The virial theorem for retarded gravity

Abstract

Galaxy Clusters are huge physical systems having a generic size of tens of millions of light years. Thus any modification at the center of the cluster will affect the outskirts only tens of millions of years afterwards. Those retardation considerations seem to be neglected in present day analysis used to estimate the total mass of the galaxy cluster, including those estimates which are based on the virial theorem. The significant differences between the velocities predicted by Newtonian action at a distance theory and observations are usually dealt with by either assuming an unobservable type of matter or by modifying gravity. Here we demonstrate that considering general relativistic effects one can explain the apparent excess matter appearing in galaxy clusters virial estimates.

An Uncertainty Relation for Retarded Gravity

“…Here, δ (3) represents a three-dimensional Dirac delta distribution. This particle induces a Newtonian potential given by:…”

“…He calculated [1,2] that the required amount of matter to explain these velocities could be about 400 times greater than that of visible matter, although later adjustments mitigated this discrepancy to some extent. Had Zwicky utilized the concept of retarded gravity in his calculations, this issue might have been resolved without significant complication [3]. In 1959, Volders [4] noted similar discrepancies on a smaller scale within the outer parts of the nearby spiral galaxy M33, where velocities did not follow the expected 1 √ r pattern.…”

Retarded Gravity in Disk Galaxies

“…His calculations showed that the amount of matter required to account for the velocities could be 400 times greater than that of visible matter (this was later mitigated somewhat). In a recent paper we showed that the retarded gravity version of the virial theory [8] may yield better estimates of the mass.…”

Retarded Gravity in Disk Galaxies

“…He calculated that the amount of matter required to account for the velocities could be 400 times greater than that of visible matter (this was later mitigated somewhat). Of course, if Zwicky would have use the retarded gravity version of the virial theory [43] no significant problem would arise. In 1959, on a smaller galactic scale, Volders observed that stars in the outer rims of a nearby spiral galaxy (M33) do not move as they should [26].…”