Found: memories of gravitational waves.

In the realm of Einstein's general theory of relativity, the curvature of space-time replaces the force of gravity. A massive body such as a star influences other objects not by acting on them directly but by warping the shape of space and time. Moreover, if such a body abruptly changes its motion or mass, space-time in its vicinity undergoes a corresponding convulsion. This disturbance travels outward as a gravitational wave that imperceptibly jostles any objects in its path.

Demetrios Christodoulou, a mathematician at New York University in New York City, has discovered a new wrinkle on gravitational waves tucked away in the intricacies of the equations that express general relativity. This unexpected mathematical result implies that a sufficiently strong, sharp burst of gravitational radiation will itself emit gravitational waves. The extra helping of gravitational waves would leave an imprint in the form of a permanent shift in the relative positions of test masses in an Earth-based gravitational-wave detector after the passage of a wave.

Christodoulou's finding has both theoretical and practical implications. "It's of considerable interest from the point of view of understanding the nature of gravity," says Kip S. Thorne of the California Institute of Technology in Pasadena.

"It's an exciting and unanticipated result," says astrophysicist Jeremiah P. Ostriker of Princeton University. Because current strategies for detecting gravitational waves focus on the observation of rapid oscillations, the idea that the passage of a wave may also cause a permanent displacement of objects opens up the possibility of developing simpler, less expensive detection techniques, he notes.

Christodoulou originally encountered this gravitational-wave effect as a mathematical formula derived from the Einstein equations describing gravitational fields located far from their sources. "I discovered this result in an abstract form [nearly two years ago], but I didn't know what it meant [physically]," Christodoulou says.

A year later, while reading to pass the time on a train commute between New York City and suburban New Jersey, he happened upon a magazine article about gravitational-wave detection. The article's discussion of the difficulties involved in observing rapidly fluctuating gravitational waves triggered a chain of reasoning that suggested his formula correspond to some kind of permanent, potentially observable displacement of objects.

Subsequent discussions with Thorne and several other theorists gradually clarified the physical meaning of Christodoulou's result. "It took a long time for it to make sense to me and for us to understand what was going on," Thorne says. "It was entirely an issue of communication and translating from a language in one community [mathematics] to the language of another [astrophysics]."

Christodoulou describes his discovery and its implications in the Sept. 16 PHYSICAL REVIEW LETTERS, and Thorne has prepared a paper that translates the results into language more accessible to astrophysicists.

A pair of orbiting, coalescing neutron stars or black holes represents the most likely source of gravitational radiation strong enough to produce an observable effect. As the two objects orbit each other, they emit gravitational waves and gradually draw closer together. Eventually the objects slam into each other, and the system sends out a final, intense burst of gravitational radiation. This, in turn, produces the secondary "Christodoulou signal."

An Earth-based sensor tuned to such an event would detect a slow, overall change in the local gravitational field superimposed on the rapidly fluctuating signal from the primary burst itself. Theorists predict that in some instances, the permanent displacement of masses in the detector -- called the "memory" of the gravitational-wave burst -- would be as large as the maximum displacement during the burst-generated fluctuations.

"The Christodoulou effect can yield measurable amplitudes and provides us with another way of looking at certain components of a gravitational wave from a coalescing black-hole binary," says astrophysicist Stuart L. Shapiro of Cornell University.

Although researchers have designed detectors, such as the proposed Laser Interferometer Gravitational Wave Observatory, without taking the Christodoulou effect into consideration, these devices should nonetheless detect both rapid fluctuations and permanent changes in a gravitational field. "If detectors are built sensitive enough to measure the previously estimated amplitudes from coalescing neutron stars, they will also be able to see this Christodoulou effect," Shapiro says.

"[The effect] can have some impact on the data analysis algorithm that one might use in a given situation," Thorne says. "There are also likely to be special cases where the secondary wave may turn out to be easier to detect than the primary burst of waves, but I think they will be rare."