Modulated Hawking radiation and a nonviolent channel for information release

Unitarization of black hole evaporation requires that quantum information escapes a black hole; an important question is to identify the mechanism or channel by which it does so. Accurate counting of black hole states via the Bekenstein-Hawking entropy would indicate this information should be encoded in radiation with average energy flux matching Hawking's. Information can be encoded with no change in net flux via fine-grained modulation of the Hawking radiation. In an approximate effective field theory description, couplings to the stress tensor of the black hole atmosphere that depend on the internal state of the black hole are a promising alternative for inducing such modulation. These can be picturesquely thought of as due to state-dependent metric fluctuations in the vicinity of the horizon. Such couplings offer the prospect of emitting information without extra energy flux, and can be shown to do so at linear order in the couplings, with motivation given for possible extension of this result to higher orders. The potential advantages of such couplings to the stress tensor thus extend beyond their universality, which is helpful in addressing constraints from black hole mining.Comment: 10 pages of text + refs. v2: cleaner figure. v3: minor updates to match published versio

Models for unitary black hole disintegration

Simple models for unitary black hole evolution are given in an effective Hilbert-space description, parameterizing a possible minimal relaxation of locality, with respect to semiclassical black hole geometry.Comment: 7 pages of text, plus refs. v2: minor rev

Hawking radiation, the Stefan-Boltzmann law, and unitarization

Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the "firewall" argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale. This is potentially important, since Hawking radiation needs to be modified to restore unitarity, and a natural assumption is that the scales relevant to such modifications are comparable to those governing the Hawking radiation. Moreover, related discussion suggests a resolution to questions regarding extra energy flux in "nonviolent" scenarios, that does not spoil black hole thermodynamics as governed by the Bekenstein-Hawking entropy.Comment: 7 pages + references. v2: references added, v3: minor typos corrected. To appear in Physics Letter

Designing and Executing a Fair Revlon Auction

The author analyzes the role of corporate boards of directors during takeover and control transactions, specifically in regards to auctions. Courts have consistently considered unfair auction attempts in light of the importance of the business judgment rule. The author examines Delaware case law and highlights the Revlon case, which holds that once an auction begins, the board’s duty shifts from preservation of the corporate entity to maximization of value shareholders will receive from the sale. The author argues that a good understanding of auction theory will not only give courts a better perspective through which to examine directors’ actions but also will give directors more information on how to run auctions and respond to bids

Beyond the Planck scale

I outline motivations for believing that important quantum gravity effects lie beyond the Planck scale at both higher energies and longer distances and times. These motivations arise in part from the study of ultra-high energy scattering, and also from considerations in cosmology. I briefly summarize some inferences about such ultra-planckian physics, and clues we might pursue towards the principles of a more fundamental theory addressing the known puzzles and paradoxes of quantum gravity.Comment: 11 pages, 1 figure. To appear in the proceedings of the XXV Max Born Symposium, "The Planck Scale," Wroclaw, Polan