Index

basis, orthonormal

Bianchi identities

Bianchi identities, contracted

Christoffel symbols

Christoffel symbols, symmetry of

Christoffel symbols, from the metric

Christoffel symbols, in polar coordinates

comma goes to semicolon rule

covariant derivative, of a one- form

covariant derivative

covariant derivative, commutator of

covariant derivative, of a vector

curvature

curvature, extrinsic

curvature, intrinsic

curvature, of a cylinder

curvature, of a sphere or balloon

Einstein tensor, definition of

equivalence principle

equivalence principle

Euclidian space ,

Euler- Lagrange equations

geodesic

geodesic, as equation of motion for a free particle

geodesic, calculating for a given metric

geodesic, definition of

geodesic, extremal length of

geodesic deviation

geodesic deviation, equation of

geodesic equation

geodesics

inertial frame, local

Lagrangian, for timelike curves

local flatness theorem

manifold

manifold, differentiable

manifold, dimension of

manifold, Riemannian

metric, as a mapping

metric, as gravitational potentials

metric, connection

metric, signature of

Newtonian gravity

one- form

one- form, basis in polar coordinates

parallel transport

parallel transport, around a loop, in flat space

parallel transport, definition of

parallel transport, around a loop, in curved space

polar coordinates, tensors in

polar coordinates, vector gradient in

proper time, for curved spacetime

proper time, for flat spacetime

Pseudo- Riemannian

Ricci scalar, definition of

Ricci tensor, definition of

Riemann tensor, definition of

Riemann tensor, in a local inertial frame

Riemann tensor, number of independent components of

Riemann tensor, symmetries of

Special Relativity

tensor

tensor, curvature

transformation, of Christoffel Symbols

vector

vector, basis in polar coordinates

worldlines