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.
Understanding Physics: General Relativity and Curved Spacetime
A key starting point is free fall. An astronaut orbiting Earth feels weightless even though Earth strongly affects the astronaut's path. A dropped object feels weightless too, until it hits the ground.
The ground pushes upward and creates the feeling called weight. This is why standing still on Earth is not the same as moving freely through space. Einstein used this insight to connect gravity with acceleration.
In a small sealed room, a person cannot always tell whether the floor pushes them because of a rocket's acceleration or because they are standing on a planet. This is called the equivalence principle.
The paths followed by freely moving objects are called geodesics. They are the closest possible thing to straight lines in a geometry that is not flat. On a flat sheet, a straight line keeps one direction.
On the surface of a sphere, a great circle is the equivalent path. Airplanes often follow parts of great circles because this gives the shortest route over Earth. Near a star, the geometry is more complicated, so an orbit is not caused by a constant sideways pull in the usual picture.
A planet moves forward along its natural path while the geometry changes how that path develops. This produces an orbit.
Time is part of the story, not just a background clock shared by everyone. Clocks at different heights above Earth run at slightly different rates. A clock farther from Earth runs faster than one closer to the surface.
The difference is tiny for people, yet it can be measured with very accurate atomic clocks. Satellite navigation depends on timing signals, so engineers include corrections from relativity. If they did not, position estimates would drift by kilometres over time.
This is a useful reminder that relativity is not only about distant black holes. It affects measurements made around Earth every day.
Light provides some of the clearest tests because it travels extremely fast yet still follows the local geometry. When light from a distant galaxy passes near a cluster of galaxies, the cluster can produce stretched arcs or multiple images of the same source. Astronomers use these patterns to estimate where matter lies, including matter that does not emit light.
General relativity also predicts small changes to planetary orbits. Mercury's orbit shifts by a little more than older gravity models predict, and the theory accounts for this shift. When learning the topic, separate a useful visual model from the full theory.
The rubber sheet picture can show curved paths, but it leaves out time and wrongly suggests that gravity needs a downward direction. The real theory describes four dimensional spacetime and uses careful measurements to test its predictions.
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.