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.
In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid. In astrophysics, fluid solutions are often employed as stellar models, since a
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid that has positive mass density but vanishing pressure.
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 ...
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.
The equations of motion are contained in the continuity equation of the stress–energy tensor: =, where is the covariant derivative. [5] For a perfect fluid, = (+) +. Here is the total mass-energy density (including both rest mass and internal energy density) of the fluid, is the fluid pressure, is the four-velocity of the fluid, and is the metric tensor. [2]
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.
In this article, we will focus on the construction of exact ssspf solutions in our current Gold Standard theory of gravitation, the theory of general relativity. To anticipate, the figure at right depicts (by means of an embedding diagram) the spatial geometry of a simple example of a stellar model in general relativity.