# Questions tagged [differential-geometry]

Mathematical discipline which uses the techniques of calculus to study geometric problems. General relativity is written in this language.

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### Is gauge covariant derivative an ordinary covariant derivative?

The formal treatment of the gauge covariant derivative in most reference texts for students is too informal and too ad hoc, so that some general issues remain unclear. For example, the gauge covariant ...
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### What is the Lie derivative of the field describing the change of mass?

I'm trying to understand Ch. 3.2 of the paper On Bubble Rings and Ink Chandeliers by Padilla et al.. I'm trying to understand the derivation of equation (15). Right now I'm stuck at the point where ...
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### Divergence of tensor fields

I have found numerous definitions for the divergence of a tensor which makes me confused as to trust which one to use. In Itskov's Tensor Algebra and Tensor Analysis for Engineers, he begins with ...
• 51
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### Extrinsic Trace and Time Reversal Symmetry

For states with time-reversal symmetry, will the extrinsic trace of the time-like Killing vector be zero? The context of the question comes from the Ryu-Takayanagi formula. On a constant time slice, a ...
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### Twin paradox with black hole (based on Interstellar) [closed]

I'm an Undergrad student working on a summer project. I'm learning about Differential Geometry, Schwarzschild's Solution, General and Special Relativity. I want to include the twin paradox as well. In ...
1 vote
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