One of today’s key challenges in physics lies in reconciling quantum mechanics and gravity. To tackle this puzzle, let’s first grasp how modern physics interprets classical gravity and uncover what quantum mechanics brings to the table.
Let’s kick off with classical gravity. Newton laid down the law, revealing an attractive interaction between any two massive bodies. The force’s intensity? Inversely proportional to the distance squared between them.
As the 20th century dawned, it became clear that space and time are inseparable categories. Special Theory of Relativity introduced our spacetime as Minkowski space, where the distance between close points is measured using a metric that isn’t positively definite. Enter gravity, and Einstein had to generalize this idea, envisioning spacetime of a more general nature (the so-called pseudo-Riemannian manifold) with a metric defined in a more complex manner.
The metric, however, isn’t arbitrary; it must satisfy Einstein’s equations. One famous solution is the Schwarzschild solution, describing a non-rotating black hole. Black holes, according to classical physics, don’t allow matter to escape once it crosses the event horizon.
The location of the horizon is tied to coordinate values where metric components diverge (not at r=0). For the Schwarzschild black hole it is called the Schwarzschild radius. Whether the horizon corresponds to a singularity, due to the divergence of the aforementioned metric components, will be revealed soon.