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Spacetime Geometry

Is the Universe flat, spherical, or shaped like a rubber ducky?

By Varun Vasudeva

March 2017

Spacetime geometry is a highly unusual thing that physicists have theorized about for decades. Originally, spacetime was thought of to be a flat Euclidean surface; however, Einstein proved this to be partially incorrect, as this flat spacetime exists in conjunction with objects that have properties of mass. This mass, occupying space on the flat surface of spacetime, bends space—and time, but we’ll get to that later on— according to how massive it is. Now, mass can have strange effects on spacetime. An average Sun-sized star would warp spacetime only slightly, whereas a black hole would warp the spacetime in its vicinity in the most unusual ways possible.

The curvature of spacetime due to normal stars and neutron stars is something we’re able to comprehend, but this curvature, when pictured with respect to black holes, starts to raise some problems. A black hole causes what’s known to physicists as a gravitational well on the surface of spacetime. This region is a total mystery to us physically, as nothing can really see past a black hole’s event horizon. Previous articles have discussed the effects of this gravitational well on human beings—“spaghettification” and eventually the transformation into atomic soup—but what usually isn’t discussed is how this gravitational well affects space and time around it.

Upon transforming a few graphs in funny ways that only physicists can truly understand, there’s reason to infer a number of things about black holes. One of these things is that once an object crosses the event horizon, it can never really escape a black hole’s gravitational pull. This seems like a fairly obvious fact now that people discuss black holes a lot more, however, it’s important to note that even if an external object or rescuer were to travel towards that black hole faster than light, with the intention of saving the first object, it’d still not be possible. Let’s assume the second object was to not just break the speed of light but to accelerate further from it. This would still be unsuccessful as black hole’s pull for the first object would be so unfathomably strong. If we draw a Penrose diagram for an object that crosses a black hole’s event horizon, every possible future line we can draw for that object leads directly into the black hole, leaving no chance of an escape.

Another inference we can draw from a black hole’s spacetime curvature is that it bends time in rather weird ways as well. Graphs reveal yet again (surprise!) that hotly debated topics such as time travel might be possible in the space-time vicinity of a powerful black hole. There is a quantity in astrophysics, known as the spacetime interval. The spacetime interval can be calculated by using the equation:

s2 = x2 – c2t2

Now, this might look like absolute rubbish to you, but the spacetime interval is very useful for one simple but powerful thing: it always remains the same for objects. For example, if you observe a sequence of events ABC and your friend observes the same in the order CAB, you will disagree on the sequence you saw those events occur in. However, you will always agree on the spacetime interval of those events occurring. Using this principle, we could say that the spacetime interval for objects in normal spacetime is fixed and a sequence of events occurs in the same manner. But black holes beg to differ. As far as these astrophysical behemoths are concerned, their spacetime curvature flips every aspect of the spacetime interval, leaving opportunities for time travel open to exploration.

It goes without saying, however, that being in the immediate surrounding of a supermassive black hole would most probably mean an imminent and painful demise, so we don’t suggest you try and do that to redo a review you flunked.

Rohil Bahl