General Relativity

Spacetime & Lorentz Transformations

Q: What is spacetime?
A: Spacetime is a four-dimensional entity combining three spatial dimensions (x, y, z) and one time dimension (t). It was introduced by Hermann Minkowski.

Q: What does a Lorentz transformation do in spacetime?
A: Lorentz transformations mix space and time coordinates when switching between reference frames moving at a velocity relative to each other. They are essentially rotations in spacetime.

Q: What is the significance of the Lorentz transformation in spacetime?
A: It shows that space and time are not absolute but change depending on the observer’s motion. However, the spacetime interval remains absolute for all observers.

Geodesics in General Relativity

Q: What is a geodesic?
A: A geodesic is the shortest path between two points in spacetime. In flat spacetime, geodesics are straight lines, while in curved spacetime (around massive objects), geodesics appear as curved paths.

General Relativity & Gravity

Q: What are the two basic axioms of General Relativity?
A:

1. The Equivalence Principle – No experiment can distinguish between acceleration and a gravitational field.

2. Mass causes spacetime to curve, and objects follow geodesics in this curved spacetime.

Q: How does General Relativity explain gravity?
A: Gravity is not a force but the effect of mass curving spacetime. Objects move along geodesics, which appear as curved paths in this warped spacetime.

Q: What are some experimental proofs of General Relativity?
A:

• Mercury’s perihelion precession: GR correctly explains the precession of Mercury’s orbit.

• Bending of light: Observed by Arthur Eddington during a solar eclipse in 1919, confirming that light bends due to gravity.

• Gravitational lensing: Light from distant galaxies is bent by massive objects in between, creating multiple images.

Einstein Ring & Gravitational Lensing

Q: What is an Einstein Ring?
A: It is a circular distortion of light from a distant object due to gravitational lensing, occurring when an observer, lensing object (e.g., galaxy), and background light source align perfectly.

Q: How does gravitational lensing provide evidence for General Relativity?
A: It shows how massive objects bend light, just as GR predicts. Multiple images or distorted rings of galaxies are observed due to this effect.

The Shape of the Universe & Cosmology

Q: What equation describes the spacetime of the entire universe?
A: Einstein’s Field Equations describe how spacetime is shaped by matter and energy.

Q: How do we determine the correct solution for our universe’s spacetime?
A: We solve Einstein’s equations and compare solutions with observations (e.g., cosmic microwave background, galaxy distributions).

Q: What is the Cosmological Principle?
A: The universe is homogeneous (same density everywhere) and isotropic (looks the same in all directions) on large scales.

Q: What three possible geometries can the universe have?
A:

1. Flat (Euclidean): Parallel lines remain parallel, total angles in a triangle = 180°.

2. Closed (Spherical): Parallel lines eventually converge, angles > 180°.

3. Open (Hyperbolic): Parallel lines diverge, angles < 180°.

Expansion of the Universe

Q: Who discovered the expanding universe?
A: Georges Lemaître (1927) and Alexander Friedman (1922) solved Einstein’s equations to predict expansion. Edwin Hubble (1929) confirmed it with redshift observations.

Q: How do we view the expansion of the universe?
A: As an expansion of spacetime itself rather than galaxies moving through space.

Q: How does the geometry of spacetime relate to expansion?
A: It depends on the Omega (Ω) parameter, which is the ratio of actual density to critical density:

• Ω > 1 → Closed universe (eventually collapses).

• Ω = 1 → Flat universe (expands forever at a slowing rate).

• Ω < 1 → Open universe (expands forever at increasing rate).

Measuring Ω and the Fate of the Universe

Q: What is the Omega (Ω) parameter?
A: The density parameter that determines the curvature and fate of the universe.

Q: How do we measure Ω?
A: By observing cosmic microwave background radiation, galaxy distribution, and supernova data.

Q: What is the ultimate fate of the universe?
A: Observations show that the expansion is accelerating due to dark energy, meaning the universe will expand foreverand eventually become cold and dark as galaxies move out of view.

Black Holes

Q: What is a black hole?
A: A region of spacetime where gravity is so strong that nothing, not even light, can escape.

Q: How do black holes form?
A: From the collapse of massive stars (>25 solar masses) after a supernova explosion. The remnant core collapses into a singularity.

Q: What is the Schwarzschild Radius?
A: The radius of the event horizon—the boundary beyond which nothing can escape.

Q: How can we observe black holes?
A:

• Gravitational effects: Observing stars orbiting an invisible massive object (e.g., Sagittarius A* at Milky Way’s center).

• X-ray emissions: Matter falling into a black hole heats up and emits X-rays.

• Event Horizon Telescope (EHT): First-ever image of a black hole (M87, 2019).