Recent content by maica

I think that I understood. If we consider the equation gikgkj = δij and if gkj = ηkj + κ hkj then gik is the inverse and its expansion is gik = ηik - κ hik + κ2 hil hlk - ... identical to the expression (I + H)-1.

I'm a little lost. The expression (I+H)-1 = I - H + HH - ... is the Taylor series in powers of "H", but gij = ηij + κhij + (1/2)κ2hilhlj, is a series in powers of "κ", and doesn't have the expoent "-1", which is responsible for the absence of the factor 1/2 in the Taylor series of "H". I can't...

but this expansion is not an expansion matrix. these objects are components, numbers

The second order term in k is HacHcb and not Haccb

Why Yab=Xab-kHab+k2HacHcb-... and not Yab=Xab-kHab+(1/2)k2Haccb-...? Y is the curved space-time metric X is the planespace-time metric