Covariant Derivatives in Curved Spacetime
Covariant derivative = Normal derivative
derivative of the metric.
The connection or Christoffel symbol ()
handles the derivatives of the metric.
";" the semicolon convention for covariant derivatives.
- Derivative = normal - change in metric.
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Covariant derivative of a contravariant vector.
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Independent of the metric because
.
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Depends on metric.
Omission: The details of the Christoffel symbol are not discussed here.
Slide 25 hopes for a cure.