PRIDE CHEKERASchwarzchild metric:
A solution derived from EFE, basing on the symmetry of
Einstein’s equations, that traversing back in time, reversing the
direction of the time arrow, a consistent theory is expounded
which predicts the existence of black holes;
(r; θ; φ; t) (r; θ; φ; -t)
This is an invariant transformation in a 4D space-time which
implies that 휕푡휕 푔휇푣 = 0, (since μ= v)
In simplified terms, Schwarzchild metric is expressed as
follows:
푑푠^2 = 푔 11 푑푟^2 + 푔 22 푑휃^2 + 푔 33 푑휙^2 + 푔 44 푑푡^2
푑푠^2 = (1- (^2) 푟퐺푀푐 2 )푑푟^2 + 푟^2 (푑휃^2 + 푠푖푛^2 θ푑휙^2 ) - 푐^2 (1- (^2) 푟퐺푀푐 2 )푑푡^2
But:^2 푐퐺푀 2 = 푟푠 (Schwarzchild radius).
푑푠^2 = (1- 푟푟푠)푑푟^2 + 푟^2 (푑휃^2 + 푠푖푛^2 θ푑휙^2 ) - 푐^2 (1- 푟푟푠)푑푡^2
When r approaches 푟푠, the metric becomes singular approaching
the event horizon defined by:
푑푠^2 = 푟^2 (푑휃^2 + 푠푖푛^2 θ푑휙^2 )