Einstein's Field Equations: Master Gravity's Secrets

Question 1

In General Relativity, which equation mathematically describes the relationship between spacetime curvature and the distribution of energy and momentum?

Accepted Answer

Einstein's Field Equations

Answer

Newton's Law of Universal Gravitation

Answer

Maxwell's Equations of Electromagnetism

Answer

Schrödinger's Equation

Question 2

Which metric characterizes the spacetime geometry around a spherically symmetric, non-rotating body?

Accepted Answer

Schwarzschild metric

Answer

Minkowski metric

Answer

Friedmann-Lemaître-Robertson-Walker metric

Answer

Kerr metric

Question 3

Which of the following is NOT a solution to Einstein's Field Equations?

Accepted Answer

Lorentz metric

Answer

Schwarzschild metric

Answer

Kerr metric

Answer

Friedmann-Lemaître-Robertson-Walker metric

Question 4

Key Concept in Einstein's Field Equations

Which concept is pivotal in understanding Einstein's Field Equations?

Accepted Answer

Spacetime curvature

Answer

Classical Newtonian gravity

Answer

Electromagnetic fields

Answer

Thermodynamic laws

Question 5

Stress-Energy Tensor's Role

What is the crucial physical significance of the stress-energy tensor?

Accepted Answer

It describes the mass-energy distribution in spacetime

Answer

It dictates object motion in a gravitational field

Answer

It determines spacetime curvature

Answer

It models energy exchange between fields

Question 6

Schwarzschild Metric Exception

Which astronomical object is NOT a valid solution to the Schwarzschild metric?

Accepted Answer

Rotating Planet

Answer

Black Hole

Answer

Neutron Star

Answer

Gravitational Lens

Question 7

'Curvature' in General Relativity

What is the essence of 'curvature' in Einstein's theory?

Accepted Answer

Spacetime bending induced by mass and energy

Answer

Trajectory determination for light and objects in spacetime

Answer

Time dilation explanation

Answer

Scalar quantification of bending amount

Question 8

Principle of Equivalence

Define the Principle of Equivalence in General Relativity:

Accepted Answer

Identical physical laws for all observers in free-fall frames

Answer

Mass proportionality to energy

Answer

Flat and Euclidean spacetime

Answer

Instantaneous gravitational action

Question 9

Einstein-Stress-Energy Tensor Relationship

How are the Einstein tensor and stress-energy tensor related?

Accepted Answer

Einstein tensor is proportional to stress-energy tensor

Answer

Einstein tensor equals stress-energy tensor

Answer

Stress-energy tensor is proportional to Einstein tensor

Answer

No direct relationship exists

Question 10

Which tensor in General Relativity describes the distribution of mass, energy, momentum, and stress in spacetime?

Accepted Answer

Stress-energy tensor

Answer

Riemann curvature tensor

Answer

Weyl curvature tensor

Answer

Killing tensor

Question 11

What is the significance of the Schwarzschild metric in the context of black hole physics?

Accepted Answer

It describes the curvature of spacetime around a spherically symmetric, non-rotating black hole.

Answer

It predicts the existence of gravitational waves.

Answer

It is used to calculate the bending of light around massive objects.

Answer

It determines the precession of the perihelion of Mercury.

Question 12

What is the core idea expressed by Einstein's Field Equations in General Relativity?

Accepted Answer

The curvature of spacetime is directly proportional to the distribution of matter and energy.

Answer

The gravitational force between two masses is inversely proportional to the square of the distance between them.

Answer

The speed of light is constant in all inertial frames of reference.

Answer

Energy and mass are interchangeable and related by the equation E=mc².

Question 13

What is the principle of equivalence as stated in the context of General Relativity?

Accepted Answer

The effects of gravity and acceleration are indistinguishable to an observer within a closed system.

Answer

The speed of light is the same for all observers, regardless of the motion of the light source or observer.

Answer

Mass and energy are equivalent, as expressed by the equation E=mc².

