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Topics referred to by the same term
Lorentzian may refer to Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution Lorentz lineshape
Lorentzian
Hypothetical topological feature of spacetime
leads to definitions such as the following, taken from Matt Visser's Lorentzian Wormholes (1996).[page needed] If a Minkowski spacetime contains a compact
Wormhole
Probability distribution
sometimes called the probable error. This function is also known as a Lorentzian function, and an example of a nascent delta function, and therefore approaches
Cauchy_distribution
Differentiable manifold with nondegenerate metric tensor
space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified
Pseudo-Riemannian_manifold
Submanifold of Lorentzian manifold
field of Lorentzian geometry, a Cauchy surface, also called more properly Cauchy hypersurface, is a certain kind of submanifold of a Lorentzian manifold
Cauchy_surface
under left multiplication by a given unit quaternion of unit norm. In a Lorentzian manifold, such as a spacetime model in general relativity (which will
Congruence_(manifolds)
Formula in X-ray diffraction and crystallography
{S(q_{P})}{1+{\frac {\Delta q^{2}}{[q_{P}^{2}\sigma _{2}^{2}/2a]^{2}}}}}} which is a Lorentzian or Cauchy function, of FWHM q P 2 σ 2 2 / a = 4 π 2 n 2 ( σ 2 / a ) 2
Scherrer_equation
Lorentzian manifold where curvature vanishes at large distances
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that
Asymptotically_flat_spacetime
Causal relationships between points in a manifold
causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified
Causal_structure
Feature observed in spectroscopy
stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position
Spectral_line_shape
Defunct theory of electromagnetism
Hermann Minkowski. Today LET is often treated as some sort of "Lorentzian" or "neo-Lorentzian" interpretation of special relativity. The introduction of length
Lorentz_ether_theory
Lorentzian manifold with vanishing Einstein tensor
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation
Vacuum_solution
Lie group of Lorentz transformations
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for
Lorentz_group
Mathematical function
The Mittag-Leffler function can be used to interpolate continuously between a Gaussian and a Lorentzian function.
Mittag-Leffler_function
Quantity in relativistic physics
Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz. It
Lorentz_factor
Theorem in differential geometry
Riemannian manifolds, although there has also been research into splitting of Lorentzian manifolds. Any connected Riemannian manifold M has an underlying metric
Splitting_theorem
Possibility of a consistent definition of "clockwise" in a mathematical space
tangent bundle is always orientable, even over nonorientable manifolds. In Lorentzian geometry, there are two kinds of orientability: space orientability and
Orientability
Philosophical argument for the existence of God
from J. M. E. McTaggart and hybrid A–B theorists. He refers to the neo‐Lorentzian interpretation of the Special Theory of Relativity, which he contends
Kalam_cosmological_argument
Spacetime manifold
condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). It is called hyperbolic in analogy with the linear theory of
Globally_hyperbolic_spacetime
Lorentzian manifold that does not contain a closed timelike curve
Suppose a Lorentzian manifold contains a closed timelike curve (CTC). No CTC can be continuously deformed as a CTC (is timelike homotopic) to a point,
Timelike_simply_connected
Maximally symmetric Lorentzian manifold with a positive cosmological constant
maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is analogue of an n-sphere, with a Lorentzian metric in place of the
De_Sitter_space
Pictorial representation of symmetry
of Coxeter graphs that progress from finite to affine to hyperbolic to Lorentzian. The determinant of the Cartan matrices determine where the series changes
Coxeter–Dynkin_diagram
24-dimensional repeating pattern of points
the Dynkin diagram) of the reflection group of the 26-dimensional even Lorentzian unimodular lattice II25,1. By comparison, the Dynkin diagrams of II9,1
Leech_lattice
Quadratic scalar invariant
In the theory of Lorentzian manifolds, particularly in the context of applications to general relativity, the Kretschmann scalar is a quadratic scalar
Kretschmann_scalar
Mathematical space with two coordinates
surfaces locally minimize their area, as is done physically by soap films. Lorentzian surfaces look locally like a two-dimensional slice of relativistic spacetime
Two-dimensional_space
Optical device with parallel mirrors
the Lorentzian linewidth Δ ν c {\displaystyle \Delta \nu _{c}} , displayed (blue line) relative to the free spectral range in the figure "Lorentzian linewidth
Fabry–Pérot_interferometer
Generalization of the Dirac equation
from flat spacetime (Minkowski space) to curved spacetime, a general Lorentzian manifold. In full generality the equation can be defined on M {\displaystyle
