"സാമാന്യ ആപേക്ഷികതാസിദ്ധാന്തം" എന്ന താളിന്റെ പതിപ്പുകൾ തമ്മിലുള്ള വ്യത്യാസം

▲:<math>\quad R_{ab}={R^d}_{adb}.\,</math>.<ref>{{Harvnb|Ehlers|1973|pp=19–22}}; for similar derivations, see sections 1 and 2 of ch. 7 in {{Harvnb|Weinberg|1972}}. The Einstein tensor is the only divergence-free tensor that is a function of the metric coefficients, their first and second derivatives at most, and allows the spacetime of special relativity as a solution in the absence of sources of gravity, cf. {{Harvnb|Lovelock|1972}}. The tensors on both side are of second rank, that is, they can each be thought of as 4×4 matrices, each of which contains ten independent terms; hence, the above represents ten coupled equations. The fact that, as a consequence of geometric relations known as [[Bianchi identities]], the Einstein tensor satisfies a further four identities reduces these to six independent equations, e.g. {{Harvnb|Schutz|1985|loc=sec. 8.3}}</ref>