can you quantify the size of the negative pressure effect for a sphere of radius R and excess charge Q and speed of light S in a superconducting state in terms of how much mass it would offset (negative mass if you will)? Never mind the energy and rest mass contributions of the sphere, just the negative pressure effect is of interest.

Here is a plot of the E field vs radial distance from the center of a charged conducting sphere. I used the FEMM Finite Element Method numerical simulation software, I specified, as required by Gauss's law, that the field in the interior is zero; and all excess charge is on the surface.It is charged with 10,000V, with sphere radius R = 0.2821 m. This gives a surface area of 1 m² (simplifying a possible later determination of tension, F/A, where A will cancel to 1):

https://i.imgur.com/jhq1nSW.png

Here is the electric field with the charged white sphere at the center:

https://i.imgur.com/A1ERR06.png

The electric field, shown in previous replies, extending out into the air from the surface is:

https://i.imgur.com/s12scfB.png

E = 1/4πε0(Q/r²⁾

We are talking about the tension in an electrons in contact with the metal lattice at the surface. These electrons all around the sphere are creating an net electric field that's acting on a particular electron on the surface. This electric field E is perpendicular, normal, to the surface. And electrostatics analysis proves that this E field acts as if the entire charge Q on the whole surface was located as if it was coming from a point charge at the center of the sphere. So a particular electron on the surface is acted on by the electric field E, as if it was created by a point charge with charge Q at the center. So the electron experiences the electric field

E = 1/4πε(Q/R^2), where R is the radius of the sphere, and Q is the total charge on the sphere surface

When this E field is passing through the electron on the surface, it is not passing thru the air yet. So the electric permittivity is not ε0 - which is the permittivity of free space (typically also used as the permittivity of air). Conductive metals have a permittivity ε ~~= 1. So the equation of the E field passing thru the surface electrons should be

E = 1/4πε(Q/R²⁾ = 1/4π(Q/R²⁾ {Equation 1}

Here are sceeenshots from my paper showing the derivation that leads to the

{negative pressure, tension, term}

in the General Relativity Poisson equation

that creates a negativve gravitational field.

At the end of the derivation you will see that this negative pressure term contains E, the electric field caused by the charged sphere. So Equation 1above that defines E can be plugged into the negative pressure term at the end of the derivation:

1.) https://i.imgur.com/SQXdiFw.png

2.) https://i.imgur.com/H4PgJJM.png

3.) https://i.imgur.com/waqZng9.png

4.) https://i.imgur.com/RLfEUtB.png

So the total Force from negative pressure, tension, causing negative gravity is Force density -GE² x sphere Area

= (-GE^2)4πR2

From Equation 1,

E = 1/4π(Q/R²⁾

So the total Force from negative pressure, tension, causing negative gravity is

(-GE²⁾ x 4πR²

= {-G[1/4π(Q/R^2)]2} x 4πR²

= {-G[1/16π^2(Q2/R4)]} x 4πR²

= -GQ^2/(16π2R4) x 4πR²

= -GQ^2/(4πR2

(Hope i didnt make any mistakes in the above 4 equations: I didn't write them on paper - just typed them here on Reddit - very confusing).

In another reply later, I will deal with the effect of the slowed speed of light within this surface electron medium at temperatures that form a BEC.