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Every Riemannian manifold can be isometrically embedded into some Euclidean space
of the metric g {\displaystyle g} . This is particularly relevant for Lorentzian signature (case ν = 1 {\displaystyle \nu =1} ) where the existence of
Nash_embedding_theorems
Riemannian manifold which satisfies vacuum Einstein equations
be arbitrary, thus not being restricted to Lorentzian manifolds (including the four-dimensional Lorentzian manifolds usually studied in general relativity)
Einstein_manifold
Natural number
pairwise connections. There are 26 sporadic groups. The 26-dimensional Lorentzian unimodular lattice II25,1 plays a significant role in sphere packing problems
26_(number)
Hypothetical approach to quantum gravity with emergent spacetime
gravity, especially with its spin foam formulations. For example, the Lorentzian Barrett–Crane model is essentially a non-perturbative prescription for
Causal dynamical triangulation
Causal_dynamical_triangulation
Mathematics award
Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture." James Maynard
Fields_Medal
fields is a pointwise classification of bivectors at each point of a Lorentzian manifold. It is used in the study of solutions of Maxwell's equations
Classification of electromagnetic fields
Classification_of_electromagnetic_fields
Scientific subjects
gravitoelectromagnetism, inertial frame of reference, invariance, length contraction, Lorentzian manifold, Lorentz transformation, mass–energy equivalence, metric tensor
Branches_of_physics
Emission spectrum with Lorentzian profile
monochromatic. Homogeneous broadening cause these lines to take on a lorentzian profile with an associated spectral linewidth. The following sections
Spectral_broadening
Application of topology
In gravitation theory, a world manifold endowed with some Lorentzian pseudo-Riemannian metric and an associated space-time structure is a space-time. Gravitation
World_manifold
Anthony Moffat, is a continuous probability distribution based upon the Lorentzian distribution. Its particular importance in astrophysics is due to its
Moffat_distribution
Maximally symmetric Lorentzian manifold with a negative cosmological constant
space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of hyperbolic space. Anti-de Sitter
Anti-de_Sitter_space
Set of integral curves of a vector field
integral curves of a (nowhere vanishing) vector field in a four-dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often
Congruence (general relativity)
Congruence_(general_relativity)
Structure defining distance on a manifold
called Lorentzian. More generally, a metric tensor in dimension n other than 4 of signature (1, n − 1) or (n − 1, 1) is sometimes also called Lorentzian. If
Metric_tensor
Probability distribution
\sigma }},} and L ( x ; γ ) {\displaystyle L(x;\gamma )} is the centered Lorentzian profile: L ( x ; γ ) ≡ γ π ( γ 2 + x 2 ) . {\displaystyle L(x;\gamma )\equiv
Voigt_profile
Affine connection on the tangent bundle of a manifold
In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine
Levi-Civita_connection
Theory of interwoven space and time by Albert Einstein
Lorentzian geometry. Distances in Euclidean geometry are calculated with the Pythagorean theorem and only involved spatial coordinates. In Lorentzian
Special_relativity
New Zealand mathematician
author of the reference book on the current state of wormhole theory, Lorentzian Wormholes — from Einstein to Hawking (1996) and co-editor of Artificial
Matt_Visser
Candidate unified theory of physics
{F}})=0} . In contemporary physical theories, the word spacetime refers to a Lorentzian manifold ( M , g ) {\displaystyle (M,g)} . This means that spacetime is
Causal_fermion_systems
Algorithm to smooth data points
maximum or minimum. The diagram shows data points belonging to a synthetic Lorentzian curve, with added noise (blue diamonds). Data are plotted on a scale of
Savitzky–Golay_filter
Model in electromagnetism
The Havriliak–Negami relaxation is an empirical modification of the Debye relaxation model in electromagnetism. Unlike the Debye model, the Havriliak–Negami
Havriliak–Negami_relaxation
Lie algebra with imaginary simple roots
Finite-dimensional semisimple Lie algebras. Affine Kac–Moody algebras Algebras with Lorentzian Cartan subalgebra whose denominator function is an automorphic form of
Generalized_Kac–Moody_algebra
Set of scalars in general relativity
Invariants are actually less powerful for distinguishing locally non-isometric Lorentzian manifolds than they are for distinguishing Riemannian manifolds. This
Curvature invariant (general relativity)
Curvature_invariant_(general_relativity)
Type of geometry in mathematics
special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental interest, as they are the solutions of Einstein's
Ricci-flat_manifold
American mathematician (born 1983)
Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture". Huh is the
