From eqs.(2.18) and (2.20) we see that if we want a static solution of Einstein's equations, that is, one in which R =0, we must have p + 3p =0, which is somewhat unphysical, because, if p > 0 then p < 0, and if p - 0 then p =0. Therefore Einstein modified his equations by adding the so-called 'cosmological term' to the field equations, as followsRμv - Rgμv-Λgμv =8πGTμv , (4.1)where A is the cosmological constant. Hence eqs.(2.14-16) in (4.1) give(R)2/R~2+ k/R~2=8πG/3ρ+ Λ/3, (4-2)and(R)/R=-4πG/3(ρ+3p)+Λ/3 (4.3)
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