General relativity is a deeply complex mathematical theory, but its description of black holes is surprisingly simple. A stable black hole can be described by only three properties: its mass, its electrical charge and its rotation or spin. Since black holes are unlikely to have much charge, only two properties are required. If you know the mass and spin of a black hole, you will know everything you need to know about the black hole.

This characteristic is often summarized by the no-hair phrase. In particular, the theorem states that once matter falls into a black hole, the only remaining property is mass. You could make a black hole out of hydrogen, chairs, or old National Geographic copies of Grandma’s attic and it wouldn’t make a difference. Mass is mass as far as general relativity is concerned. In either case, a black hole’s event horizon is perfectly smooth with no additional features. As Jacob Bekenstein said, black holes don’t have hair.

The conflict between relativity and quantum theory leads to the firewall paradox. Photo credit: Jeremy Perkins / Unsplash

For all its predictive power, general relativity has a problem with quantum theory. This is especially true for black holes. If the sentence without the hair is correct, the information contained in an object is destroyed when it crosses the event horizon. Quantum theory says that information can never be destroyed. The valid theory of gravity thus contradicts the valid quantum theory. This leads to problems like the firewall paradox, which cannot decide whether an event horizon should be hot or cold.

Various theories have been proposed to resolve this contradiction, often including extensions to the theory of relativity. However, the difference between standard relativity and these modified theories can only be seen in extreme situations, making them difficult to examine observationally. However, a new paper in Physical Review Letters shows how they can be examined by rotating a black hole.

The temperature in a room is an example of a scalar field. Photo credit: Lucas Vieira

Many modified theories of relativity have an additional parameter that is not included in standard theory. Known as a massless scalar field, Einstein’s model allows it to connect to quantum theory in non-contradicting ways. In this new work, the team investigated how such a scalar field relates to the rotation of a black hole. They found that a modified black hole is indistinguishable from the standard model at low rotations, but at high rotations the scalar field allows a black hole to have additional features. In other words, in these alternative models, rapidly rotating black holes can have hair.

The hairy aspects of rotating black holes would only be seen near the event horizon itself, but they would also affect the merging of black holes. As the authors point out, future gravitational wave observatories should be able to use rapidly rotating black holes to determine whether an alternative to general relativity is valid.

Einstein’s general theory of relativity has so far passed all the observation challenges but is likely to collapse in the most extreme environments in the universe. Studies like this show how we can discover the next theory.

**Reference:** Alexandru Dima et al. “Spin-Induced Spontaneous Scaling of the Black Hole.” Physical Review Letters 125.23 (2020): 231101.

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