Effect of surfaces on the static distribution of orientations in suspensions of rod-like particles

2003 ◽  
Vol 47 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Raffy Mor ◽  
Moshe Gottlieb ◽  
Lisa A. Mondy ◽  
Alan L. Graham
Keyword(s):  
Static Distribution

scholarly journals Some solutions of Einstein's gravitational equations for systems with axial symmetry

1930 ◽  
Vol 126 (803) ◽  
pp. 592-602 ◽  
Keyword(s):  
Angular Velocity ◽  
Axial Symmetry ◽  
Second Order ◽  
Newtonian Potential ◽  
Static Distribution ◽  
Gravitational Equations

§1. In this paper we find solutions of Einstein’s gravitational equations G μν = 0 which give the field due to any static distribution of matter sym­metrical about an axis; in the later part of the paper an angular velocity about the axis is introduced. We take the ground form ds 2 = - e λ ( dx 2 + dr 2 ) - e -ρ r 2 d θ 2 + e ρ dt 2 , (1) where λ, ρ are functions of x and r . Further we take ρ to be the Newtonian potential of an auxiliary distribution of matter of density σ ( x, r ), the potential being calculated as though our co-ordinates were Euclidean. We find that it is then possible to determine λ, so that the equations G μν = 0 are exactly satisfied everywhere outside the auxiliary body. λ is nearly equal to —ρ, the quantity μ = λ + ρ being of the second order in terms of σ.

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