General Relativity

Question 1

What is the Bianchi identity, and what tips are there for contracting it?

Answer 1

Question 2

How does the Jacobian transform coordinates?

Answer 2

Question 3

What are the Euler-Lagrange equations, and first integrals?

Answer 3

Question 4

What is Schur’s theorem?

Answer 4

Question 5

How do we define a Local Intertial Frame?

Answer 5

Question 6

How do we define the Ricci identity : the Reimann tensor derivation using covariant derivatives?

Answer 6

Question 7

What is the geodesic equation, and how is it derived?

Answer 7

Question 8

What is the covariant derivative, and how does it act on a (1,1) tensor?

Answer 8

Question 9

What are the equations (Doppler & gravitational) for redshift?

Answer 9

Question 10

What is the Schwarzchild solution, and what are the massless limits?

Answer 10

Question 11

What is the light deflection around a massive body?

Answer 11

Question 12

What is the angle for perihelion precession?

Answer 12

Question 13

What is Birkhoff’s theorem?

Answer 13

Any spherically symmetric mass distribution must create the same exterior static vaccum-solution: the Schwarzchild solution.

Question 14

What are the equations for Shapiro light delay?

Answer 14

Question 15

What are the tortoise & Eddington-Finkelstein coordinates for redefining the Schwarzchild metric for black holes?

Answer 15

Question 16

What is an useful equivalent of the Freidmann equation (in density parameters), the fluid equation and the deceleration parameter?

Answer 16

Question 17

What are the equations of states used in cosmology?

Answer 17

Question 18

What is the stress-energy tensor, specifically for dust and perfect fluids?

Answer 18

Question 19

What are the diagrams that convey the equivalence principles?

Answer 19

Question 20

What is the spacetime map of Rindler space, and what regions can the accelerating object effect/be effected by.

Answer 20

Question 21

What is the diagram describing motion in the Schwarzchild metric?

Answer 21

Question 22

What diagram describes the deflection of light around a star?

Answer 22

Question 23

What diagram conveys Shapiro light delay as a pulsar orbits its companion star?

Answer 23

Question 24

What diagram shows incoming/outgoing light rays in the Schwarzchild metric?

Answer 24

Question 25

What are the Eddington-Finkelstein diagrams for incoming & outgoing light?

Answer 25

Question 26

What is the diagram presenting Kruskal-Szekeres coordinates?

Answer 26

Question 27

What diagram, depending on the mass & vacuum energy parameters, details the universe's possible pasts & futures?

Answer 27

Question 28

What is the general method for solving the universe's age using density & scale factors?

Answer 28

Question 29

How do you derive the equation for cosmological redshit?

Answer 29

Question 30

What was Einstein's main philosophy for deriving general relativity?

Answer 30

General covariance : the laws of nature should be independent of coordinates chosen.

Question 31

What is a tangent vector defined as, and how does it relate to the absolute derivative of a contravariant vector?

Answer 31

Question 32

How is torsion defined?

Answer 32

Question 33

How do we define affine & metric geodesics mathematically?

Answer 33