PRIDE CHEKERAaspect also below in that section of general relativity.
Besides the Kronecker delta and metric tensor, other
mathematical objects such as the Christoffel symbol, 훤μ푣훼 , Ricci
curvature tensor, 푅휇푣, and stress-energy tensor, 푇휇푣 have been
parts of that engine which drives Einstein’s Field Equations. It’s
a great story of how Einstein reached this destiny, a story which
physics historians narrate in an elegant way vividly showing the
creativeness and intellectual superiority of Einstein. But that
story doesn’t begin with Einstein, there are some people before
who had set their feet on its shores.
Why l introduced you to this mathematical framework? My goal
here, is to conspicuously reveal to the reader the transition from
Euclidean geometry in a flat space to curved, dynamic,
manifolds in which space-time is not what we perceive it, but
it’s totally beyond imagination. Thus from what l had discussed
above we can deduce three spatial topologies as below, with
different geometries. Curved space can be regarded as positively
or negatively curved depending on the nature of its topology:
(1) In a positively curved space, which curve onto itself, space
takes topology of a 3-sphere, parallel lines converge and sum of
angles of a triangle is greater than 180°. Earth has a spherical
shape thus it is positively curved onto itself.
(2) In a negatively curved space, space has a saddle topology,
here parallel lines diverge and sum of angles of a triangle is less