Relativity and Cosmology

    

Examining Toroidal Geometry in Terms of a 3-Dimensional "Tokamak", and the Use of a Toroidal Universe

Authors: Andrew Beckwith

We begin with a review of Friedman geometry in order to get a relationship between vacuum energy density and Hubble expansion parameter, Furthermore, in line with Utpal Sarkar, we can write the Hubble parameter as proportional to the square of background temperature, which is important in our derivational work. Furthermore, in line with work presented by Guth and Vilikin we can obtain g_00 = 1 for a time component in the Toroidal universe by setting a three dimensional line element as embedded in the square of a scale factor a (t) at times the "line element" given by R. Murdzek (which has a 3 dimensional presentation of a Ricci scale factor ). Incorporating the Guth and Vilikin "line element" trick, for a Toroidal universe allows 9_00 =1 for obtaining a non-zero stress energy tensor we can write as T_00 as a non-zero value even if the Ricci component R_00 in our construction is zero.

Comments: 13 Pages. Accepted for publication in JHEPGC

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[v1] 2026-03-07 22:15:12

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