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Boundary region of asymptotically flat spacetimes in general relativity
In theoretical physics, null infinity is a region at the boundary of asymptotically flat spacetimes. In general relativity, straight paths in spacetime
Null_infinity
Causal relationships between points in a manifold
the future null infinity. Past-directed null geodesics end up on ℐ−, the past null infinity. Spacelike geodesics end up on spacelike infinity. In various
Causal_structure
Asymptotic symmetry group of General Relativity
symmetry group of asymptotically flat, Lorentzian spacetimes at null (i.e., light-like) infinity. It was originally formulated in 1962 by Hermann Bondi, M.
Bondi–Metzner–Sachs_group
Formulation in general relativity
boundary regions such as null infinity, timelike infinity, spacelike infinity, black hole horizons and cosmological horizons, null tetrads adapted to spacetime
Construction of a complex null tetrad
Construction_of_a_complex_null_tetrad
flat spacetime satisfying the null energy condition, every causal curve from past null infinity to future null infinity is fixed-endpoint homotopic to
Topological_censorship
Predicted physical phenomenon
expected in Bondi–Metzner–Sachs group through the infrared triangle. At null infinity, passing GWs leave a permanent distortion in spacetime, changing distances
Gravitational_memory_effect
Diagram of different points in spacetime
boundary lines of a Penrose diagram correspond to the region called "null infinity", or to singularities where light rays must end. Thus, Penrose diagrams
Penrose_diagram
Mathematical concept
Infinity is something which is boundless, limitless, or endless. It is denoted by ∞, called the infinity symbol. From the time of the ancient Greeks, the
Infinity
Infinite cardinal number
the infinity ( ∞ {\displaystyle \infty } ) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly
Aleph_number
Conjecture in physics
singularity visible from future null infinity. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a black
Cosmic_censorship_hypothesis
Facet of general relativity
spacelike hypersurface chosen. Closely related notions can be defined at null infinity. These are known as the Bondi energy, momentum, and mass, and describe
Mass_in_general_relativity
Result in general relativity
causal past of null infinity. Such boundaries are generated by null geodesics. The affine parameter goes to infinity as we approach null infinity, and no caustics
Raychaudhuri_equation
Theorem describing tensor behavior
to null infinity. Let γ {\displaystyle \gamma } be a null geodesic in a spacetime ( M , g a b ) {\displaystyle (M,g_{ab})} from a point p to null infinity
Peeling_theorem
Principle in theoretical physics
terms of a lower-dimensional CFT defined on the celestial sphere at null infinity. Strominger and others in the subfield aim to approach it as testable
Holographic_principle
Generalization of electrodynamics
{\displaystyle r\to \infty } . Indeed, to study asymptotic symmetries as null infinity Bondi coordinates are introduced ( u , r , x i ) {\displaystyle (u,r
P-form_electrodynamics
Type of horizon in spacetime
"future null infinity". This is the set of points which are approached asymptotically by null rays (light rays, for example) which can escape to infinity. This
Absolute_horizon
Finnish theoretical physicist
theory, string theory and QCD matter, cosmological phase transitions and null infinity in general relativity. Kajantie was awarded the Finnish Academy of Science
Keijo_Kajantie
Signature pavilion at Expo 2025
null² (Japanese: ヌルヌル, pronounced Nurunuru) was a Signature Pavilion at the Expo 2025 Osaka, Kansai, Japan, held on Yumeshima Island in Osaka. It was produced
Null²
Indian-American theoretical physicist
treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity". Journal
Abhay_Ashtekar
System consisting of two black holes in close orbit around each other
at retarded time U. f is a surface integral of the news function at null infinity varied by solid angle. The Arnowitt–Deser–Misner (ADM) energy, or ADM
Binary_black_hole
Indian-American black hole physicist
nearly extreme black hole hair along with its measurement at future null infinity as a transient phenomenon. Furthermore, he studied about the stability
Gaurav_Khanna_(physicist)
Proposed quasi-local mass in general relativity
infinity. In a spacetime setting, when the Hawking energy is evaluated on suitable families of surfaces approaching null infinity along outgoing null
Hawking_energy
American computer security researcher
disclosure at conferences including DEFCON, Black Hat Briefings, Kernelcon, and null. Curry grew up in Omaha, Nebraska and attended Elkhorn High School. He began
Sam_Curry
American physicist
interior Cauchy evolution with exterior characteristic evolution to null infinity, applicable to various hyperbolic systems in astrophysics and beyond
Jeffrey_H._Winicour
Statistical test comparing two probability distributions
distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the
Kolmogorov–Smirnov_test
Infinity Train is an American animated anthology television series created by Owen Dennis, formerly a writer and storyboard artist on Regular Show, for
List of Infinity Train episodes
List_of_Infinity_Train_episodes
Duality between FRW models and conformal field theory
