Einstein's radius is the radius of curvature of stationary (or less properly called "static") Einstein's universe model that was proposed by Einstein in 1917 and later given up after consensus of astronomers assumed that the universe is expanding. In 1985 it turned out that expansion is only a relativistic illusion produced by coupling of time with space but relativists didn't accept that and started to suppress notion of illusion by not allowing publications of papers explaining this illusion . Relativists insisted that it is not an illusion but a real expansion. Though no scientific theory of expansion could be constructed as it contradicted the conservation laws (conservation of energy and conservation of momentum separately) so the hypothesis of expansion became a true cargo cult science as described by Richard Feynman in his rant against relativists.
The illusion of expansion is explained in Gravitation demystified and so Einstein's radius would be about 13 billion light years. The number coming from division of speed of light by Hubble constant that represent the intrinsic redshift in the universe that is result of Newtonian calculation of dynamical friction of photons in a stationary Einstein's universe . The exact value of Einstein's radius predicted theoretically as value at which the Einstein's field equation is stable or derived from intrinsic redshift of photons, is
where is speed of light in vacuum, is Newtonian gravitational constant, and is the density of space of universe.
- See Essay:Hubble redshift in Einstein's universe and also Einstein's paper dropped from the bibloigraphy of Einstein's papers in 1973 "Gravitation" in which Einstein advocated non symmetric metric tensor of spacetime while the Big Bang relativists assume symmetric metric in that book.
- See the step-by-step derivation of intrinsic redshift and Hubble constant in Gravitation demystified that an intelligent high school student may follow.