What Bothers Physicists About Black Holes (Interview with Brian Cox)

Brian Cox outlines the theoretical origins of black holes shortly after Einstein's 1915 theory of general relativity. He explains how space-time warps around matter and energy, leading to the concept of a black hole as a region where gravity is so strong that nothing, not even light, can escape. He introduces Karl Schwarzschild's solution to Einstein's equations, which described the geometry of a black hole, and the concept of a star collapsing without limit once it exhausts its nuclear fuel.

Cox further elaborates on the Schwarzschild radius, the point at which a star would collapse into a black hole. For the sun, this is 3 km, where escape velocity exceeds the speed of light. He introduces the concept of the event horizon, a boundary from which nothing can return. Using the 'river model' analogy, he describes how space itself flows faster than light inwards, trapping everything within it. The singularity, often imagined as an infinitely dense point, is described as an end of time rather than a place in space according to Einstein's theory.

The discussion moves to Sagittarius A*, the black hole at the center of our galaxy, and its image captured by the Event Horizon Telescope. Cox explains that the light visible in the image comes from the accretion disk of material spiraling around the black hole, distorted by its immense gravity. He compares the size of Sagittarius A* (6 million solar masses) to other black holes like M87 (6 billion solar masses) and discusses the minimum size for black holes, which are typically a few solar masses, as smaller stars are prevented from collapsing by electron degeneracy pressure (white dwarfs) or neutron degeneracy pressure (neutron stars).

Cox explains that, according to Einstein's equivalence principle, a free-falling observer would not feel the pull of gravity until tidal forces become significant. For a supermassive black hole, an observer would cross the event horizon without feeling anything, experiencing subsequent spaghettification only inside. However, from the perspective of an external observer, time would appear to slow down for the falling object, eventually stopping on the horizon. The external observer would never see the object fall in, only fading and redshifted light, indicating different realities depending on the observer's frame of reference.

The conversation shifts to Stephen Hawking's discovery that black holes are 'not so black' due to Hawking radiation. This radiation, arising from quantum effects near the event horizon, implies that black holes have a temperature and an entropy and eventually evaporate. The core problem, known as the information paradox, is that Hawking's initial calculation suggested this radiation is information-free, meaning any information falling into the black hole would be lost, violating a fundamental law of physics. Recent research suggests that information might eventually be imprinted in the Hawking radiation, but the mechanism remains a mystery.

Cox introduces black hole complementarity, which suggests that both the internal (spaghettification) and external (incineration before crossing the horizon) descriptions of falling into a black hole are valid from different perspectives. This leads to the concept of the holographic principle, where information about a 3D volume can be encoded on a 2D surface. He explains that black holes, through their temperature and entropy, hint at an underlying, more fundamental structure of space and time, possibly resembling a network of qubits, a concept central to quantum computing.

The discussion concludes by emphasizing that black hole research is not just about understanding these cosmic objects but serves as a crucial window into the most profound questions about the universe, quantum gravity, and the fundamental nature of space and time. Cox explains the firewall paradox as an ongoing challenge to reconcile quantum mechanics and general relativity near the event horizon. He also touches upon the relationship between black hole singularities and the Big Bang singularity, noting that both represent extremes of physical understanding.