General Relativity Definitions

Question 1

Covariant derivation?

Answer 1

Differentiation that accounts for the changing basis vectors as you move across a Reimannian manifold.

Question 2

Local inertial frame?

Answer 2

A frame that is Minkowskian in the local region. In general relativity we can always transform into this frame.

Question 3

Gravitational Lensing

Answer 3

Light moves along geodesics that curve around massive objects, distorting the image into a ring.

Question 4

Weak equivalence principle?

Answer 4

No experiment can distinguish between free-falling in a gravitational field and uniform motion in free-space.

Question 5

Strong equivalence principle?

Answer 5

No experiment can distinguish between acceleration in free-space and being held in a gravitational field.

Question 6

Gravitational redshift?

Answer 6

From the WEP, the local inertial frame of light aquires motion towards the gravitating body, stretching the wavelength of light as it clmibs out of the gravitational potential.

Question 7

Deflection of light by the sun?

Answer 7

Spacetime curvature causes null geodesics to be bent at twice the angle expected by naive application of the WEP.

Question 8

Perihelion precession?

Answer 8

An elliptical orbit close to a massive object is distorted: the exterior focal point precesses about the interior.

Question 9

Shapiro light delay?

Answer 9

An observer will see light moving along null geodesics in a curved manifold take longer than predicted by the Minkowski metric.

Question 10

Parallel transport?

Answer 10

A vector is transported along a manifold such that its angles with the local basis vectors are preserved.

Question 11

Reimann tensor?

Answer 11

Describes the curvature over smooth manifolds.

Question 12

Line elements for Reimannian surface?

Answer 12

Describes the infintesimal distance bewteen points on a smooth manifold, as a sum of products of basis vectors.

Question 13

Metric tensor?

Answer 13

A rank 2 tensor that describes the changes in basis vectors of a manifold as a function of its coordinates. It is used to derive the line element.

Question 14

Affine geodesic?

Answer 14

A curve which follows the tangent vector to the curve at every point as it’s parallel transported along itself. In torsion-free manifolds this is equal to metric geodesics.

Question 15

Confomally flat metric?

Answer 15

A metric that can be trnasformed into a flat metric via a conformal transformation (a transformation which preserves internal angles).

Question 16

Reimannian manifold?

Answer 16

A smooth manifold described by a metric tensor. The set of all tangent vectors at all points form a vector space.

Question 17

Birkhoff’s theorem.

Answer 17

Any spherically symmetric mass distribution must be static & described by the Schwarzchild metric.

Question 18

Metric geodesic?

Answer 18

A spacetime path which minimises spacetime separation between two points.

Question 19

Event horizon.

Answer 19

Constant acceleration defines spacetime regions where light cannot reach you, and you become causually disconnected from these region.

Question 20

Black holes.

Answer 20

An object (dead star) that has shrunk below it’s Schwarzchild radius, which becomes an event horizon. The region below the horizon is causually disconnected to the rest of the universe.

Question 21

Coordinate transform?

Answer 21

A relation between coordinate systems described by a Jacobian matrix, which details the relations between old & new basis vectors.

Question 22

Torsion.

Answer 22

The spacetime twisting of coordinate systems, not present in classical GR. Its nonclusion allows for affine & metric geodesics to be equated, and for certain symmetries in the curvature tensors.

Question 23

Geodesic deviation?

Answer 23

The divergence/conbpvergence of geodesics through negative/positive curved spacetimes.

Question 24

Isometry?

Answer 24

An isometric tensor is equal in all frames-of-reference. In coordiante transformations it preserves distances (equivalent to how confromal transformations preserves angles).