Search results
Results from the WOW.Com Content Network
Perfect fluids are used in general relativity to model idealized distributions of matter, such as the interior of a star or an isotropic universe. In the latter case, the equation of state of the perfect fluid may be used in Friedmann–Lemaître–Robertson–Walker equations to describe the evolution of the universe.
A radiation fluid is a perfect fluid with =: = (+). The last two are often used as cosmological models for (respectively) matter-dominated and radiation-dominated epochs. Notice that while in general it requires ten functions to specify a fluid, a perfect fluid requires only two, and dusts and radiation fluids each require only one function.
[4] [5] The form of the equation given here was derived by J. Robert Oppenheimer and George Volkoff in their 1939 paper, "On Massive Neutron Cores". [1] In this paper, the equation of state for a degenerate Fermi gas of neutrons was used to calculate an upper limit of ~0.7 solar masses for the gravitational mass of a neutron star .
Fluid solutions: must arise entirely from the stress–energy tensor of a fluid (often taken to be a perfect fluid); the only source for the gravitational field is the energy, momentum, and stress (pressure and shear stress) of the matter comprising the fluid.
A scalar field can be viewed as a sort of perfect fluid with equation of state = ˙ ˙ + (), where ˙ is the time-derivative of and () is the potential energy. A free ( V = 0 {\displaystyle V=0} ) scalar field has w = 1 {\displaystyle w=1} , and one with vanishing kinetic energy is equivalent to a cosmological constant: w = − 1 {\displaystyle ...
The stress–energy tensor of a relativistic pressureless fluid can be written in the simple form T μ ν = ρ 0 U μ U ν . {\displaystyle T^{\mu \nu }=\rho _{0}U^{\mu }U^{\nu }.} Here, the world lines of the dust particles are the integral curves of the four-velocity U μ {\displaystyle U^{\mu }} and the matter density in dust's rest frame is ...
Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. From FLRW metric we compute Christoffel symbols, then the Ricci tensor. With the stress–energy tensor for a perfect fluid, we substitute them into Einstein's field equations and the resulting equations are described below.
For a perfect fluid in thermodynamic equilibrium, the stress–energy tensor takes on a particularly simple form = (+) + where is the mass–energy density (kilograms per cubic meter), is the hydrostatic pressure , is the fluid's four-velocity, and is the matrix inverse of the metric tensor.