2 00 2 Criteria for ( in ) finite extent of static perfect fluids
نویسنده
چکیده
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely related to ones which are known to ensure finite or infinite extent of the fluid region if the assumption of spherical symmetry is replaced by certain asymptotic falloff conditions on the solutions. We improve this result by relaxing the asymptotic assumptions. Our conditions on the equation of state are also related to (but less restrictive than) ones under which it has been shown in Relativity that static, asymptotically flat fluid solutions are spherically symmetric. We present all these results in a unified way.
منابع مشابه
Static perfect fluids with Pant-Sah equations of state
We analyze the 3-paramter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein’s equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and ”rediscovered” by Rosquist and by the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically real...
متن کاملar X iv : g r - qc / 0 40 30 12 v 1 2 M ar 2 00 4 Static fluid cylinders and their fields : global solutions
The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of state of the fluid. In the case of a fluid admitting a non-vanishing density for zero pressure, it is shown that the cylinder's radius has to be finite. For i...
متن کاملEffect of Through Stationary Edge and Center Cracks on Static Buckling Strength of Thin Plates under Uniform Axial Compression
Thin plate structures are more widely used in many engineering applications as one of the structural members. Generally, buckling strength of thin shell structures is the ultimate load carrying capacity of these structures. The presence of cracks in a thin shell structure can considerably affect its load carrying capacity. Hence, in this work, static buckling strength of a thin square plate wit...
متن کامل2 00 5 On the simple normality to base 2 of √ s , for s not a perfect square
On the simple normality to base 2 of √ s, for s not a perfect square Abstract Since E. Borel proved in 1909 that almost all real numbers with respect to Lebesgue measure are normal to all bases, an open problem has been whether simple irrational numbers like √ 2 are normal to any base. This paper shows that each number of the form √ s for s not a perfect square is simply normal to the base 2. T...
متن کاملar X iv : h ep - p h / 04 07 10 1 v 1 8 J ul 2 00 4 Perfect Fluid Theory and its Extensions
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserv...
متن کامل