Like some unstoppable evil in a horror movie, a black hole constantly feeds and grows. Now, 30 years after that discovery, researchers can finally describe this inexorable growth quantitatively. A team publishing in the 23 December print issue of PRL derives an explicit relationship between the size of a black hole and the energy it has absorbed. Such knowledge may aid in computer simulations of black hole mergers, understanding gravitational wave physics, and other astrophysical studies.
Black holes are easiest to study theoretically when they are unchanging and isolated from everything else. But real black holes absorb matter–such as stars and gas–and radiation, including light and gravitational waves. The only major result for such dynamic holes came in 1971 when Stephen Hawking proposed that a black hole’s event horizon, the point of no return for infalling matter and radiation, never decreases its surface area. In other words, black holes grow. “That’s all one knew,” says Abhay Ashtekar of Penn State University in University Park, Pennsylvania. “But what one wants [to know], to do realistic calculations, is how much the area changes.”
To tackle this question , Ashtekar and Badri Krishnan, now at Germany’s Max Planck Institute for Gravitational Physics, formulated a measure of the total gravitational wave energy absorbed by a black hole that isn’t isolated from other matter and radiation. From there, the pair derived “balance laws” relating the amount of infalling energy from matter and radiation with changes in horizon area and black hole mass and angular momentum. Whereas previous results could describe minute changes between static black hole states, Ashtekar explains, “now [we can] consider really dynamical processes in which the black holes bang and collide.”
In black hole computer simulations, he says, the new laws could be used to ensure that a result is physically reasonable and not mere computer fantasy. For example, simulations could check that energy and angular momentum are conserved properly on the horizon. The new equations could also help researchers extract basic properties of a simulated black hole, such as its mass and angular momentum. In addition, the result suggests that black holes could form with large amounts of angular momentum–much larger than was allowed by the theory for an idealized, isolated black hole.
“I think this will become a very important paper,” says Jorge Pullin of Louisiana State University in Baton Rouge. The relationships they develop are like those used in the 1960s to demonstrate that gravitational waves aren’t just figments of the imagination, he says, and might become similarly important. Stephen Fairhurst of the University of Alberta in Canada says that, with a method to calculate the mass of a dynamical black hole, “numerical relativists should be able to calculate the energy contained in gravitational radiation more accurately.” That in turn could improve predictions for gravitational wave observations in detectors such as LIGO, he says.