“An IITian View Regarding The Signature Of Spacetime and Structure Of Signature Of Spacetime “(ref:Relativity:The General Theory by J.L. SYNGE;p2)
gopalan sudhakaran
PROFESSOR OF PHYSICS at I AM DOING RESEARCH ON MY OWN WAY AT "CHETHANA,H&C ROAD, WEST MUNDAKKAL,KOLLAM, INDIA,PIN-691001
Honourable Friends,
An infinitemal vector dx(i) at a point x(i) has a Norm ds given by Square of ds
ds.ds=gij dx(i)dx(j) which is greater than Zero/less than Zero/Equals to Zero.
When ds.ds is greater than zero,let us call dx(i)is Time Like.
When ds.ds is equals Zero,we call dx(i) in Null Like
When ds..ds is less than zero,we call dx(i) Space Like
And we define two structures Signature diag(+1,—1,—1,—1) and. diag(—1,+1,—1,—1).In the structure of signature diag(—1,+1,—1 ,—1) Space and time INTERCHANGE their rolls.Here time becomes Space and Space becomes Time.We see that definition of Structure of Signature is a Must. When consider Schwarzschild blak hole,with in the event horizon structure of signature (—1,+1;—1,—1):here Space becomes Time,and Time becomes Space. i.e g00=—1,gxx=+1.gyy=—1 and gzz=—1.
[Critical Comments]
As I am not professional in computer typing,kindly forgive me.
gij is second rank covariant metric tensor of spacetime.
dx(i) is contravariant vector separation between events x(i) and x(i)+dx(i).
Love &Regards
Professor Sudhakaran Gopalan