June_Huh
Spectral linewidth of a laser beam
mode can be equivalently expressed by the following parameters. The FWHM Lorentzian linewidth Δ ν c {\displaystyle \Delta \nu _{\rm {c}}} of the passive resonator
Laser_linewidth
Distinctive narrow spectral feature of chemical species
and a broad emission. This broadening effect results in an unshifted Lorentzian profile. The natural broadening can be experimentally altered only to
Spectral_line
Type of hypersurface
the pullback of the metric onto the tangent space is degenerate. For a Lorentzian metric, all the vectors in such a tangent space are space-like except
Null_hypersurface
Mathematical formula for relative permittivity
refractive index of materials with absorption lineshapes exhibiting non-Lorentzian broadening, such as metals and amorphous insulators, across broad spectral
Brendel–Bormann oscillator model
Brendel–Bormann_oscillator_model
Coordinate system in black hole physics
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important
Schwarzschild_coordinates
Obsolete postulated medium for the propagation of light
have been a few individuals who advocated a neo-Lorentzian approach to physics, which is Lorentzian in the sense of positing an absolute true state of
Luminiferous_aether
Theoretical physicist and mathematician (b. 1975)
Rychkov (2019) Lorentzian methods in conformal field theory". YouTube. IPhT-TV. October 1, 2019. "[2/4] Slava Rychkov (2019) Lorentzian methods in conformal
Vyacheslav_Rychkov
Concept in statistics and wave theory
width at half maximum (here γ), HWHM, is in common use. For example, a Lorentzian/Cauchy distribution of height 1/πγ can be defined by f ( x ) = 1 π γ
Full_width_at_half_maximum
describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1 in terms of the Leech lattice. Let Γ < I s o m ( H n )
Vinberg's_algorithm
Wrapped probability distribution
sometimes known as a Lorentzian distribution, and the wrapped Cauchy distribution may sometimes be referred to as a wrapped Lorentzian distribution. The
Wrapped_Cauchy_distribution
Measure of the strength of a spectral line
The shape of this profile is initially Gaussian but moves towards a Lorentzian profile as the column density increases. Formally, the equivalent width
Equivalent_width
two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue of a Riemann surface in indefinite signature
Lorentz_surface
Mathematical functions
hyperbola x 2 − y 2 = 1 {\displaystyle x^{2}-y^{2}=1} as measured in the Lorentzian plane (not the length of a hyperbolic arc in the Euclidean plane), and
Inverse_hyperbolic_functions
Type of scattering resonance
shows that this last expression boils down to the expected Breit–Wigner (Lorentzian) formula, as 1 − σ ( q = 0 ) ≈ ( Γ r e s / 2 ) 2 ( Γ r e s / 2 ) 2 + (
Fano_resonance
Classification used in differential geometry and general relativity
the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold. It is most often applied in studying exact solutions of Einstein's
Petrov_classification
Continuous deformation between two continuous functions
example, a path between two smooth embeddings is a smooth isotopy. On a Lorentzian manifold, certain curves are distinguished as timelike (representing something
Homotopy
this geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description
Mathematics of general relativity
Mathematics_of_general_relativity
Key result in general relativity
given unit normal is k. This definition is motivated from Lorentzian geometry. Given a Lorentzian manifold (M, g) of dimension n + 1 and a spacelike immersion
Positive_energy_theorem
Scientific method to study solutions, gels, and other polymeric systems
scenarios, the above formula is approximated by the (much more convenient) Lorentzian: S D ( k → ) ≈ 1 1 + 1 2 ( k R g ) 2 {\displaystyle S_{D}({\vec {k}})\approx
Polymer_scattering
Fluctuation of spacetime on very small scales
vacuum Geon Hawking radiation Holographic principle Loop quantum gravity Lorentzian wormhole Planck time Stochastic quantum mechanics String theory Wormhole
Quantum_foam
Approach to quantum gravity using discrete spacetime
1994, p. 249; (Closeness of Lorentzian manifolds) L. Bombelli, Statistical Lorentzian geometry and the closeness of Lorentzian manifolds, J. Math. Phys.41:6944-6958
Causal_sets
Thin piece of material used to fill small gaps or spaces
generate homogeneous magnetic field along the sample volume to obtain pure Lorentzian line shapes of various resonances in the spectrum. This is accomplished
Shim_(spacer)
American theoretical physicist (1911–2008)
foam Coining the terms "neutron moderator", "superspace", "wormhole" Lorentzian wormhole "It from bit" Participatory anthropic principle Spouse Janette
John_Archibald_Wheeler
2013 novel by Greg Egan
universe of the novel is therefore based on a Riemannian instead of a Lorentzian manifold (which describes our own universe, where time only flows in one
The_Arrows_of_Time
