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When Gravity Fails

When Gravity Fails

Einstein's General Theory of Relativity is now over 100 years old and still remains our best description of gravity.

But the elegant Tensor form of Einstein's Field Equations (EFE) masks a critical property - they are basically differential equations of derivatives with respect to spacetime i.e. with respect to the x,y,z and t coordinates.

But, as any mathematician will tell you, derivatives are only valid for "very smooth" functions. Meaning if spacetime becomes "granular" EFE will not apply - for the simple reason that the derivatives are no longer defined.

At some point this granularity of spacetime will become apparent - the center of a rotating black hole could be an example.

So, it's not that you can't solve the EFE in this situation - it's that you can't even write them down!

Content written and posted by Ken Abbott