While special relativity describes motion along flat spacetime—the underlying fabric of the universe—general relativity extends this theory to explain motion through curved spacetime.

Recognizing the mathematical complexities of generalizing special relativity with a new picture of gravity and acceleration, Albert Einstein had Grossman introduce him to tensor calculus. Years before developing the precursor to GR together, Einstein would use Grossman's lecture notes to prepare for his exams.

Besides accurately explaining the slight wobble observed in Mercury's orbit, general relativity predicted that light would bend around massive objects by an amount matching what was observed when background starlight bent around the sun during an eclipse. The theory also predicted the existence of gravitational waves and black holes decades before they were found.

Using Penrose diagrams—mathematical structures that compress all of space and time—physicists can observe the path of light and which events can affect one another. The space-time maps help visualize the structure of black holes and describe what happens when objects fall in.

Although working independently of one another, the two exchanged correspondence in the lead up to November 1915, when Hilbert submitted their gravitational field equations five days before Einstein presented their work. An error in Hilbert's formulation and its nonpublication until March 1916 would leave credit for general relativity to Einstein.

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

Einstein's theory of general relativity—that mass literally bends space and time—can be difficult for the human brain to imagine. This interactive resource lets you create celestial objects, imagine their effect on space-time, and see how they interact with each other (best viewed on desktop).

General relativity predicted that the gravity of all the matter in the universe would cause it to collapse, contradicting the belief at the time that the universe was constant and unchanging. Albert Einstein added the cosmological constant to his equations, which acted like anti-gravity, to "fix" his math.

Rewinding the universe to the big bang compresses all matter, energy, space, and time into a single point, necessitating a model that combines general relativity with quantum mechanics. Although physicists understand time to have begun when the universe did, a clear understanding of the mechanisms involved remains unclear.

Within the pages are calculations, sketches and his first attempts at deriving what would be the field equations for gravity. It also documents some dead ends and the difficulties Einstein encountered as he describes part of the mathematics of what would become general relativity, describing it as "too involved."

Such objects, also known as Einstein-Rosen bridges, would resemble funnel-like tunnels connecting two regions of spacetime, allowing for instant travel across the universe. However, such structures would be incredibly unstable and require undiscovered materials with negative energy to keep them open.

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

The theory of general relativity posits that mass and energy bend space and slow down the passage of time. One consequence is that massive objects, such as black holes, curve spacetime to such an extent that light from background sources can loop around them, producing multiple images or ring-like patterns.

The equations of special relativity require these objects to possess imaginary mass, and they would travel faster the more energy is taken away from them. The existence of tachyons would necessitate an unknown form of matter and lead to paradoxes involving information that can hypothetically travel backward in time.

Data from a 16-year study of an orbiting pair of spinning neutron stars showed that measurements of gravitational wave energy and the bending of light around the system were consistent with predictions made by general relativity to an accuracy of at least 99.99% across seven tests.

Combining the general theory of relativity with quantum field theory creates nonsensical mathematical outcomes, such as probabilities of infinity. These are resolved by treating particles as vibrating strings rather than points of matter. However, probing the scale of these strings to validate the theory requires technology equivalent to a particle accelerator the size of the solar system.

Space-time is a complex subject, but this Livescience article makes an effort to disentangle the topic. Somewhat akin to a sheet of rubber that can be warped and bent in parts, space-time is a bit more involved that that. However, the analogy makes this and other aspects of the concept simpler to grasp.

About seven base units, such as meters for length, have historically been used to describe everything in our physical reality. However, researchers have shown that, through relativistic space-time, clocks can serve as replacements for rulers, scales, and other instruments, allowing everything to be measured in terms of time.

The experiment involved attaching four freely floating gyroscopes to a telescope aimed at a distant star for a year. The observed angular shift of the gyroscopes as a result of Earth's rotation pulling on spacetime was approximately 0.0000012 degrees from the amount predicted by general relativity.

While the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model.

After confirming that the accuracy of some laws of physics is limited to certain domains, science became more hesitant to categorize identified mathematical relationships, such as quantum mechanics, as unchanging laws. Instead, these recent, complex frameworks are designated as theories to acknowledge that they are conditional and may be part of a larger, more complete future framework.

When renowned theoretical physicist Stephen Hawking did not rule out the possibility of time travel in his posthumous book Brief Answers to the Big Questions, many hopefuls got excited. But, unfortunately for them, Hawking believed that yet-to-be discovered laws of physics will prove time travel impossible. This piece outlines some practicalities about the speed of light and wormholes that lend way to Hawking’s prediction.

Although Newton's "universal" law is unreliable in strong gravitational fields when compared with the field equations of general relativity, it is still taught for its accuracy on everyday scales. However, gravity's effect on small scales is too weak to be measured reliably, its accuracy at atomic scales remains unknown.