**By Malcolm W. Browne**

**The New York Times**
**February 12, 1997**

Dr. Stephen W. Hawking of Cambridge University in England -- the brilliant theorist regarded as one of Albert Einstein's intellectual successors -- has conceded defeat in a famous bet he made six years ago on a matter of cosmic significance.

The bet he made with two professors at the California Institute of Technology was that naked singularities could not exist, and now, it seems, they could -- maybe.

During a visit to Caltech last week, Dr. Hawking, the author of ''A Brief History of Time,'' a book that delves into the origins of the universe, conceded defeat ''on a technicality'' to Dr. John P. Preskill and Dr. Kip S. Thorne. The stake was for $:100, plus clothing ''embroidered with a suitable concessionary message.''

A singularity is a mathematical point at which space and time are infinitely distorted, where matter is infinitely dense, and where the rules of relativistic physics and quantum mechanics break down. Singularities are believed to lurk at the hearts of black holes, which conceal their existence from the outer world. A naked singularity would be a singularity bereft of a concealing black-hole shell, and therefore visible, in principle, to outside observers.

Although neither light nor any other kind of signal can escape from them, a half-dozen or so black holes have been revealed by their gravitational effects on nearby stars. Black holes have also betrayed their presence by sucking in matter from nearby space. As it spirals toward the hole, the matter is heated to incandescence and the emission of X-rays and other radiation has been detected by observatories in space and on the ground.

Dr. Hawking, Dr. Preskill and Dr. Thorne are leaders in the study of relativity as applied to cosmology, and they meet often at scientific symposiums. Subjects they take up often include conjectures about time machines, relativistic tunnels called wormholes to distant points in space and time, the origin of the universe and many other intriguing questions.

It was at such a meeting in 1991 that Dr. Hawking, although he was unable to prove his disbelief in naked singularities, proposed his bet to Dr. Preskill and Dr. Thorne. Because of the issue's far-reaching theoretical implications, news of their bet spread among physicists throughout the world.

Dr. Preskill and Dr. Thorne won the bet last week on the strength of supercomputer calculations by Dr. Matthew Choptuik of the University of Texas in Austin. Dr. Choptuik concluded from his mathematical analysis that there could be special circumstances in which a naked singularity might be created from a collapsing black hole, either by nature or perhaps even by some advanced civilization. The chance of this happening, Dr. Choptuik said in an interview, would be comparable to standing a pencil upright on its sharpened tip. Although it is improbable, it is theoretically possible.

No one has ever seen or directly detected a singularity, much less a naked singularity. The very word ''singularity'' reflects the failure of scientists to explain adequately what this bizarre object is, what it does, and how it stands in relation to the rest of the universe or parallel universes.

Singularities within black holes are deduced from relativity theory as the result of the gravitational collapse of degenerate stars 1.6 times the mass of the sun or greater. At a certain point, the space around the collapsing object becomes infinitely curved, trapping any light that might impinge on it and forming a black hole.

Some theorists believe in a cosmic censorship that is supposed to thwart all efforts to see naked singularities. But some weighty questions may be resolved by investigating naked singularities, including an explanation of the Big Bang, a naked singularity that is believed to have created our universe 15 billion years ago (and perhaps an infinity of other universes in other spaces and times).

Astrophysicists regard the existence of singularities as a baffling but inevitable consequence of Einstein's theory of gravity.

The problem for astrophysicists seeking direct information about singularities within known black holes is that the black holes are bounded by event horizons that forever conceal everything inside them, including their central pointlike cores: their singularities. If the event horizon could be eliminated from a black hole, the singularity inside would be laid bare.

If such a naked singularity somehow came into being, Dr. Preskill said in an interview, ''you might get a flash or explosion -- some highly luminous event that you might have a hope of seeing.''

Several astrophysical theorists, including Dr. John A. Wheeler of Princeton University and Dr. Roger Penrose of Oxford University, have cast doubt on the existence of naked singularities. Dr. Penrose has hypothesized that cosmic censorship conspires to shield singularities from any direct observation.

Dr. Hawking, who is paralyzed but who speaks electronically by tapping out words on a telegraph key, said that even in light of the new calculations, there is no ''generic'' way in which naked singularities might form according to the known laws of physics.

But Dr. Preskill replied: ''Stephen, I'm surprised to hear you, of all people, say that. There's one naked singularity that we all agree existed: the Big Bang. The universe itself.''

Dr. Hawking declined to yield unequivocally on his bet with Dr. Preskill and Dr. Thorne. He made another bet with the Caltech physicists last week that although a very limited set of conditions had been found for creating naked singularities, no general conditions would be found.

And what was supposed to be the concessionary message from the bet that Dr. Hawking had printed on the T-shirts was hardly an admission of defeat: ''Nature Abhors a Naked Singularity.''

''All this has a very serious undertone,'' Dr. Preskill said. ''If we are ever to understand singularities, we must do so in terms of some yet-to-be-discovered theory of quantum gravity, and that would be a revolution in physics. We're not there yet.''

Copyright 1997 The New York Times Company

February 12, 1997