variables

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

New!!: List of mathematical topics in relativity and Ashtekar variables · See more »

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).

New!!: List of mathematical topics in relativity and Batalin–Vilkovisky formalism · See more »

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.

New!!: List of mathematical topics in relativity and Big Bang · See more »

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.

New!!: List of mathematical topics in relativity and Biquaternion · See more »

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.

New!!: List of mathematical topics in relativity and Black hole · See more »

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.

New!!: List of mathematical topics in relativity and Black hole thermodynamics · See more »

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).

New!!: List of mathematical topics in relativity and Cauchy horizon · See more »

Charged black hole

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

New!!: List of mathematical topics in relativity and Charged black hole · See more »

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.

New!!: List of mathematical topics in relativity and Chronology protection conjecture · 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!!: List of mathematical topics in relativity and Closed timelike curve · See more »

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.

New!!: List of mathematical topics in relativity and Conjugate diameters · See more »

Cosmic censorship hypothesis

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

New!!: List of mathematical topics in relativity and Cosmic censorship hypothesis · See more »

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.

New!!: List of mathematical topics in relativity and Cosmic microwave background · See more »

Cosmic variance

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

New!!: List of mathematical topics in relativity and Cosmic variance · 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!!: List of mathematical topics in relativity and Cosmological constant · 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.

New!!: List of mathematical topics in relativity and Dark energy · See more »

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.

New!!: List of mathematical topics in relativity and Dark matter · See more »

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.

New!!: List of mathematical topics in relativity and De Sitter space · 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!!: List of mathematical topics in relativity and Einstein field equations · See more »

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.

New!!: List of mathematical topics in relativity and Einstein–Cartan theory · See more »

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.

New!!: List of mathematical topics in relativity and Faster-than-light · See more »

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).

New!!: List of mathematical topics in relativity and Four-acceleration · See more »

Four-force

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

New!!: List of mathematical topics in relativity and Four-force · See more »

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.

New!!: List of mathematical topics in relativity and Four-gradient · See more »

Four-momentum

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

New!!: List of mathematical topics in relativity and Four-momentum · See more »

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.

New!!: List of mathematical topics in relativity and Four-vector · See more »

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.

New!!: List of mathematical topics in relativity and Four-velocity · 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.

New!!: List of mathematical topics in relativity and Friedmann–Lemaître–Robertson–Walker metric · 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.

New!!: List of mathematical topics in relativity and General relativity · See more »

Geodesic

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

New!!: List of mathematical topics in relativity and Geodesic · See more »

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.

New!!: List of mathematical topics in relativity and Gravitational redshift · See more »

Hawking radiation

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

New!!: List of mathematical topics in relativity and Hawking radiation · See more »

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.

New!!: List of mathematical topics in relativity and Horizon problem · See more »

Hyperbolic orthogonality

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

New!!: List of mathematical topics in relativity and Hyperbolic orthogonality · See more »

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+.

New!!: List of mathematical topics in relativity and Hyperboloid model · See more »

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.

New!!: List of mathematical topics in relativity and Immirzi parameter · See more »

Inflation (cosmology)

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

New!!: List of mathematical topics in relativity and Inflation (cosmology) · See more »

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.

New!!: List of mathematical topics in relativity and Length contraction · 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!!: List of mathematical topics in relativity and Lorentz covariance · See more »

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.

New!!: List of mathematical topics in relativity and Lorentz group · See more »

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.

New!!: List of mathematical topics in relativity and Lorentz transformation · See more »

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.

New!!: List of mathematical topics in relativity and Mass in special relativity · See more »

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.

New!!: List of mathematical topics in relativity and Micro black hole · See more »

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.

New!!: List of mathematical topics in relativity and Minkowski diagram · 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.

New!!: List of mathematical topics in relativity and Minkowski space · See more »

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.

New!!: List of mathematical topics in relativity and No-hair theorem · See more »

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.

New!!: List of mathematical topics in relativity and Observable universe · See more »

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.

New!!: List of mathematical topics in relativity and Penrose–Hawking singularity theorems · See more »

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.

New!!: List of mathematical topics in relativity and Physical cosmology · See more »

Poincaré group

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

New!!: List of mathematical topics in relativity and Poincaré group · See more »

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.

New!!: List of mathematical topics in relativity and Principle of relativity · See more »

Proper length

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

New!!: List of mathematical topics in relativity and Proper length · See more »

Proper time

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

New!!: List of mathematical topics in relativity and Proper time · 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.

New!!: List of mathematical topics in relativity and Pseudo-Riemannian manifold · See more »

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.

New!!: List of mathematical topics in relativity and Randall–Sundrum model · See more »

Rapidity

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

New!!: List of mathematical topics in relativity and Rapidity · See more »

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.

New!!: List of mathematical topics in relativity and Reissner–Nordström metric · See more »

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.

New!!: List of mathematical topics in relativity and Relativistic wave equations · See more »

Rotating black hole

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

New!!: List of mathematical topics in relativity and Rotating black hole · See more »

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.

New!!: List of mathematical topics in relativity and Schwarzschild metric · See more »

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.

New!!: List of mathematical topics in relativity and Schwarzschild radius · 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!!: List of mathematical topics in relativity and Spacetime · See more »

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.

New!!: List of mathematical topics in relativity and Special relativity · See more »

Speed of light

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

New!!: List of mathematical topics in relativity and Speed of light · See more »

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.

New!!: List of mathematical topics in relativity and Split-complex number · 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!!: List of mathematical topics in relativity and Stress–energy tensor · See more »

Theory of relativity

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

New!!: List of mathematical topics in relativity and Theory of relativity · See more »

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.

New!!: List of mathematical topics in relativity and Unit hyperbola · See more »

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.

New!!: List of mathematical topics in relativity and Warped geometry · See more »

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.

New!!: List of mathematical topics in relativity and Weyl curvature hypothesis · See more »

World line

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

New!!: List of mathematical topics in relativity and World line · See more »

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.

New!!: List of mathematical topics in relativity and Wormhole · See more »

Redirects here:

Outline of mathematical topics in relativity.

References

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

OutgoingIncoming
Hey! We are on Facebook now! »