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Gibbons–Hawking Space
In mathematical physics, a Gibbons–Hawking space, named after Gary Gibbons and Stephen Hawking, is essentially a hyperkähler manifold with an extra U(1) symmetry. (In general, Gibbons–Hawking metrics are a subclass of hyperkähler metrics.) Gibbons–Hawking spaces, especially ambipolar ones, find an application in the study of 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. Th ... microstate geometries. See also * Gibbons–Hawking effect References {{DEFAULTSORT:Gibbons-Hawking space Structures on manifolds Complex manifolds Riemannian manifolds Algebraic geometry Stephen Hawking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gary Gibbons
Gary William Gibbons (born 1 July 1946) is a British theoretical physicist. Education Gibbons was born in Coulsdon, Surrey. He was educated at Purley County Grammar School and the University of Cambridge, where in 1969 he became a research student under the supervision of Dennis Sciama. When Sciama moved to the University of Oxford, he became a student of Stephen Hawking, obtaining his PhD from Cambridge in 1973. Career and research Apart from a stay at the Max Planck Institute in Munich in the 1970s he has remained in Cambridge throughout his career, becoming a full professor in 1997, a Fellow of the Royal Society in 1999, and a Fellow of Trinity College, Cambridge in 2002. Having worked on classical general relativity for his PhD thesis, Gibbons focused on the quantum theory of black holes afterwards. Together with Malcolm Perry, he used thermal Green's functions to prove the universality of thermodynamic properties of horizons, including cosmological event horizons. He ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Hawking
Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between 1979 and 2009, he was the Lucasian Professor of Mathematics at Cambridge, widely viewed as one of the most prestigious academic posts in the world. Hawking was born in Oxford into a family of physicians. In October 1959, at the age of 17, he began his university education at University College, Oxford, where he received a First Class Honours, first-class Honours degree, BA degree in physics. In October 1962, he began his graduate work at Trinity Hall, Cambridge, where, in March 1966, he obtained his PhD in applied mathematics and theoretical physics, specialising in general relativity and cosmology. In 1963, at age 21, Hawking was diagnosed with an early-onset slow-progressing form of motor neurone disease that gradually, over decades, pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperkähler Manifold
In differential geometry, a hyperkähler manifold is a Riemannian manifold (M, g) endowed with three integrable almost complex structures I, J, K that are Kähler with respect to the Riemannian metric g and satisfy the quaternionic relations I^2=J^2=K^2=IJK=-1. In particular, it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds. Hyperkähler manifolds were first given this name by Eugenio Calabi in 1979. Early history Marcel Berger's 1955 paper on the classification of Riemannian holonomy groups first raised the issue of the existence of non-symmetric manifolds with holonomy Sp(''n'')·Sp(1). Interesting results were proved in the mid-1960s in pioneering work by Edmond Bonan and Kraines who have independently proven that any such manifold admits a parallel 4-form \Omega. Bonan's later results include a Lefschetz-type result: wedging with this powers of this 4-form induces isomorphisms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
U(1)
In mathematics, the circle group, denoted by \mathbb T or , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers \mathbb T = \. The circle group forms a subgroup of , the multiplicative group of all nonzero complex numbers. Since \C^\times is abelian, it follows that \mathbb T is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized by the angle measure : \theta \mapsto z = e^ = \cos\theta + i\sin\theta. This is the exponential map for the circle group. The circle group plays a central role in Pontryagin duality and in the theory of Lie groups. The notation \mathbb T for the circle group stems from the fact that, with the standard topology (see below), the circle group is a 1-torus. More generally, \mathbb T^n (the direct product of \mathbb T with itself n times) is geometrically an n-toru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ohio State University
The Ohio State University (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one of the List of largest United States university campuses by enrollment, largest universities by enrollment in the United States, with nearly 50,000 undergraduate students and nearly 15,000 graduate students. The university consists of sixteen colleges and offers over 400 degree programs at the undergraduate and Graduate school, graduate levels. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". the university has an List of colleges and universities in the United States by endowment, endowment of $7.9 billion. Its athletic teams compete in NCAA Division I as the Ohio State Buckeyes as a member of the Big Ten Conference for the majority of fielde ... [...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] |
Journal Of High Energy Physics
The ''Journal of High Energy Physics'' is a monthly peer-reviewed open access scientific journal covering the field of high energy physics. It is published by Springer Science+Business Media on behalf of the International School for Advanced Studies. The journal is part of the SCOAP3 initiative. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.810. References External links *Journal pageat International School for Advanced Studies The International School for Advanced Studies (Italian: ''Scuola Internazionale Superiore di Studi Avanzati''; SISSA) is an international, state-supported, post-graduate-education and research institute in Trieste, Italy. SISSA is active in th ... website English-language journals Monthly journals Physics journals Academic journals established in 1997 Springer Science+Business Media academic journals Academic journals associated with learned and professional societies Particle physics journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International School For Advanced Studies
The International School for Advanced Studies (Italian: ''Scuola Internazionale Superiore di Studi Avanzati''; SISSA) is an international, state-supported, post-graduate-education and research institute in Trieste, Italy. SISSA is active in the fields of mathematics, physics and neuroscience, offering both undergraduate and post-graduate courses. Each year, about 70 PhD students are admitted to SISSA based on their scientific qualifications. SISSA also runs master's programs in the same areas, in collaboration with both Italian and other European universities. History SISSA was founded in 1978, as a part of the reconstruction following the Friuli earthquake of 1976. Although the city of Trieste itself did not suffer any damage, physicist Paolo Budinich asked and obtained from the Italian government to include in the interventions the institution of a new, post-graduate teaching and research institute, modeled on the Scuola Normale Superiore di Pisa. The school became operativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbons–Hawking Effect
In the theory of general relativity, the Gibbons–Hawking effect is the statement that a temperature can be associated to each solution of the Einstein field equations that contains a causal horizon. It is named after Gary Gibbons and Stephen Hawking. The term "causal horizon" does not necessarily refer to event horizons only, but could also stand for the horizon of the visible universe, for instance. For example, Schwarzschild spacetime contains an event horizon and so can be associated a temperature. In the case of Schwarzschild spacetime this is the temperature T of a black hole of mass M, satisfying T \propto M^ (see also Hawking radiation). A second example is de Sitter space which contains an event horizon. In this case the temperature T is proportional to the Hubble parameter H, i.e. T \propto H. See also *Hawking radiation *Gibbons–Hawking space In mathematical physics, a Gibbons–Hawking space, named after Gary Gibbons and Stephen Hawking, is essentially a hyperk� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structures On Manifolds
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological organisms, minerals and chemicals. Abstract structures include data structures in computer science and musical form. Types of structure include a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space. Load-bearing Buildings, aircraft, skeletons, anthills, beaver dams, bridges and salt domes are all examples of load-bearing structures. The results of construction are divided into buildings and non-building structures, and make up the infrastructure of a human society. Built structures are broadly divided by their varying design approaches and standards, into categories including building structures, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
