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After playing around with the formula for gravitational time dilation, I have noticed that, as the gravitational potential equals (- c2/2) time "stops". If you go beyond that time becomes imaginary. Of course, using this formula I'm not able to calculate how far "back" in time an outside observer will perceive someone going if they encounter a gravitational potential of this value (the formula wont let me calculate that). However, I know that, in general relativity, the gravitational potential is replaced by the metric tensor. I assume that if I was to implement the metric tensor I would be able to calculate how far "back" in time someone will travel (from the perspective of an outside observer) in the same way that the author of Space-time physics was able to calculate how far back in time an object will travel if it moves faster than light (from the perspective of an outside observer). I have included another copy of that information in the attachment. What metric tensor do I use to perform the coordinate calculations in order to calculate how far "back" in time an object would go (from the perspective of an outside observer)? How do I perform those calculations? Thank you for the help!
Best,
Answer 1:

My simple qualitative recollection is that tensors are sort of like vectors and sort of like matrices; you know that a vector can be expressed as is a one-dimensional matrix, but has a direction, which a two-dimensional matrix does not have. Checking Wikipedia, I see that a tensor is a multidimensional matrix that has a direction: it describes the linear relationships between other things, as well as having multiple dimensions of elements.

As I said, imaginary time is not something that you can travel "backwards" in - an imaginary number is neither positive, nor negative, or zero. It's imaginary.



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