Posts Tagged 'nonlinear dynamics'

Portrait of a black hole, part 1

BOOOOOING! [Credit: xkcd. Click for the original comic.]

BOOOOOING! [Credit: xkcd. Click for the original comic.]

General relativity is inherently challenging to understand. It requires thinking about a four-dimensional reality in which the natural paths of light and matter are curved in the presence of gravity, something we refer to as the curvature of spacetime. Yet unlike the curvature of Earth or topographic features on Earth’s surface, spacetime isn’t an object embedded in a higher-dimensional reality from which we can see the curvature directly. (Or at least if there is a higher-dimensional reality — a scenario including the braneworld hypothesis — we haven’t figured out how yet, and there’s no way we mere humans can access those extra dimensions.)

So, we must resort to analogy and metaphor, whether visual or mathematical. The most famous analogy is the “rubber sheet”, as seen (sorta) in the xkcd comic above. In this view, spacetime is a soft stretchy surface, into which masses sink. Particles of matter and light are like balls rolling on that surface, so that they roll toward masses, emulating the attractive force of gravity.

Part of the problem with the rubber sheet metaphor is that it requires gravity in the world of the rubber sheet to work: nothing sinks in or rolls properly without gravity to provide a “down” direction (which doesn’t really correspond to anything in spacetime). Don’t get me wrong: it’s a useful analogy, and I’ve used it when teaching general relativity. However, it has more serious flaws, to the point that I generally prefer other metaphors.

One flaw is that the rubber sheet analogy is that it’s difficult to represent many real gravitational systems, including rotating objects like spinning black holes — or the expanding Universe. For those purposes, I like another: the “flowing current” or “moving sidewalk” analogy. Continue reading ‘Portrait of a black hole, part 1’


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