General Relativity

Spacetime

A four-dimensional entity combining three spatial dimensions (x, y, z) and one time dimension (t), introduced by Hermann Minkowski.

Lorentz Transformation

A transformation that mixes space and time coordinates when switching between reference frames moving at a velocity relative to each other.

Geodesic

The shortest path between two points in spacetime, which is straight in flat spacetime and curved in curved spacetime.

The Equivalence Principle

The principle in General Relativity stating that no experiment can distinguish between acceleration and a gravitational field.

Mass and Spacetime Curvature

Mass causes spacetime to curve, resulting in objects following geodesics.

Experimental proofs of General Relativity

Observations such as Mercury's perihelion precession, the bending of light during a solar eclipse, and gravitational lensing that confirm GR predictions.

Einstein Ring

A circular distortion of light from a distant object due to gravitational lensing, occurring when an observer, lensing object, and background light source align.

Einstein's Field Equations

Equations describing how spacetime is shaped by matter and energy.

The Cosmological Principle

The principle that the universe is homogeneous and isotropic on large scales.

Flat universe

A universe where parallel lines remain parallel and the total angles in a triangle equal 180°.

Closed universe

A universe where parallel lines converge and angles are greater than 180°.

Open universe

A universe where parallel lines diverge and angles are less than 180°.

Omega (Ω) parameter

The density parameter that determines the curvature and fate of the universe.

Accelerating expansion of the universe

The phenomenon observed indicating that the expansion of the universe is accelerating due to dark energy.

Black Hole

A region of spacetime where gravity is so strong that nothing, not even light, can escape.

Schwarzschild Radius

The radius of the event horizon, the boundary beyond which nothing can escape a black hole.

Event Horizon Telescope (EHT)

A telescope that captured the first-ever image of a black hole (M87, 2019).

How does gravitational lensing provide evidence for General Relativity?

It shows how massive objects bend light, just as GR predicts. Multiple images or distorted rings of galaxies are observed due to this effect.

How do we determine the correct solution for our universe’s spacetime?

We solve Einstein’s equations and compare solutions with observations (e.g., cosmic microwave background, galaxy distributions).

Who discovered the expanding universe?

Georges Lemaître (1927) and Alexander Friedman (1922)

How do we view the expansion of the universe?

As an expansion of spacetime itself rather than galaxies moving through space.

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)

How do we measure Ω?

By observing cosmic microwave background radiation, galaxy distribution, and supernova data.

What is the ultimate fate of the universe?

Observations show that the expansion is accelerating due to dark energy, meaning the universe will expand forever and eventually become cold and dark as galaxies move out of view.

How do black holes form?

From the collapse of massive stars (>25 solar masses) after a supernova explosion. The remnant core collapses into a singularity.

How can we observe black holes?

Gravitational effects, X-ray emissions, and Event Horizon Telescope (EHT): First-ever image of a black hole

What is the significance of the Lorentz transformation in spacetime?

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.

How does General Relativity explain gravity?

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.

What are some experimental proofs of General Relativity?

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.