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De Sitter–Schwarzschild Metric
In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. It is the positive-curvature case of the Kottler metric. Unlike a flat-space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime (named after ). The Nariai limit has no singularities, the cosmological and black hole horizons have the same area, and they can be mapped to each other by a discrete reflection symmetry in any causal patch. Introduction In general relativity, spacetimes can have black hole event horizons and also cosmological horizons. The de Sitter–Schwarzschild solution is the simplest solution that has both. Metric The metric of any spherically symmetric solution in Schwarzschild form is: : ds^2 = - f(r) dt^2 + + r^2(d\theta^2 + \sin^2\theta \,d\phi^2) The vacuum Einstein equations give a ''linear'' equation for ''f''(''r''), which has as solutions: : f(r)=1-2a/r : f(r)= 1 - b r^2 The fir ... [...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] |
Inflation (cosmology)
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago). Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Starobinsky, Guth, and Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kerr–Newman–de–Sitter Metric
The Kerr–Newman–de–Sitter metric (KNdS) is one of the most general stationary spacetime, stationary solutions of the Einstein's field equation#Einstein–Maxwell equations, Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mass embedded in an expanding universe. It generalizes the Kerr–Newman metric by taking into account the cosmological constant \Lambda. Boyer–Lindquist coordinates In those coordinates the local clocks and rulers are at constant \rm r and have no local orbital angular momentum \rm (L_z=0), therefore they are corotating with the frame-dragging velocity relative to the fixed stars. In Metric signature, signature and in Nondimensionalization, natural units of \rm G=M=c=k_e=1 the KNdS metric is g_= \rm -\frac g_= \rm -\frac g_= \rm -\frac g_= \rm\frac g_= \rm \frac with all the other metric tensor components g_=0, where \rm a is the black hole's spi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Sitter Universe
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter universe at about a time after the fiducial Big Bang singularity, and far into the future. Mathematical expression A de Sitter universe has no ordinary matter content but with a positive cosmological constant (\Lambda) that sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate: : H \propto \sqrt , where the constants of proportionality depen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anti-de Sitter Space
In mathematics and physics, ''n''-dimensional anti-de Sitter space (AdS''n'') is a symmetric_space, maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (6 May 1872 – 20 November 1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe. Paul Dirac was the first person to rigorously explore anti-de Sitter space, doing so in 1963. Manifolds of constant curvature are most familiar in the case of two dimensions, where the elliptic plane or surface of a sphere is a surface of constant positive curvature, a flat (i.e., Euclidean space, Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature. Einstein's general theory of relat ... [...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] |
Imaginary Time
Imaginary time is a mathematical representation of time that appears in some approaches to special relativity and quantum mechanics. It finds uses in certain cosmological theories. Mathematically, imaginary time is real time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary unit ''i''. Imaginary time is ''not'' imaginary in the sense that it is unreal or made-up; it is simply expressed in terms of imaginary numbers. Origins In mathematics, the imaginary unit i is \sqrt, such that i^2 is defined to be -1. A number which is a direct multiple of i is known as an imaginary number. A number that is the sum of an imaginary number and a real number is known as a complex number. In certain physical theories, periods of time are multiplied by i in this way. Mathematically, an imaginary time period \tau may be obtained from real time t via a Wick rotation by \pi/2 in the complex plane: \tau = it. Stephen Hawking popularized the concept of imagina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach's Principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference. The proposition is that the existence of absolute rotation (the distinction of local inertial frames vs. rotating reference frames) is determined by the large-scale distribution of matter, as exemplified by this anecdote: You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move? Mach's princ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Static Universe
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean. A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595). In contrast to this model, Albert Einstein proposed a temporally infinite but spatially finite model - ''static eternal universe'' - as his preferred cosmology during 1917, in his paper ''Cosmological Considerations in the General Theory of Relativity''. After the discovery of the redshift-distance relationship (deduced by the inverse correlation of galactic brightness to redshift) by American astronomers Vesto Slipher and Edwin Hubble, the Belgian astrophysicist and priest Georges Lemaître interpreted the redshift as evidence of un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holographic Principle
The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region – such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string theoretic interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Susskind said, "The three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence. The holographic pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole Complementarity
Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Lárus Thorlacius, John Uglum, and Gerard 't Hooft. Overview Ever since Stephen Hawking suggested information is lost in an evaporating black hole once it passes through the event horizon and is inevitably destroyed at the singularity, and that this can turn pure quantum states into mixed states, some physicists have wondered if a complete theory of quantum gravity might be able to conserve information with a unitary time evolution. But how can this be possible if information cannot escape the event horizon without traveling faster than light? This seems to rule out Hawking radiation as the carrier of the missing information. It also appears as if information cannot be "reflected" at the event horizon as there is nothing special about the horizon locally. Leonard Susskind, Lárus Thorlacius, and John Uglum proposed a radical resolution to this problem by c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birth anniversary was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American theoretical physicist, professor of theoretical physics at Stanford University and founding director of the Stanford Institute for Theoretical Physics. His research interests are string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study. Susskind is widely regarded as one of the fathers of string theory. He was the first to give a precise string-theoretic interpretation of the holographic principle in 1995 and the first to introduce the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
