child farzand (#) Fr.: enfant 1) A person between birth and puberty; a son or daughter; an offspring. M.E.; O.E. cild "fetus, infant;" akin to Goth. kilthai "womb." Farzand, from Mid.Pers. frazand "child;" Av. frazanti- "progeny, offspring," from fra- "forward, along," → pro-, + zan "to give birth;" → birth. |
Schwarzschild barrier varqe-ye Schwarzschild Fr.: barrière de Schwarzschild An upper theoretical limit to the → eccentricity of orbits near a → supermassive black hole (SBH). It results from the impact of → relativistic precession on the stellar orbits. This phenomenon acts in such a way as to "repel" inspiralling bodies from the eccentric orbits that would otherwise lead to capture as → extreme mass ratio inspiral (EMRI)s. In other words, the presence of the Schwarzschild barrier reduces the frequency of EMRI events, in contrast to that predicted from → resonant relaxation. Resonant relaxation relies on the orbits having commensurate radial and azimuthal frequencies, so they remain in fixed planes over multiple orbits. In the strong-field potential of a massive object, orbits are no longer Keplerian but undergo significant perihelion precession. Resonant relaxation is only efficient in the regime where precession is negligible. The Schwarzschild barrier refers to the boundary between orbits with and without significant precession. Inside this point resonant relaxation is strongly quenched, potentially reducing inspiral rates. |
Schwarzschild black hole siyahcâl-e Schwarzschild Fr.: trou noir de Schwarzschild A → black hole with zero → angular momentum (non-rotating) and zero electric charge derived from Karl Schwarzschild 1916 exact solution to Einstein's vacuum → field equations. Karl Schwarzschild (1873-1916), German mathematical physicist, who carried out the first relativistic study of black holes. → black hole. |
Schwarzschild metric metrik-e Schwarzschild Fr.: métrique de Schwarzschild In → general relativity, the → metric that describes the → space-time outside a static mass with spherically symmetric distribution. |
Schwarzschild radius šo'â'-e Schwarzschild Fr.: rayon de Schwarzschild The critical radius at which a massive body becomes a → black hole, i.e., at which light is unable to escape to infinity: R_{s} = 2GM / c^{2}, where G is the → gravitational constant, M is the mass, and c the → speed of light. The fomula can be approximated to R_{s}≅ 3 x (M/Msun), in km. Therefore, the Schwarzschild radius for Sun is about 3 km and for Earth about 1 cm. |
Schwarzschild singularity takini-ye Schwarzschild Fr.: singularité de Schwarzschild A region of infinite → space-time curvature postulated to lie within a → black hole. |
Schwarzschild solution luyeš-e Schwarzschild Fr.: solution de Schwarzschild The first exact solution of → Einstein's field equations that describes the → space-time geometry outside a spherical distribution of mass. Briefly following Einstein's publication of → General Relativity, Karl Schwarzschild discovered this solution in 1916 (Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, Phys.-Math. Klasse, 189); → Schwarzschild black hole. |
Schwarzschild's criterion sanjdiâr-e Schwarzschild Fr.: critère de Schwarzschild The condition in stellar interior under which → convection occurs. It is expressed as: |dT/dr|_{ad} < |dT/dr|_{}rad, where the indices ad and rad stand for adiabatic and radiative respectively. This condition can also be expressed as: ∇_{ad}<∇_{rad}, where ∇ = d lnT / d lnP = P dT / T dP with T and P denoting temperature and pressure respectively. More explicitly, in order for convection to occur the adiabatic temperature gradient should be smaller than the actual temperature gradient of the surrounding gas, which is given by the radiative temperature gradient if convection does not occur. Suppose a hotter → convective cell or gas bubble rises accidentally by a small distance in height. It gets into a layer with a lower gas pressure and therefore expands. Without any heat exchange with the surrounding medium it expands and cools adiabatically. If during this rise and → adiabatic expansion the change in temperature is smaller than in the medium the gas bubble remains hotter than the medium. The expansion of the gas bubble, adjusting to the pressure of the medium, happens very fast, with the speed of sound. It is therefore assumed that the pressure in the gas bubble and in the surroundings is the same and therefore the higher temperature gas bubble will have a lower density than the surrounding gas. The → buoyancy force will therefore accelerate it upward. This always occurs if the adiabatic change of temperature during expansion is smaller than the change of temperature with gas pressure in the surroundings. It is assumed that the mean molecular weight is the same in the rising bubble and the medium. See also → Ledoux's criterion; → mixing length. Named after Karl Schwarzschild (1873-1916), German mathematical physicist (1906 Göttinger Nachrichten No 1, 41); → criterion. |