100

Question 1

What does it mean that General Relativity is a metric theory?

Answer 1

It means the metric tensor fully describes spacetime geometry and determines how objects move and light propagates.

Question 2

What is the role of the metric tensor g_{μν}?

Answer 2

It defines distances and angles in curved spacetime; used to compute intervals and raise/lower indices.

Question 3

What is the geodesic equation used for?

Answer 3

To find the path of free-falling particles or light rays in curved spacetime.

Question 4

What is a null geodesic?

Answer 4

A path followed by massless particles like photons; ds² = 0.

Question 5

What is a timelike geodesic?

Answer 5

A geodesic with ds² < 0, followed by massive particles.

Question 6

What is the Riemann curvature tensor?

Answer 6

It measures the failure of vectors to return to their original direction after parallel transport around a loop.

Question 7

Why does Riemann curvature imply gravity?

Answer 7

Because curvature tells how spacetime bends due to energy-matter content, influencing particle motion.

Question 8

What is Ricci flat spacetime?

Answer 8

A spacetime where Ricci tensor vanishes: R_{μν} = 0; e.g. vacuum solutions like Schwarzschild.

Question 9

What does the Einstein tensor represent?

Answer 9

A combination of curvature that is divergence-free and matches the energy-momentum content via Einstein’s equation.

Question 10

What is the stress-energy tensor?

Answer 10

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 11

Planck constant h-bar in natural units?

Answer 11

ħ = 1

Question 12

What is the reduced Planck mass M_P?

Answer 12

M_P = 1/√(8πG) in natural units.

Question 13

Speed of light in GR units?

Answer 13

c = 1

Question 14

What is the value of 1 parsec in meters?

Answer 14

1 pc ≈ 3.086 × 10^16 m

Question 15

What is the Hubble constant H_0?

Answer 15

Current expansion rate of the universe, e.g. ~70 km/s/Mpc

Question 16

What is the full Einstein Field Equation?

Answer 16

G_{μν} + Λg_{μν} = 8πGT_{μν}

Question 17

Expression for Schwarzschild radius?

Answer 17

r_s = 2GM

Question 18

Conservation law from Bianchi identity?

Answer 18

∇^μ T_{μν} = 0

Question 19

FLRW metric with spatial curvature?

Answer 19

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 20

Ricci scalar R for FRW universe?

Answer 20

R = 6[(ä/a) + (ȧ² + k)/a²]

Question 21

How to check if a vector is a Killing vector?

Answer 21

Check if Lie derivative of metric vanishes along that vector: ℒ_ξ g_{μν} = 0

Question 22

Shortcut for computing Christoffel symbols?

Answer 22

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 23

How to find conserved quantities in a metric?

Answer 23

Use time and angular symmetries: conserved E and L from Killing vectors.

Question 24

How to identify coordinate singularity?

Answer 24

If a metric component diverges but curvature scalars remain finite.

Question 25

How to determine if a path is geodesic?

Answer 25

Plug into geodesic equation or check if extremizes the proper time.

Question 26

What's the signature of the metric in GR?

Answer 26

Mostly plus: (-,+,+,+)

Question 27

Condition for inflation to occur?

Answer 27

ä > 0; accelerated expansion.

Question 28

What defines conformal time η?

Answer 28

dη = dt / a(t)

Question 29

In Schwarzschild, what happens at r = 2GM?

Answer 29

An event horizon; light cannot escape.

Question 30

What causes the perihelion shift of Mercury?

Answer 30

Curvature corrections from Schwarzschild geometry.

Question 31

Why does light bend in GR?

Answer 31

Because spacetime is curved and light follows null geodesics.

Question 32

What are the junction conditions in GR?

Answer 32

Conditions to match two spacetime regions across a boundary.

Question 33

What is the weak field limit of GR?

Answer 33

It approximates to Newtonian gravity: g_{00} ≈ -(1 + 2Φ)

Question 34

How to identify coordinate singularity?

Answer 34

If a metric component diverges but curvature scalars remain finite.

Question 35

What is the stress-energy tensor?

Answer 35

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 36

How to identify coordinate singularity?

Answer 36

If a metric component diverges but curvature scalars remain finite.

Question 37

FLRW metric with spatial curvature?

Answer 37

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 38

What is the stress-energy tensor?

Answer 38

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 39

Speed of light in GR units?

Answer 39

c = 1

Question 40

What is the full Einstein Field Equation?

Answer 40

G_{μν} + Λg_{μν} = 8πGT_{μν}

Question 41

Planck constant h-bar in natural units?

Answer 41

ħ = 1

Question 42

FLRW metric with spatial curvature?

Answer 42

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 43

FLRW metric with spatial curvature?

Answer 43

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 44

Speed of light in GR units?

Answer 44

c = 1

Question 45

FLRW metric with spatial curvature?

Answer 45

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 46

Planck constant h-bar in natural units?

Answer 46

ħ = 1

Question 47

Shortcut for computing Christoffel symbols?