shaped like a hat for future null infinity. A Euclidean Liouville quantum field theory is assumed to reside there. The null coordinate corresponds to the
FRW/CFT_duality
Axiom of Zermelo-Fraenkel set theory
natural numbers, aleph null ( ℵ 0 {\displaystyle \aleph _{0}} ), has many of the properties of a large cardinal. Thus the axiom of infinity is sometimes regarded
Axiom_of_infinity
Australian physicist
general relativity, e.g., for the study of gravitational radiation and null infinity. In gravitational theory, Buchdahl's contribution on the Einstein field
Hans_Adolf_Buchdahl
Value to which an infinite sequence tends
elementa (1659). He used the term quasi-infinite for unbounded and quasi-null for vanishing. Newton dealt with series in his works on Analysis with infinite
Limit_of_a_sequence
JavaScript syntax extension
createElement("div", null, React.createElement("p", null, "Header"), React.createElement("p", null, "Content"), React.createElement("p", null, "Footer")); };
JSX_(programming)
Mathematical set containing no elements
textbooks and popularizations, the empty set is referred to as the "null set". However, null set is a distinct notion within the context of measure theory,
Empty_set
Type of spacetime horizon
principal null directions once the Petrov type is known; also, at some typical boundary regions such as null infinity, timelike infinity, spacelike infinity, black
Non-expanding_horizon
Japanese science fiction visual novel
Infinity is a visual novel video game developed by KID. It is the second entry in the Infinity series; it is preceded by Never 7: The End of Infinity
Ever_17:_The_Out_of_Infinity
Science fiction book series by Lois McMaster Bujold
the series is based on 20th-century engineering situations, projected into null-g or alternative solar system situations. Biomedical advances such as cloning
Vorkosigan_Saga
Statistical test that compares goodness of fit
the ratio of their likelihoods. If the more constrained model (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should
Likelihood-ratio_test
Japanese academic, artist, and entrepreneur
Sunbeam of null in forest (Sunbeam of null in forest)(Jun.9 – Jul.8, 2022 / Tokyo, Otemachi) Yoichi Ochiai x Shinichi Wakasa, Guwa Guwa Null Null: Circumscribing
Yoichi_Ochiai
Mathematical set that can be enumerated
{\displaystyle |S|} is less than or equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null), the cardinality of the set of natural numbers N {\displaystyle \mathbb
Countable_set
Number that is larger than all finite numbers
incomparable with aleph-one and larger than aleph-null. Either way, there are no cardinals between aleph-null and aleph-one. The continuum hypothesis is the
Transfinite_number
Infinite set that is not countable
number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers. Examples of uncountable sets include
Uncountable_set
Counting song
End"). "Aleph-null bottles of beer on the wall". Aleph-null is the size of the set of all natural numbers, and is the smallest infinity and the only countable
99_Bottles_of_Beer
1980 novel by Rudy Rucker
and things he calls bloogs which are not aleph-null or c infinitely divisible, but a higher infinity, then the hypothesis will have been disproven. With
White_Light_(novel)
Borel set Analytic set C-measurable set Projective set Inductive set Infinity-Borel set Suslin set Homogeneously Suslin set Weakly homogeneously Suslin
List of properties of sets of reals
List_of_properties_of_sets_of_reals
Coordinate system used in general relativity
a spherically symmetric black hole) which are adapted to radial null geodesics. Null geodesics are the worldlines of photons; radial ones are those that
Eddington–Finkelstein coordinates
Eddington–Finkelstein_coordinates
Open 3-manifold that is contractible but not homeomorphic to R3
T_{1}} is a thickened Whitehead link. Note that T 2 {\displaystyle T_{2}} is null-homotopic in the complement of the meridian of T 1 . {\displaystyle T_{1}
Whitehead_manifold
Type of geometric algebra
therefore represents the (conformal) point at infinity. This motivates the subscripts o and ∞ for identifying the null basis vectors. The choice of the origin
Conformal_geometric_algebra
Line along which a quadratic form applied to any two points' displacement is zero
In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any
Isotropic_line
In mathematics, with negligible exceptions
the mathematical context; for instance, it can mean finite, countable, or null. In contrast, "almost no" means "a negligible quantity"; that is, "almost
Almost_all
Fictional character
between a human character and an android from another dimension known as Null Space. The character has also appeared in non-speaking roles on television
Darkhawk
Statistical method
null}\left({\text{reject }}H_{null}\right)\\&=P_{null}\left(\exists i\in \{1,\ldots ,N\}:|t_{i}|>\zeta _{\alpha ,N}\right)\\&=1-P_{null}\left(\forall
Šidák_correction_for_t-test
List of statements that appear to contradict themselves
the average operator of the buses. Lindley's paradox: Tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false
List_of_paradoxes
Statistical model for a binary dependent variable
to the null model, denoted by ε φ 2 {\displaystyle \varepsilon _{\varphi }^{2}} where the φ {\displaystyle \varphi } subscript denotes the null model.
