General relativity is Einstein’s theory of gravity, and it explains gravity as the curvature of spacetime rather than as an invisible pulling force. Massive objects such as planets, stars, and black holes change the geometry around them, causing other objects to follow curved paths. This idea matters because it explains planetary orbits, black holes, gravitational waves, and the way light bends near massive objects.
It also affects real technology, including GPS satellites that must correct for relativistic time differences.
Key Facts
- General relativity describes gravity as curved spacetime, not as a force acting at a distance.
- Mass-energy tells spacetime how to curve, and curved spacetime tells matter how to move.
- The equivalence principle says that being in a gravitational field can be locally indistinguishable from accelerating.
- Approximate gravitational time dilation near a spherical mass: t_far = t_near / sqrt(1 - 2GM/(rc^2)).
- For weak gravity, gravitational acceleration near a planet is approximately g = GM/r^2.
- Light follows curved paths called geodesics, so massive objects can bend light and create gravitational lensing.
Vocabulary
- Spacetime
- Spacetime is the four-dimensional combination of three dimensions of space and one dimension of time.
- Geodesic
- A geodesic is the straightest possible path through curved spacetime.
- Equivalence principle
- The equivalence principle states that the effects of gravity and acceleration are locally indistinguishable.
- Gravitational time dilation
- Gravitational time dilation is the effect in which clocks run slower deeper in a gravitational field.
- Gravitational lensing
- Gravitational lensing is the bending of light by curved spacetime near a massive object.
Common Mistakes to Avoid
- Thinking spacetime curvature is only a rubber-sheet dip, which is wrong because the rubber-sheet model is only a 2D analogy for a 4D geometry.
- Saying gravity disappears in orbit, which is wrong because orbiting objects are still falling under gravity while moving forward fast enough to keep missing Earth.
- Assuming light bends because it has mass, which is wrong because photons have no rest mass but still follow curved paths through spacetime.
- Ignoring time curvature, which is wrong because general relativity affects both space and time, including measurable clock rate changes.
Practice Questions
- 1 Use g = GM/r^2 to find the gravitational acceleration at Earth’s surface. Use G = 6.67 x 10^-11 N m^2/kg^2, M = 5.97 x 10^24 kg, and r = 6.37 x 10^6 m.
- 2 A GPS satellite clock runs about 45 microseconds per day faster than a clock on Earth due to gravitational time dilation, but about 7 microseconds per day slower due to special relativity. What is the net time difference per day before correction?
- 3 Explain why a beam of light passing near the Sun bends even though photons have no rest mass.