Answer 47

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 48

What is the stress-energy tensor?

Answer 48

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 49

In Schwarzschild, what happens at r = 2GM?

Answer 49

An event horizon; light cannot escape.

Question 50

FLRW metric with spatial curvature?

Answer 50

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 51

Shortcut for computing Christoffel symbols?

Answer 51

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 52

Shortcut for computing Christoffel symbols?

Answer 52

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 53

Speed of light in GR units?

Answer 53

c = 1

Question 54

Shortcut for computing Christoffel symbols?

Answer 54

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 55

Condition for inflation to occur?

Answer 55

ä > 0; accelerated expansion.

Question 56

What's the signature of the metric in GR?

Answer 56

Mostly plus: (-,+,+,+)

Question 57

Condition for inflation to occur?

Answer 57

ä > 0; accelerated expansion.

Question 58

What causes the perihelion shift of Mercury?

Answer 58

Curvature corrections from Schwarzschild geometry.

Question 59

What is the stress-energy tensor?

Answer 59

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 60

Condition for inflation to occur?

Answer 60

ä > 0; accelerated expansion.

Question 61

What is the reduced Planck mass M_P?

Answer 61

M_P = 1/√(8πG) in natural units.

Question 62

In Schwarzschild, what happens at r = 2GM?

Answer 62

An event horizon; light cannot escape.

Question 63

In Schwarzschild, what happens at r = 2GM?

Answer 63

An event horizon; light cannot escape.

Question 64

Planck constant h-bar in natural units?

Answer 64

ħ = 1

Question 65

What is the stress-energy tensor?

Answer 65

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 66

What is a timelike geodesic?

Answer 66

A geodesic with ds² < 0, followed by massive particles.

Question 67

What is the reduced Planck mass M_P?

Answer 67

M_P = 1/√(8πG) in natural units.

Question 68

What's the signature of the metric in GR?

Answer 68

Mostly plus: (-,+,+,+)

Question 69

What is the role of the metric tensor g_{μν}?

Answer 69

It defines distances and angles in curved spacetime; used to compute intervals and raise/lower indices.

Question 70

Expression for Schwarzschild radius?

Answer 70

r_s = 2GM

Question 71

Planck constant h-bar in natural units?

Answer 71

ħ = 1

Question 72

Why does light bend in GR?

Answer 72

Because spacetime is curved and light follows null geodesics.

Question 73

What is the stress-energy tensor?

Answer 73

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 74

What is the stress-energy tensor?

Answer 74

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 75

Why does light bend in GR?

Answer 75

Because spacetime is curved and light follows null geodesics.

Question 76

What is the stress-energy tensor?

Answer 76

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 77

FLRW metric with spatial curvature?

Answer 77

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 78

What causes the perihelion shift of Mercury?

Answer 78

Curvature corrections from Schwarzschild geometry.

Question 79

What is the stress-energy tensor?

Answer 79

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 80

How to identify coordinate singularity?

Answer 80

If a metric component diverges but curvature scalars remain finite.

Question 81

FLRW metric with spatial curvature?

Answer 81

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 82

What is the stress-energy tensor?

Answer 82

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 83

Condition for inflation to occur?

Answer 83

ä > 0; accelerated expansion.

Question 84

Why does light bend in GR?

Answer 84

Because spacetime is curved and light follows null geodesics.

Question 85

FLRW metric with spatial curvature?

Answer 85

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 86

What is the stress-energy tensor?

Answer 86

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 87

What is the reduced Planck mass M_P?

Answer 87

M_P = 1/√(8πG) in natural units.

Question 88

FLRW metric with spatial curvature?

Answer 88

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 89

What is the reduced Planck mass M_P?

Answer 89

M_P = 1/√(8πG) in natural units.

Question 90

What are the junction conditions in GR?

Answer 90

Conditions to match two spacetime regions across a boundary.

Question 91

Shortcut for computing Christoffel symbols?

Answer 91

Use symmetry and non-zero metric components; look at diagonal terms first.

Question 92

FLRW metric with spatial curvature?

Answer 92

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 93

What is the reduced Planck mass M_P?

Answer 93

M_P = 1/√(8πG) in natural units.

Question 94

Planck constant h-bar in natural units?

Answer 94

ħ = 1

Question 95

What is the stress-energy tensor?

Answer 95

It encodes energy, momentum, pressure, and stresses in a fluid or field.

Question 96

What are the junction conditions in GR?

Answer 96

Conditions to match two spacetime regions across a boundary.

Question 97

What is the reduced Planck mass M_P?

Answer 97

M_P = 1/√(8πG) in natural units.

Question 98

What is the full Einstein Field Equation?

Answer 98

G_{μν} + Λg_{μν} = 8πGT_{μν}

Question 99

FLRW metric with spatial curvature?

Answer 99

ds² = -dt² + a²(t)[dr²/(1-kr²) + r²dΩ²]

Question 100

What is the stress-energy tensor?

Answer 100

It encodes energy, momentum, pressure, and stresses in a fluid or field.