![]() So, according to a simple mashup of James Clerk Maxwell’s 19th-century theory of electromagnetism and Einsteinian gravity, Q = M must be the limit. If Q increased further, the radius of the event horizon would become a complex number (involving the square root of a negative number), rather than a real one. As Q increases, the black hole’s inner horizon expands while the event horizon contracts until, at Q = M, the two horizons coincide. Meanwhile, the black hole’s charge also creates a second, “inner” horizon, hidden behind the event horizon. Together, the black hole’s mass and charge determine its size-the radius of the event horizon. When they combine Einstein’s gravity equations and the equations of electromagnetism, they calculate that a black hole’s charge, Q, can never surpass its mass, M, when both are converted into the same fundamental units. Physicists see very easily that charged black holes reach an extremal limit. The newfound formula applies to a system such as a gas as well as a black hole. In a paper published in March in Physical Review Letters, Goon and Riccardo Penco broadened the lessons of the earlier work by proving a simple, universal formula relating energy and entropy. In the latest surprise, that link turns out to exemplify a general fact about nature. “It’s like, wow, OK, two very cool things are connected,” Cheung said. Entropy is one of the most studied features of black holes, but it wasn’t thought to have anything to do with their extremal limit. Then, two years ago, Remmen and collaborators Clifford Cheung and Junyu Liu of the California Institute of Technology discovered that whether extremal black holes can decay depends directly on another key property of black holes: their entropy-a measure of how many different ways an object’s constituent parts can be rearranged. This conclusion brought greater scrutiny to extremal black holes’ fates. Four physicists realized in 2006 that if extremal black holes can decay, this implies that gravity must be the weakest force in any possible universe, a powerful statement about quantum gravity’s relationship to the other quantum forces. ![]()
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