## Stephen Hawking Presents New Idea On How Information Could Escape Black Holes

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[Stephen Hawking Presents New Idea On How Information Could Escape Black Holes]

**[Stephen William Hawking:]** Source: LYBIO.net

Can you hear me?

Yes, sir.

Yes, sir.

**[Stephen Hawking:]**

Forty years ago I wrote a paper, braved on the predictability of gravitational collapse in which I claimed there would be loss of predictability of the final state if a black hole evaporated completely. This was because one could not measure the quantum state of what fell into the black hole. The loss of information would have meant the outgoing radiation is in a mixed state and the S-Matrix was non-unitary.

The paper was very controversial. It was rejected by the physical review and accepted only after much argument and a delay of a year. Since the publication of the paper, the AdS/CFT correspondence has shown there is no information loss. This is the information paradox. How does the information of the quantum state of the in-falling particles reemerge in the outgoing radiation?

This has been an outstanding problem in theoretical physics for the last forty years. Despite a large number of papers, see the AMPS Firewall paper for a list, no satisfactory resolution has been advanced. I propose that the information is stored, not in the interior of the black hole as one might expect, but on this boundary the event horizon in the form of supertranslations of the horizon.

This is a form of holography, recording the state of a four-dimensional region on its boundary, the horizon. The concept of supertranslations was introduced in 1962 by Bondi, Metzner and Sachs BMS to describe the asymptotic group of asymptotically flat space in the presence of gravitational radiation. The BMS group is the semi-direct product of the Lorentz group with supertranslations.

A supertranslation alpha moves each point [in] the future null infinity a distance alpha to the future along the null geodesic generators of future null infinities tri plus while keeping theta and phi on the 2-sphere unchanged. In other words, the retard of time U is replaced by U prime equals U plus alpha. The U-fill time and space translations form a four parameter subgroup of the infinite dimensional supertranslations, but they are not an invariant subgroup of the BMS group!

Listening to a lecture by Strominger on the BMS group at the Texas and England workshop this April, I realized that stationary black hole horizons also have supertranslations. In this case, the advanced time V is shifted by Alpha. V-prime equals V plus alpha. I discussed my idea with Malcolm Perry and Andrew Strominger. The null geodesics generators of the horizon need not have a common past end point and there is no canonical cross section of the horizon. I take the tangent vector L of the horizon to be normalized to agree with the co in-vector, time translation plus rotation, on the horizon.

Classically, a black hole is independent of its past history. I shall assume this is also true in the quantum domain. How then can a black hole emit the information about the particles that fell in? The answer, I propose, is that the information is stored in a supertranslation of the horizon that the in-going particles caused.

In this recent paper, Chaos in the Black Hole S-Matrix, Polchinski has used a shockwave approximation to calculate the shift on the generator of the horizon caused by an in-going wave packet. Even if though the calculation may need corrections, the shows in principle had the in-going particles determine a supertranslation of the horizon. This in term will determine varied delays in the emission of wave packets along each null geodesic generator. The information about in-going particles is returned, but in a chaotic and useless form. This resolves the information paradox. For all practical purposes the information is lost.

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