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Null Infinity
In theoretical physics, null infinity is a region at the boundary of asymptotically flat spacetimes. In general relativity, straight paths in spacetime, called geodesics, may be space-like, time-like, or light-like (also called null). The distinction between these paths stems from whether the Spacetime Interval, spacetime interval of the path is positive (corresponding to space-like), negative (corresponding to time-like), or zero (corresponding to null). Light-like paths physically correspond to physical phenomena which propagate through space at the speed of light, such as electromagnetic radiation and Gravitational wave, gravitational radiation. The boundary of a flat spacetime is known as conformal infinity, and can be thought of as the end points of all geodesics as they go off to infinity. The region of null infinity corresponds to the terminus of all null geodesics in a flat Minkowski space. The different regions of conformal infinity are most often visualized on a Penrose dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topological spaces. One suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentzian Manifolds
Lorentzian may refer to * Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution * Lorentz lineshape (spectroscopy) * Lorentz transformation * Lorentzian manifold In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere non-degenerate bilinear form, nondegenerate. This is a generalization of a Riema ... See also * Lorentz (other) * Lorenz (other), spelled without the 't' {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General theory of relativity, relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time in physics, time, or four-dimensional spacetime. In particular, the ''curvature of spacetime'' is directly related to the energy and momentum of whatever is present, including matter and radiation. The relation is specified by the Einstein field equations, a system of second-order partial differential equations. Newton's law of universal gravitation, which describes gravity in classical mechanics, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graviton
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity. In string theory, believed by some to be a consistent theory of quantum gravity, the graviton is a massless state of a fundamental string. If it exists, the graviton is expected to be massless because the gravitational force has a very long range and appears to propagate at the speed of light. The graviton must be a spin-2 boson because the source of gravitation is the stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rainer K
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Rainer may refer to: People * Rainer (surname) * Rainer (given name) Other * Rainer Island, an island in Franz Josef Land, Russia * 16802 Rainer, an asteroid * Rainer Foundation, British charitable organisation See also * Rainier (other) * Rayner (other) * Raynor * Reiner (other) * Reyner Reyner is a surname, and has also been used as a given name. Notable people with the name include: * Reyner Banham (1922–1988), English architectural critic * Clement Reyner (1589–1651), English Benedictine monk * Edward Reyner (1600–c.16 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Bondi
Sir Hermann Bondi (1 November 1919 – 10 September 2005) was an Austrian-British people, British mathematician and physical cosmology, cosmologist. He is best known for developing the steady state model of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory. He contributed to the theory of general relativity,Obituaries: Professor Sir Hermann Bondi(12 September 2005) in ''The Independent''. Professor Sir Hermann Bondi(2005-09-13) in ''The Daily Telegraph, The Telegraph''. Sir Hermann Bondi(2005-09-14) in ''The Guardian''. Sir Hermann Bondi: 1919–2005(2005-09-14) in ''Physics World'', Institute of Physics, IOP. Black hole scientist Bondi dies(2005-09-17), BBC News. and was the first to analyze the Mass#Inertial vs. gravitational mass, inertial and gravitational interaction of negative mass and the first to explicate correctly the nature of gravitational waves. In his 1990 autobiography, Bondi regarded the 1962 work on gravitational waves as h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bondi–Metzner–Sachs Group
In general relativity, the Bondi–Metzner–Sachs (BMS) group, or the Bondi–Van der Burg–Metzner–Sachs group, is an asymptotic symmetry group of asymptotically flat, Lorentzian spacetimes at null (''i.e.'', light-like) infinity. It was originally formulated in 1962 by Hermann Bondi, M. G. Van der Burg, A. W. Metzner and Rainer K. Sachs in order to investigate the flow of energy at infinity due to propagating gravitational waves. Instead of the expected ordinary four spacetime translations of special relativity associated with the well-known conservation of momentum and energy, they found, much to their puzzling surprise, a novel infinite superset of direction-dependent time translations, which were named ''supertranslations''. Half a century later, this work of Bondi, Van der Burg, Metzner, and Sachs is considered pioneering and seminal. In his autobiography, Bondi considered the 1962 work as his "best scientific work". The group of supertranslations is key to understan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poincaré Group
The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics. Overview The Poincaré group consists of all coordinate transformations of Minkowski space that do not change the spacetime interval between events. For example, if everything were postponed by two hours, including the two events and the path you took to go from one to the other, then the time interval between the events recorded by a stopwatch that you carried with you would be the same. Or if everything were shifted five kilometres to the west, or turned 60 degrees to the right, you would also see no change in the interval. It turns out that the proper length of an object is also unaffected by such a shift. In total, there are ten degrees of freedom for such transformations. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event Horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact objects that even light cannot escape. At that time, the Newtonian theory of gravitation and the so-called corpuscular theory of light were dominant. In these theories, if the escape velocity of the gravitational influence of a massive object exceeds the speed of light, then light originating inside or from it can escape temporarily but will return. In 1958, David Finkelstein used general relativity to introduce a stricter definition of a local black hole event horizon as a boundary beyond which events of any kind cannot affect an outside observer, leading to information and firewall paradoxes, encouraging the re-examination of the concept of local event horizons and the notion of black holes. Several theories were subsequently d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole
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 (topology), 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 thermal radiation, the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the Orders of magnitude (temperature), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
