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Tolman–Oppenheimer–Volkoff Equation
In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modelled by general relativity. The equation is :\frac=-\frac\rho\left(1+\frac\right)\left(1+\frac\right)\left(1-\frac\right)^ Here, r is a radial coordinate, and \rho(r) and P(r) are the density and pressure, respectively, of the material at radius r. The quantity m(r), the total mass within r, is discussed below. The equation is derived by solving the Einstein equations for a general time-invariant, spherically symmetric metric. For a solution to the Tolman–Oppenheimer–Volkoff equation, this metric will take the form :ds^2=e^ c^2 \,dt^2 - \left(1-\frac\right)^ \,dr^2 - r^2\left(d\theta^2 + \sin^2 \theta \,d\phi^2\right) where \nu(r) is determined by the constraint :\frac=- \left(\frac \right) \frac When supplemented with an equation of state, F(\rho,P)=0, which relates den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space–''what'' they are, rather than ''where'' they are." Among the subjects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, ''astrophysicists'' apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to electromagnetic waves but the gravitational equivalent. Gravitational waves were later predicted in 1916 by Albert Einstein on the basis of his general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)showing one of the ways the methods of Newtonian physics are unable to explain p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Static Spherically Symmetric Perfect Fluid
In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure. Such solutions are often used as idealized models of stars, especially compact objects such as white dwarfs and especially neutron stars. In general relativity, a model of an ''isolated'' star (or other fluid ball) generally consists of a fluid-filled interior region, which is technically a perfect fluid solution of the Einstein field equation, and an exterior region, which is an asymptotically flat vacuum solution. These two pieces must be carefully ''matched'' across the ''world sheet'' of a spherical surface, the ''surface of zero pressure''. (There are various mathematical criteria called matching conditions for checking that the required matching has been successfully achieved.) Sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solutions Of The Einstein Field Equations
:''Where appropriate, this article will use the abstract index notation.'' Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as ''exact'' or ''non-exact''. The Einstein field equations are :G_ + \Lambda g_ \, = \kappa T_ , where G_ is the Einstein tensor, \Lambda is the cosmological constant (sometimes taken to be zero for simplicity), g_ is the metric tensor, \kappa is a constant, and T_ is the stress–energy tensor. The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime manifold. The Einstein tensor is built up from the metric tensor and its partial derivatives; thus, given the stress–energy tensor, the Einstein field equations are a system of ten partial differential equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tolman–Oppenheimer–Volkoff Limit
The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of cold, nonrotating neutron stars, analogous to the Chandrasekhar limit for white dwarf stars. If the mass of the said star reaches the limit it will collapse to a denser form. Theoretical work in 1996 placed the limit at approximately 1.5 to 3.0 solar masses, corresponding to an original stellar mass of 15 to 20 solar masses; additional work in the same year gave a more precise range of 2.2 to 2.9 solar masses. Observations of GW170817, the first gravitational wave event due to merging neutron stars (which are thought to have collapsed into a black hole within a few seconds after merging), placed the limit at close to 2.17 (solar masses). This value was inconsistent with short gamma-ray burst X-ray plateau data however, which suggested a value of ''M''TOV = 2.37 . Reanalysis of the GW170817 event data in 2019 resulted in a higher value of ''M''TOV = 2.3 . If GW ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrostatic Equation
Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an immersed body". It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, the study of fluids in motion. Hydrostatics is a subcategory of fluid statics, which is the study of all fluids, both compressible or incompressible, at rest. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Law Of Universal Gravitation
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.It was shown separately that separated spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the " first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work '' Philosophiæ Naturalis Principia Mathematica'' ("the ''Principia''"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post-Newtonian Expansion
In general relativity, the post-Newtonian expansions (PN expansions) are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher order terms can be added to increase accuracy, but for strong fields sometimes it is preferable to solve the complete equations numerically. This method is a common mark of effective field theories. In the limit, when the small parameters are equal to 0, the post-Newtonian expansion reduces to Newton's law of gravity. Expansion in 1/''c''2 The post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of the matter that creates the gravitational field, to the speed of light, which in this case is more precisely called the ''speed of gravity''. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Astronomy And Astrophysics
''Astronomy & Astrophysics'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. The journal is run by a Board of Directors representing 27 sponsoring countries plus a representative of the European Southern Observatory. The journal is published by EDP Sciences and the editor-in-chief is . History Origins ''Astronomy and Astrophysics'' (A&A) was created as an answer to the publishing scenario found in Europe in the 1960s. At that time, multiple journals were being published in several countries around the continent. These journals usually had a limited number of subscribers, and published articles in languages other than English, resulting in a small number of citations compared to American and British journals. Starting in 1963, conversations between astronomers from European countries assessed the need for a common astronomical journal. On 8 April 1968, leading astronomers from Belgium, Denmark, F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goethe University Frankfurt
Goethe University (german: link=no, Johann Wolfgang Goethe-Universität Frankfurt am Main) is a university located in Frankfurt am Main, Germany. It was founded in 1914 as a citizens' university, which means it was founded and funded by the wealthy and active liberal citizenry of Frankfurt. The original name was Universität Frankfurt am Main. In 1932, the university's name was extended in honour of one of the most famous native sons of Frankfurt, the poet, philosopher and writer/dramatist Johann Wolfgang von Goethe. The university currently has around 45,000 students, distributed across four major campuses within the city. The university celebrated its 100th anniversary in 2014. The first female president of the university, Birgitta Wolff, was sworn into office in 2015, and was succeeded by Enrico Schleiff in 2021. 20 Nobel Prize winners have been affiliated with the university, including Max von Laue and Max Born. The university is also affiliated with 18 winners of the Gottfr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kilonova
A kilonova (also called a macronova) is a transient astronomical event that occurs in a compact binary system when two neutron stars or a neutron star and a black hole merge. These mergers are thought to produce gamma-ray bursts and emit bright electromagnetic radiation, called ''kilonova'', due to the radioactive decay of heavy r-process nuclei that are produced and ejected fairly isotropically during the merger process. History The existence of thermal transient events from neutron star mergers was first introduced by Li & Paczyński in 1998. The radioactive glow arising from the merger ejecta was originally called mini-supernova, as it is to the brightness of a typical supernova, the self-detonation of a massive star. The term ''kilonova'' was later introduced by Metzger et al. in 2010 to characterize the peak brightness, which they showed reaches 1000 times that of a classical nova. The first candidate kilonova to be found was detected as a short gamma-ray burst, GRB 13 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GW170817
GW 170817 was a gravitational wave (GW) signal observed by the LIGO and Virgo detectors on 17 August 2017, originating from the shell elliptical galaxy . The signal was produced by the last minutes of a binary pair of neutron stars' inspiral process, ending with a merger. It is the first GW observation that has been confirmed by non-gravitational means. Unlike the five previous GW detections, which were of merging black holes not expected to produce a detectable electromagnetic signal, the aftermath of this merger was also seen by 70 observatories on 7 continents and in space, across the electromagnetic spectrum, marking a significant breakthrough for multi-messenger astronomy. The discovery and subsequent observations of GW 170817 were given the Breakthrough of the Year award for 2017 by the journal ''Science''. The gravitational wave signal, designated GW 170817, had a duration of approximately 100 seconds, and shows the characteristics in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
