This integration constant C, on the other hand is directly related with the pressures gradient according to the x axis through the expression:
Also the integration constant D is calculated keeping in mind that the wall interference should be null, and then it remains defined like:
We calculate the integration constant
B from the condition [omega] = [[omega].
Putting the integration constant
C equal to zero we see that the cosmological constant should be negative for the existence of the solution to the field equation.
which is easily checked by substitution into (13), and where b is the integration constant
alpha] is an integration constant
related to the mass,
2] are arbitrary integration constants
, and G(R) and H(R) are homogeneous solutions.
We also use the no-slip boundary conditions on the two plates, namely u(0)=u(L)=0 which are used to solve for the integration constants
2p] are integration constants
, p the separation parameter, and [I.
z] are integration constants
which can be determined from the boundary conditions for [Mathematical Expression Omitted] and [Mathematical Expression Omitted].
The related boundaries specify the discrete values of the integration constants
from field equations .
In this paper, solutions of known linear field equations (electromagnetism and gravitation) with and without sources are compared, in which, integration constants
from source-free equations take the role of sources.