Einstein's theory of general relativity revolutionized our understanding of gravity. Instead of a force between objects, gravity is the warping of spacetime by massive bodies. This warping causes objects to follow curved paths, explaining planetary orbits and falling apples.

Light also follows these curved paths, leading to gravitational lensing. This effect can distort and magnify distant objects. General relativity introduces concepts like time dilation and gravitational redshift, showing how gravity affects the passage of time and the energy of light.

Spacetime and Gravity

Spacetime warping by massive objects

• Einstein's theory of general relativity describes gravity as the curvature of spacetime
  • Spacetime is the 4D fabric of the universe (3D space + 1D time)
  • Massive objects (stars, planets) cause spacetime to curve or warp around them
    • More massive objects create greater spacetime curvature (black holes)
• Objects in curved spacetime follow the straightest possible path called a geodesic
  • Geodesics appear as curved paths in space, interpreted as the effect of gravity (orbits)
• Spacetime curvature explains the motion of objects under the influence of gravity
  • Planets orbit the Sun by following the curved spacetime around it
  • Objects fall towards Earth because they follow the geodesic in Earth's curved spacetime (apples falling from trees)
  • Tidal forces arise from differences in spacetime curvature across an object's size

Newton's gravity vs Einstein's spacetime

• Newton's law of universal gravitation describes gravity as a force between objects
  • Gravity force is proportional to mass product and inversely proportional to distance squared
  • $F = G \frac{m_1 m_2}{r^2}$ ($F$ = force, $G$ = gravitational constant, $m_1$, $m_2$ = masses, $r$ = distance)
  • Newton's theory explains motion under gravity as a result of the gravitational force (cannonball trajectories)
• Einstein's general relativity describes gravity as the curvature of spacetime
  • Massive objects warp spacetime, causing other objects to follow curved paths (geodesics)
  • Motion under gravity is a result of spacetime geometry, not a force (Earth orbiting Sun)
• Both theories accurately predict motion under gravity in most cases
  • Einstein's theory is more accurate in extreme situations (near black holes, strong gravitational fields)
  • Newton's theory is simpler and sufficient for most practical applications (calculating orbits of planets and satellites)

Light paths in curved spacetime

• Light follows the curvature of spacetime caused by massive objects
  • In the presence of a massive object, light follows a geodesic (straightest possible path in curved spacetime)
  • The path of light appears curved in space because spacetime itself is curved (starlight bending near the Sun)
• Gravitational lensing is an observable effect of light following curved paths in spacetime
  • Light from a distant source passing near a massive object (galaxy, galaxy cluster) is deflected by spacetime curvature
  • Deflection of light can cause the distant source to appear distorted, magnified, or appear in multiple places (multiple images)
• The amount of deflection depends on the mass of the object and the distance between light and object
  • Stronger gravitational fields (more massive objects) cause greater light deflection (supermassive black holes)
  • Light passing closer to a massive object experiences more deflection than light passing farther away (light grazing the Sun vs passing far from it)
• The curvature of light paths due to massive objects provides evidence for Einstein's theory of general relativity and spacetime curvature (Eddington's 1919 solar eclipse observations)

Principles and effects of general relativity

• The equivalence principle states that gravitational acceleration is indistinguishable from acceleration due to other forces in a local inertial frame of reference
• Time dilation occurs when time passes at different rates for observers in different gravitational fields or relative motion
• Gravitational redshift is the phenomenon where light moving out of a gravitational field loses energy, shifting to longer wavelengths