|
Black Hole Stability Conjecture
The black hole stability conjecture is the conjecture that a perturbed Kerr black hole in Minkowski space will settle back down to a stable state. The question developed out of work in 1952 by the French mathematician Yvonne Choquet-Bruhat. The stability of empty Minkowski space is a result of Klainerman and Christodoulou from 1993. A 2016 by Hintz and Vasy paper proved the stability of slowly rotating Kerr black holes in de Sitter space. A limited stability result for Kerr black holes in Schwarzschild space-time was published by Klainerman and Szeftel in 2017. Culminating in 2022, a series of papers was published by Giorgi, Klainerman and Szeftel which present a proof of the conjecture for slowly rotating Kerr black holes in Minkowski space-time. See also * Final state conjecture * Stability of matter * Positive energy theorem * Birkhoff's theorem (relativity) * Penrose–Hawking singularity theorems * Hoop conjecture The hoop conjecture, proposed by Kip Thorne in 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kerr Black Hole
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find. Overview The Kerr metric is a generalization to a rotating body of the Schwarzschild metric, discovered by Karl Schwarzschild in 1915, which described the geometry of spacetime around an uncharged, spherically symmetric, and non-rotating body. The corresponding solution for a ''charged'', spherical, non-rotating body, the Reissner–Nordström metric, was discovered soon afterwards (1916–1918). However, the exact solution for an uncharged, ''rotating'' black hole, the Kerr metric, remained unsolved until 1963, when it was discovered by Roy Kerr.Melia, Fulvio (2009). "Cracking the Einstein code: relativity and the birth of black ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Final State Conjecture
The final state conjecture is that the end state of the universe will consist of black holes and gravitational radiation. It was originally proposed by Roger Penrose in the 1980s, and is considered a central problem in mathematical general relativity. See also * Black hole stability conjecture The black hole stability conjecture is the conjecture that a perturbed Kerr black hole in Minkowski space will settle back down to a stable state. The question developed out of work in 1952 by the French mathematician Yvonne Choquet-Bruhat. The st ... References Conjectures Ultimate fate of the universe {{astrophysics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Holes
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hoop Conjecture
The hoop conjecture, proposed by Kip Thorne in 1972, states that an imploding object forms a black hole when, and only when, a circular hoop with a specific critical circumference could be placed around the object and rotated about its diameter. In simpler terms, the entirety of the object's mass must be compressed to the point that it resides in a perfect sphere whose radius is equal to that object's Schwarzschild radius, if this requirement is not met, then a black hole will not be formed. The critical circumference required for the imaginary hoop is given by the following equation listed below. : c=2\pi r_s\,\! where : c\,\! is the critical circumference; : r_s\,\! is the object's Schwarzschild radius; Thorne calculated the effects of gravitation on objects of different shapes (spheres, and cylinders that are infinite in one direction), and concluded that the object needed to be compressed in all three directions before gravity led to the formation of a black hole. With cylin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Penrose–Hawking Singularity Theorems
The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose shared half of the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity". Singularity A singularity in solutions of the Einstein field equations is one of three things: * Spacelike singularities: The singularity lies in the future or past of all events within a certain region. The Big Bang singularity and the typical singularity inside a non-rotating, uncharge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhoff's Theorem (relativity)
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, nonrotating, gravitating body) must be given by the Schwarzschild metric. The converse of the theorem is true and is called Israel's theorem. The converse is not true in Newtonian gravity. The theorem was proven in 1923 by George David Birkhoff (author of another famous '' Birkhoff theorem'', the ''pointwise ergodic theorem'' which lies at the foundation of ergodic theory). Israel's theorem was proved by Werner Israel. Intuitive rationale The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin; if there were another concentration of mass–energy somewhere else, this would disturb the spherical symmetry, so we can expect the solution to represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Energy Theorem
The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an isolated system is nonnegative, and can only be zero when the system has no gravitating objects. Although these statements are often thought of as being primarily physical in nature, they can be formalized as mathematical theorems which can be proven using techniques of differential geometry, partial differential equations, and geometric measure theory. Richard Schoen and Shing-Tung Yau, in 1979 and 1981, were the first to give proofs of the positive mass theorem. Edward Witten, in 1982, gave the outlines of an alternative proof, which were later filled in rigorously by mathematicians. Witten and Yau were awarded the Fields medal in mathematics in part for their work on this topic. An imprecise formulation of the Schoen-Yau / Witten pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stability Of Matter
In physics, the stability of matter refers to the ability of a large number of charged particles, such as electrons and protons, to form macroscopic objects without collapsing or blowing apart due to electromagnetic interactions. Classical physics predicts that such systems should be inherently unstable due to attractive and repulsive electrostatic forces between charges, and thus the stability of matter was a theoretical problem that required a quantum mechanical explanation. The first solution to this problem was provided by Freeman Dyson and Andrew Lenard in 1967–1968, but a shorter and more conceptual proof was found later by Elliott Lieb and Walter Thirring in 1975 using the Lieb–Thirring inequality. The stability of matter is partly due to the uncertainty principle and the Pauli exclusion principle. Description of the problem In statistical mechanics, the existence of macroscopic objects is usually explained in terms of the behavior of the energy or the free ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Space-time
Minkowski, Mińkowski or Minkovski (Slavic feminine: Minkowska, Mińkowska or Minkovskaya; plural: Minkowscy, Mińkowscy; , ) is a surname of Polish origin. It may refer to: * :pl:Minkowski (herb szlachecki), Minkowski or Mińkowski, a coat of arms of Polish nobility *Alyona Minkovski (born 1986), Russian-American correspondent and presenter * Eugène Minkowski (1885–1972), French psychiatrist * Hermann Minkowski (1864–1909) Russian-born German mathematician and physicist, known for: ** Minkowski addition ** Minkowski–Bouligand dimension ** Minkowski diagram ** Minkowski distance ** Minkowski functional ** Minkowski inequality ** Minkowski space *** Null vector (Minkowski space) ** Minkowski plane ** Minkowski's theorem ** Minkowski's question mark function ** Abraham–Minkowski controversy ** Hasse–Minkowski theorem ** Separating axis theorem, Minkowski separation theorem ** Smith–Minkowski–Siegel mass formula *Christopher Minkowski (born 1953), American Indologist *Kh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Space
In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized. While the individual components in Euclidean space and time might differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total interval in spacetime between events.This makes spacetime distance an inva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwarzschild Metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact 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. The solution is a useful approximation for describing slowly rotating astronomical objects such as many stars and planets, including Earth and the Sun. It was found by Karl Schwarzschild in 1916. According to Birkhoff's theorem, the Schwarzschild metric is the most general spherically symmetric vacuum solution of the Einstein field equations. A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum (non-rotating). A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Sitter Space
In mathematical physics, ''n''-dimensional de Sitter space (often denoted dS''n'') is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of an ''n''-sphere (with its canonical Riemannian metric). The main application of de Sitter space is its use in general relativity, where it serves as one of the simplest mathematical models of the universe consistent with the observed accelerating expansion of the universe. More specifically, de Sitter space is the maximally symmetric vacuum solution of Einstein's field equations in which the cosmological constant \Lambda is positive (corresponding to a positive vacuum energy density and negative pressure). De Sitter space and anti-de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked closely together in Le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