Answer

Spacetime is flat in the absence of matter and energy.

Question 14

The stress-energy tensor in Einstein's Field Equations represents:

Accepted Answer

The density and flow of mass, energy, and momentum

Answer

The curvature of spacetime

Answer

The gravitational field strength

Answer

The electromagnetic field

Question 15

Which of the following is a key assumption in Einstein's Field Equations?

Accepted Answer

The laws of physics are the same in all inertial frames of reference

Answer

Spacetime is flat and Euclidean

Answer

Gravity is a fundamental force of nature

Answer

The speed of light is infinite

Question 16

The equation Gμν = 8πTμν in Einstein's Field Equations represents:

Accepted Answer

The curvature of spacetime due to mass-energy

Answer

The conservation of mass-energy

Answer

The equivalence of gravity and acceleration

Answer

The expansion rate of the universe

Question 17

General Relativity, a cornerstone of modern physics, has revolutionized our understanding of gravity. However, it also has certain limitations. Discuss two key limitations of General Relativity and identify potential areas for future research and development in the field.

Accepted Answer

General Relativity fails to explain the nature of dark matter and dark energy.

Accepted Answer

General Relativity is incompatible with quantum mechanics at very small scales.

Answer

General Relativity has been experimentally verified in all regimes of gravity.

Answer

Research in General Relativity has reached a standstill and no further progress is expected.

Question 18

Which of the following is the correct form of Einstein's Field Equations in the absence of matter or energy?

Accepted Answer

Rμν = 0

Answer

Rμν - (1/2)gμνR = 0

Answer

Rμν - gμνR = 0

Question 19

In the Field Equations, what does the stress-energy tensor represent?

Accepted Answer

The distribution and flow of mass, energy, momentum, and stress within spacetime

Answer

The gravitational field

Answer

The curvature of spacetime

Answer

The motion of objects in spacetime

Question 20

Which of the following is the Schwarzschild metric?

Accepted Answer

ds^2 = (1 - (2GM/r))dt^2 - (1 - (2GM/r))^-1 dr^2 - r^2dΩ^2

Answer

ds^2 = dt^2 - dr^2 - r^2dΩ^2

Answer

ds^2 = (1 + (2GM/r))dt^2 - (1 + (2GM/r))^-1 dr^2 - r^2dΩ^2

Question 21

What is the physical significance of the Schwarzschild radius?

Accepted Answer

It is the radius of the event horizon around a black hole, beyond which nothing, not even light, can escape

Answer

It is the distance at which gravitational effects become negligible

Answer

It is the maximum radius of a stable star

Question 22

Which of the following is a consequence of spacetime curvature?

Accepted Answer

Gravitational lensing, where light is bent as it passes by massive objects

Answer

Electric force

Answer

Magnetic force

Question 23

In General Relativity, what is the term 'geodesic motion' used to describe?

Accepted Answer

The path of an object moving freely in spacetime, influenced solely by the curvature of spacetime

Answer

The path of an object moving with constant acceleration

Answer

The path of an object moving with constant velocity

Answer

The path of an object moving in a circular orbit

Question 24

Which of the following is NOT a confirmed prediction of General Relativity?

Accepted Answer

The existence of antimatter

Answer

Gravitational lensing

Answer

Time dilation

Answer

Gravitational waves

Question 25

In Einstein's Field Equations, what is the role of the cosmological constant?

Accepted Answer

It allows for a non-zero energy density of the vacuum, which is believed to contribute to the observed accelerated expansion of the universe

Answer

It is responsible for the initial expansion of the universe

Answer

It determines the strength of the gravitational force

Question 26

Which of the following phenomena provides strong experimental evidence for Einstein's Field Equations?

Accepted Answer

The bending of starlight around the Sun during a solar eclipse, as observed in 1919 by Sir Arthur Eddington

Answer

The double-slit experiment

Answer

The Michelson-Morley experiment

Answer

The photoelectric effect