infinite-dimensional Kac–Moody algebra whose root lattice is the even Lorentzian unimodular lattice II9,1 of dimension 10. Some of its root multiplicities
En_(Lie_algebra)
Set of mathematical concepts in quantum gravity
reconstruct the geometry of space-time from "first principles" is Discrete Lorentzian quantum gravity. Noncommutative geometry Quantum spacetime Tomasiello
Quantum_geometry
Physical characteristic of oscillating systems
defined as the square of the amplitude of the oscillations. This is a Lorentzian function, or Cauchy distribution, and this response is found in many physical
Resonance
Topological structure of 4D spacetime
physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important
Spacetime_topology
Mathematical technique in general relativity
by Fermi in 1921 and rediscovered by Walker in 1932. In the theory of Lorentzian manifolds, Fermi–Walker differentiation is a generalization of covariant
Fermi–Walker_transport
Classifications of Lorentzian manifolds
Causality conditions are classifications of Lorentzian manifolds according to the types of causal structures they admit. In the study of spacetimes, there
Causality_conditions
Topics referred to by the same term
law case Moffat distribution, a probability distribution based upon the Lorentzian distribution Moffatt, New Translation, a 1926 translation of the Bible
Moffat
Concept in quantum optics
ω 0 τ {\displaystyle \gamma ^{(1)}(\tau )=e^{-i\omega _{0}\tau }} For Lorentzian chaotic light (e.g. collision broadened): γ ( 1 ) ( τ ) = e − i ω 0 τ
Higher_order_coherence
Scalar-valued bilinear function
while the case of a single minus, R(n−1, 1) is called Lorentzian space. If n = 4, then Lorentzian space is also called Minkowski space or Minkowski spacetime
Bilinear_form
Topic in semi-Riemannian geometry
general relativity.[citation needed] This is the case of four-dimensional Lorentzian manifolds, for which there are only three pieces with simple properties
Bel_decomposition
Measure of the electric polarizability of a dielectric material
the energy levels. In general, the broadening is intermediate between Lorentzian and Gaussian; for an alloy it is somewhat closer to Gaussian because of
Permittivity
Concept in Astronomy
space by a Lorentzian curve, the width of which corresponds to the lifetime of the mode: the faster it decays, the broader is the Lorentzian. All stars
Solar-like_oscillations
Spacetime modeled by four pointwise-orthonormal vector fields
pointwise-orthonormal vector fields, one timelike and three spacelike, defined on a Lorentzian manifold that is physically interpreted as a model of spacetime. The timelike
Frame fields in general relativity
Frame_fields_in_general_relativity
Study of angle-preserving transformations of a geometric space
conformal automorphisms of a space can be quite large (as in the case of Lorentzian quadratic form) or variable (as with the case of definite (Euclidean)
Conformal_geometry
Euclidean geometry without distance and angles
associated to the Lorentzian vector space L2" was described by Graciela Birman and Katsumi Nomizu in an article entitled "Trigonometry in Lorentzian geometry"
Affine_geometry
Measure of curvature in differential geometry
This is significant in general relativity, where scalar curvature of a Lorentzian metric is one of the key terms in the Einstein field equations. Furthermore
Scalar_curvature
Hypothetical object usable as a time machine
backwards through time along a closed timelike curve. CTCs are associated, in Lorentzian manifolds which are interpreted physically as spacetimes, with the possibility
Tipler_cylinder
Regression analysis
complex models often requires robust regression techniques (e.g., using a Lorentzian loss function to mitigate outliers) and global optimization algorithms
Nonlinear_regression
have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy
List of probability distributions
List_of_probability_distributions
Topological space that locally resembles Euclidean space
Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity. The study of manifolds
Manifold
Topics referred to by the same term
relativity), in general relativity, a congruence in a four-dimensional Lorentzian manifold that is interpreted physically as a model of spacetime or a bundle
Congruence
2012 science-fiction book
work, the universe of the novel is based on a Riemannian instead of a Lorentzian manifold (which describes our own universe, where emitting radiation instead
The_Eternal_Flame_(novel)
Research program on the symmetries of geometry
n-dimensional anti-de Sitter space and (n−1)-dimensional conformal space with "Lorentzian" signature (in contrast with conformal space with "Euclidean" signature
Erlangen_program
In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice. It has several unusual properties, arising from Conway's discovery that
II25,1
Condition in which spacetime itself breaks down
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that
Gravitational_singularity
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