Logistic_regression
Statistical significance test
exact tests, so called because the significance of the deviation from a null hypothesis (e.g., p-value) can be calculated exactly, rather than relying
Fisher's_exact_test
the future null cone in Minkowski space, with the origin deleted. The celestial sphere at infinity is the conformal manifold M, and the null rays in the
Ambient_construction
Mathematical model combining space and time
moving at the speed of light is zero. Such an interval is termed lightlike or null. A photon arriving in our eye from a distant star will not have aged, despite
Spacetime
Flat-sided three-dimensional shape
regular octahedron in the Poincaré ball model of hyperbolic space (sphere at infinity not shown). All dihedral angles of this shape are right angles.
Polyhedron
American speculative fiction writer (born 1961)
Giants of Pangaea (2020) Gods of Pangaea (2020) Null-A Continuum (sequel to A. E. van Vogt's The World of Null-A, 2008) Somewhither: A tale of the Unwithering
John_C._Wright_(author)
the Infinity Stones akin to the Infinity Gauntlet and created to reverse the Blip. After the Avengers retrieve alternate versions of the six Infinity Stones
Features of the Marvel Cinematic Universe
Features_of_the_Marvel_Cinematic_Universe
The real numbers or their cardinality
cardinality c {\displaystyle {\mathfrak {c}}} is larger than the smallest infinity, namely, ℵ 0 {\displaystyle \aleph _{0}} . He also proved that c {\displaystyle
Continuum_(set_theory)
Whole number
"none" are often used. The English words "nought" or "naught", "nil", and null are also synonymous. It is often called "oh" in the context of reading out
0
Branch of mathematics that studies sets
theory also provides the framework to develop a mathematical theory of infinity, and has various applications in computer science (such as in the theory
Set_theory
Study of angle-preserving transformations of a geometric space
"Euclidean space with a point added at infinity", or a "pseudo-Euclidean space with a null cone added at infinity". That is, the setting is a compactification
Conformal_geometry
Compact astronomical body
singularity would be stretched and squeezed by an infinite amount. They are also null singularities, meaning that a photon could travel parallel to them without
Black_hole
Manifold or algebraic variety of dimension n in a space of dimension n+1
singular point, which is at infinity, in the direction x = 0, y = 0. Affine sphere Coble hypersurface Dwork family Null hypersurface Polar hypersurface
Hypersurface
General-purpose programming language
the / operator represents classic division. Rounding towards negative infinity, though a different method than in most languages, adds consistency to
Python_(programming_language)
Axiom of Set Theory
In axiomatic set theory, the axiom of empty set, also called the axiom of null set and the axiom of existence, is a statement that asserts the existence
Axiom_of_empty_set
Algorithm for finding the shortest paths in graphs
the distance to all vertices to infinity distance[v] := inf // And having a null predecessor predecessor[v] := null // The distance from the source to
Bellman–Ford_algorithm
Path planning algorithm
already in the open list gScore(neighbor) := infinity parent(neighbor) := Null update_vertex(s, neighbor) return Null function update_vertex(s, neighbor) //
Theta*
2nd-degree plane curve which is reducible
line and the line at infinity), a single point (in fact, two complex conjugate lines), or the null set (twice the line at infinity or two parallel complex
Degenerate_conic
Branch of mathematics
special interest like singular points, inflection points and points at infinity. More advanced questions involve the topology of the curve and the relationship
Algebraic_geometry
Cardinality of the set of real numbers
uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument
Cardinality_of_the_continuum
Rational function of the form (az + b)/(cz + d)
are called spacelike. The null cone S consists of those points where Q = 0; the future null cone N+ are those points on the null cone with x0 > 0. The celestial
Möbius_transformation
Exact spherically symmetric solution in GR
spherically symmetric and nonrotating star which is either emitting or absorbing null dusts. It is named after the Indian physicist Prahalad Chunnilal Vaidya and
Vaidya_metric
Marvel Comics fictional character
again attempts to destroy the Earth, on this occasion using a powerful "Null-Life" bomb. After a battle with the Silver Surfer and learning that a human
Stranger_(Marvel_Comics)
Null hypersurface in general relativity
Cauchy horizon and spacetime backreactions by infalling matter, a weak, null curvature singularity forms at the horizon. As the Cauchy horizon is approached
Cauchy_horizon
Geometry founded on spheres
point at infinity is added to Euclidean space so that lines (or planes) can be regarded as circles (or spheres) passing through the point at infinity (i.e
Lie_sphere_geometry
System of mathematical set theory
up to some finite stage can be built up using null set, pairing, and union. From the axiom of infinity, we get the existence of ω and its element 2 =
Kripke–Platek_set_theory
Property of statistical procedures
the procedure converges to the correct outcome as sample size goes to infinity. Use of the term in statistics derives from Sir Ronald Fisher in 1922.
