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Dynamical Horizon
In theoretical physics, a dynamical horizon (DH) is a local description (i.e. independent of the global structure of Space–time) of evolving black-hole horizons. In the literature there exist two different mathematical formulations of DHs—the 2+2 formulation developed by Sean Hayward and the 3+1 formulation developed by Abhay Ashtekar and others (see ). It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass-energy influx). A related formalism, for black holes with zero influx, is an isolated horizon. Formal definition The formal definition of a dynamical horizon is as follows: See also *Isolated horizon It was customary to represent black hole horizons via stationary solutions of field equations, i.e., solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole. While this simple ... * Non-expanding horizon References Cross-reference Sources used * Furth ... [...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 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 Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sean Hayward
Sean, also spelled Seán or Séan in Irish English, is a male given name of Irish origin. It comes from the Irish versions of the Biblical Hebrew name ''Yohanan'' (), Seán (Anglicisation of names, anglicized as ''Shaun/Shawn (given name), Shawn/Shon (given name), Shon'') and Séan (Ulster variant; anglicized ''Shane/Shayne''), rendered ''John (given name), John'' in English and Johannes/Johann/Johan in other Germanic languages. The Norman language, Norman French ''Jehan'' (see ''Jean (male given name), Jean'') is another version. For notable people named Sean, refer to List of people named Sean. Origin The name was adopted into the Irish language most likely from ''Jean'', the French variant of the Hebrew name ''Yohanan''. As Gaelic has no letter (derived from ; English also lacked until the late 17th Century, with ''John'' previously been spelt ''Iohn'') so it is substituted by , as was the normal Gaelic practice for adapting Biblical names that contain in other languages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abhay Ashtekar
Abhay Vasant Ashtekar (born 5 July 1949) is an Indian theoretical physicist. He is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University. As the creator of Ashtekar variables, he is one of the founders of loop quantum gravity and its subfield loop quantum cosmology. He has also written a number of descriptions of loop quantum gravity that are accessible to non-physicists. In 1999, Ashtekar and his colleagues were able to calculate the entropy for a black hole, matching a legendary 1974 prediction by Hawking. Oxford mathematical physicist Roger Penrose has described Ashtekar's approach to quantum gravity as "The most important of all the attempts at 'quantizing' general relativity." Ashtekar was elected as Member to National Academy of Sciences in May 2016. Biography Abhay Ashtekar grew up in several cities, including Mumbai, in the state of Maharashtra, India. After completing his undergra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary (topology), boundary of no escape is called the event horizon. Although it has a great effect on the fate and circumstances of an object crossing it, it 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. Moreover, 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 order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly. Obje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isolated Horizon
It was customary to represent black hole horizons via stationary solutions of field equations, i.e., solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole. While this simple idealization was natural as a starting point, it is overly restrictive. Physically, it should be sufficient to impose boundary conditions at the horizon which ensure only that the black hole itself is isolated. That is, it should suffice to demand only that the intrinsic geometry of the horizon be time independent, whereas the geometry outside may be dynamical and admit gravitational and other radiation. An advantage of isolated horizons over event horizons is that while one needs the entire spacetime history to locate an event horizon, isolated horizons are defined using local spacetime structures only. The laws of black hole mechanics, initially proved for event horizons, are generalized to isolated horizons. An isolated horizon (\De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Submanifold
In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. Formal definition In the following we assume all manifolds are differentiable manifolds of class ''C''''r'' for a fixed , and all morphisms are differentiable of class ''C''''r''. Immersed submanifolds An immersed submanifold of a manifold ''M'' is the image ''S'' of an immersion map ; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) – it can have self-intersections. More narrowly, one can require that the map be an injection (one-to-one), in which we call it an injective immersion, and define an immersed submanifold to be the image subset ''S'' together with a topology and differentia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize Special relativity, relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based wikisource:Translation:On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foliation
In mathematics (differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition of the real coordinate space R''n'' into the cosets ''x'' + R''p'' of the standardly embedded subspace R''p''. The equivalence classes are called the leaves of the foliation. If the manifold and/or the submanifolds are required to have a piecewise-linear, differentiable (of class ''Cr''), or analytic structure then one defines piecewise-linear, differentiable, or analytic foliations, respectively. In the most important case of differentiable foliation of class ''Cr'' it is usually understood that ''r'' ≥ 1 (otherwise, ''C''0 is a topological foliation). The number ''p'' (the dimension of the leaves) is called the dimension of the foliation and is called its codimension. In some papers on general relativity by mathematical physicists, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isolated Horizon
It was customary to represent black hole horizons via stationary solutions of field equations, i.e., solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole. While this simple idealization was natural as a starting point, it is overly restrictive. Physically, it should be sufficient to impose boundary conditions at the horizon which ensure only that the black hole itself is isolated. That is, it should suffice to demand only that the intrinsic geometry of the horizon be time independent, whereas the geometry outside may be dynamical and admit gravitational and other radiation. An advantage of isolated horizons over event horizons is that while one needs the entire spacetime history to locate an event horizon, isolated horizons are defined using local spacetime structures only. The laws of black hole mechanics, initially proved for event horizons, are generalized to isolated horizons. An isolated horizon (\De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-expanding Horizon
A non-expanding horizon (NEH) is an enclosed null surface whose intrinsic structure is preserved. An NEH is the geometric prototype of an isolated horizon which describes a black hole in equilibrium with its exterior from the quasilocal perspective. It is based on the concept and geometry of NEHs that the two quasilocal definitions of black holes, weakly isolated horizons and isolated horizons, are developed. Definition of NEHs A three-dimensional submanifold ∆ is defined as a ''generic'' (rotating and distorted) NEH if it respects the following conditions:Abhay Ashtekar, Christopher Beetle, Olaf Dreyer, et al. "Generic isolated horizons and their applications". ''Physical Review Letters'', 2000, 85(17): 3564-3567arXiv:gr-qc/0006006v2/ref>Abhay Ashtekar, Christopher Beetle, Jerzy Lewandowski. "Geometry of generic isolated horizons". ''Classical and Quantum Gravity'', 2002, 19(6): 1195-1225arXiv:gr-qc/0111067v2/ref>Abhay Ashtekar, Stephen Fairhurst, Badri Krishnan. "Isolated ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cardiff
, latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1883 (/)2005 (independent university status) , type = Public , endowment = £45.5 million (2021) , budget = £603.4 million (2020–21) , total_staff = 6,900 (2019/20) , academic_staff = 3,350 (2019/20) , chancellor = Jenny Randerson , vice_chancellor = Colin Riordan , students = () , undergrad = () , postgrad = () , other = , city = Cardiff , country = Wales, United Kingdom , coor = , campus = Urban , colours = , mascot = , affiliations = Russell Group EUAUniversities UKGW4 , website cardiff.ac.uk, logo = Cardiff University ( cy, Prifysgol Caerdydd) is a public research university in Cardiff, Wales, United Kingdom. It was established in 1883 as the University College of South Wales and Monmouthshire an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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