## Einstein's Field Equations in Cosmology Using Harrison's Formula

**Authors:** Ioannis Iraklis Haranas

The most important tool for the study of the gravitational field in Einstein's theory of gravity is his
field equations. In this short paper, we demonstrate the derivation of Einstein field equations for
the Freedman cosmological model using the Robertson-Walker metric, and furthermore Harrison's formula
for the Ricci tensor. The difference is that Harrison's formula is an actually shorter way of obtaining
the field equations. The advantage is that the Cristoffel symbols do not have to be directly calculated
one by one. This can actually be a very useful demonstration for somebody who would like to understand
a slightly different but faster way of deriving the field equations, something that is actually rarely
seen in many of undergraduate and even graduate textbooks.

**Comments:** Published, Galilean Electrodynamics, vol. 18, SPI/3,pp. 49-53, 2007

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### Submission history

[v1] 16 Feb 2010

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