The formula does not depend on the duration of the cycle, or anything having to do with simultaneity.

 

As for temperature, I don't know what you want. Fission is exothermic. Things are going to heat up. It gets a tad warm when a nuke goes off.

From what I see, the "rate" that neutrons are produced plays a role in the equation. In terms of mathematical arguments, I think saying that the gamma factor divides itself out of the equation is the same as saying it was never there. But, thanks for your help so far, I will have to research the equation more before I can make any final decisions.

From what I see, the "rate" that neutrons are produced plays a role in the equation.

 

Nope. There is the number of neutrons produced per fission — not per unit time. There are absorption cross-section ratios that could be written as a ratio of rates, but anything time-dependent cancels out.

That's perfect, there's a time component usable for time dilation effects, but since the rate is both in the numerator and denomitor they cancel out leaving a dimensionless ratio.

 

Would the cross section be initially vefire the final calcilation becaffected by any sort of length contraction? I mean a cross section is only two dimensional, but the material would uniformly decrease in volume which might make the object seem like it his a higher number of nuclie in a given slice.

That's perfect, there's a time component usable for time dilation effects, but since the rate is both in the numerator and denomitor they cancel out leaving a dimensionless ratio.

 

Would the cross section be initially vefire the final calcilation becaffected by any sort of length contraction? I mean a cross section is only two dimensional, but the material would uniformly decrease in volume which might make the object seem like it his a higher number of nuclie in a given slice.

 

Possibly. You'd have to work through it, but it's also possible any effect cancels out with e.g. the increase in neutron flux, leaving you with the same reaction rate.