Consistency_(statistics)
Evaluates how likely it is that any difference between data sets arose by chance
O_{6})} , the number of times that the die has fallen on each number. The null hypothesis is M u l t i n o m i a l ( N ; 1 / 6 , . . . , 1 / 6 ) {\displaystyle
Pearson's_chi-squared_test
Infinite Cardinal number
noted above) this is equal to ℵ 0 {\displaystyle \aleph _{0}} , or aleph null, sets with cardinality ℶ 0 {\displaystyle \beth _{0}} include: the natural
Beth_number
Oranguru Passimian Wimpod Golisopod Sandygast Palossand Pyukumuku Type: Null Silvally Minior Komala Turtonator Togedemaru Mimikyu Bruxish Drampa Dhelmise
List of generation VII Pokémon
List_of_generation_VII_Pokémon
Used to count, measure, and label
to the number zero. In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi, an early example of an algebraic grammar
Number
Notation in general relativity
the case of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The two real
Newman–Penrose_formalism
is a matrix, then the orthogonal complement of the row space of M is the null space of M: ( row M ) ⊥ = ker M . {\displaystyle (\operatorname {row}
Fredholm's_theorem
Euclidean geometry without distance and angles
called a null-vector; then the parallel transport in question is such that it carries any null-vector at one point into the position of a null-vector at
Affine_geometry
Phenomenon within general relativity
unbounded at the Cauchy horizon. It also predicts the existence of a weak null singularity at the Cauchy horizon of a spinning or charged black hole. Mass
Mass_inflation
Lowest possible energy of a quantum system or field
idea of incorporating renormalization into QED to deal with zero-point infinities. Renormalization was originally developed by Hans Kramers and also Victor
Zero-point_energy
Search algorithm
minimizing player is assured of. Initially, alpha is negative infinity and beta is positive infinity, i.e. both players start with their worst possible score
Alpha–beta_pruning
Model of the extended complex plane plus a point at infinity
called the closed complex plane): the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is,
Riemann_sphere
Completion of the usual space with "points at infinity"
at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in
Projective_space
worship of a holy figure. In legal context, occasionally a backing for nulling information that was presented by an attorney. Without any tangible proof
List_of_Latin_phrases_(full)
Distance between probability distributions
statistical potential energy which is zero only when an underlying statistical null hypothesis is true. Energy statistics are functions of distances between
Energy_distance
American punk rock band
slowcore band Null. An official breakup announcement was not made until 2017. In 2023, the three members reunited and released Infinity Shit under the
Coliseum_(band)
2003 Canadian film
be entertained on some level." In his review in Film Critic, Christopher Null wrote, "A little The Edge, a little Dances with Wolves, this adventure oddity
The_Snow_Walker
System of mathematical set theory
T ." AXIOM VII. Axiom of infinity (Axiom des Unendlichen) "There exists in the domain at least one set Z that contains the null set as an element and is
Zermelo_set_theory
Fictional extraterrestrial race
Gardener, who tried to bring life to the Null Space and planted it in the Darkforce Dimension. Eventually the Null Space and the Tree of Shadows were discovered
Skrull
Region in spacetime from which nothing can escape
horizon is defined from the causal structure as the past null cone of future conformal timelike infinity. A black hole event horizon is teleological in nature
Event_horizon
2001 collection of science fiction stories by William Tenn
Science Fiction, May 1953 "Eastward Ho!" - short story - F&SF, Oct. 1958 "Null-P" - short story - Worlds Beyond, Jan. 1951 "The Masculinist Revolt" - novelette
Immodest_Proposals
Set of rules defining correctly structured programs
the language. true false null JavaScript also defines the following global constants, which are not keywords. NaN Infinity undefined The following words
JavaScript_syntax
Fictional character from Ben 10
gather the four pieces of the Map of Infinity. Despite Ben's efforts, Aggregor manages to obtain the Map of Infinity. With no other options, Kevin absorbs
Ben_Tennyson
travel, tourism, insurance
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travel, tourism, insurance