Black holes, quantum information, and unitary evolution

The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and in particular unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with "minimal" departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert space approach an apparently "coarser" form of localization can be described in terms of tensor decompositions of the Hilbert space of the complete system. This suggests a general framework in which to seek a consistent description of quantum gravity, and approximate emergence of spacetime. Other possible aspects of such a framework -- in particular symmetries -- are briefly discussed.Comment: 39 pages, 5 figures. v2: refs added, very minor clarifications v3: few small changes to agree with published version v4: corrected sign in eq. 3.3

Quantization in black hole backgrounds

Quantum field theory in a semiclassical background can be derived as an approximation to quantum gravity from a weak-coupling expansion in the inverse Planck mass. Such an expansion is studied for evolution on "nice-slices" in the spacetime describing a black hole of mass M. Arguments for a breakdown of this expansion are presented, due to significant gravitational coupling between fluctuations, which is consistent with the statement that existing calculations of information loss in black holes are not reliable. For a given fluctuation, the coupling to subsequent fluctuations becomes of order unity by a time of order M^3. Lack of a systematic derivation of the weakly-coupled/semiclassical approximation would indicate a role for the non-perturbative dynamics of gravity, and possibly for the proposal that such dynamics has an essentially non-local quality.Comment: 28 pages, 4 figures, harvmac. v2: added refs, minor clarification

Do Hot Haloes Around Galaxies Contain the Missing Baryons?

Galaxies are missing most of their baryons, and many models predict these baryons lie in a hot halo around galaxies. We establish observationally motivated constraints on the mass and radii of these haloes using a variety of independent arguments. First, the observed dispersion measure of pulsars in the Large Magellanic Cloud allows us to constrain the hot halo around the Milky Way: if it obeys the standard NFW profile, it must contain less than 4-5% of the missing baryons from the Galaxy. This is similar to other upper limits on the Galactic hot halo, such as the soft X-ray background and the pressure around high velocity clouds. Second, we note that the X-ray surface brightness of hot haloes with NFW profiles around large isolated galaxies is high enough that such emission should be observed, unless their haloes contain less than 10-25% of their missing baryons. Third, we place constraints on the column density of hot haloes using nondetections of OVII absorption along AGN sightlines: in general they must contain less than 70% of the missing baryons or extend to no more than 40 kpc. Flattening the density profile of galactic hot haloes weakens the surface brightness constraint so that a typical L$_*$ galaxy may hold half its missing baryons in its halo, but the OVII constraint remains unchanged, and around the Milky Way a flattened profile may only hold $6-13$ of the missing baryons from the Galaxy ($2-4 \times 10^{10} M_{\odot}$). We also show that AGN and supernovae at low to moderate redshift - the theoretical sources of winds responsible for driving out the missing baryons - do not produce the expected correlations with the baryonic Tully-Fisher relationship and so are insufficient to explain the missing baryons from galaxies. We conclude that most of missing baryons from galaxies do not lie in hot haloes around the galaxies, and that the missing baryons never fell into the potential wells of protogalaxies in the first place. They may have been expelled from the galaxies as part of the process of galaxy formation.Comment: accepted for publication in the Astrophysical Journa

Weak Lensing Mass Reconstruction using Wavelets

This paper presents a new method for the reconstruction of weak lensing mass maps. It uses the multiscale entropy concept, which is based on wavelets, and the False Discovery Rate which allows us to derive robust detection levels in wavelet space. We show that this new restoration approach outperforms several standard techniques currently used for weak shear mass reconstruction. This method can also be used to separate E and B modes in the shear field, and thus test for the presence of residual systematic effects. We concentrate on large blind cosmic shear surveys, and illustrate our results using simulated shear maps derived from N-Body Lambda-CDM simulations with added noise corresponding to both ground-based and space-based observations.Comment: Accepted manuscript with all figures can be downloaded at: http://jstarck.free.fr/aa_wlens05.pdf and software can be downloaded at http://jstarck.free.fr/mrlens.htm

Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity

We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $\Lambda$. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Now however, the underlying colored graph $\Gamma$ lives in a two-dimensional spacelike surface $\Sigma$, and some of its links cross the black hole horizon, which is viewed as a circular boundary of $\Sigma$. Each link $\ell$ crossing the horizon is colored by a spin $j_\ell$ (at the kinematical level), and the length $L$ of the horizon is given by the sum $L=\sum_\ell L_\ell$ of the fundamental length contributions $L_\ell$ carried by the spins $j_\ell$ of the links $\ell$. We propose an estimation for the number $N^\text{BTZ}_\Gamma(L,\Lambda)$ of the Euclidean BTZ black hole microstates (defined on a fixed graph $\Gamma$) based on an analytic continuation from the case $\Lambda>0$ to the case $\Lambda<0$. In our model, we show that $N^\text{BTZ}_\Gamma(L,\Lambda)$ reproduces the Bekenstein-Hawking entropy in the classical limit. This asymptotic behavior is independent of the choice of the graph $\Gamma$ provided that the condition $L=\sum_\ell L_\ell$ is satisfied, as it should be in three-dimensional quantum gravity.Comment: 14 pages. 1 figure. Paragraph added on page 7 to clarify the horizon conditio

Gibbs' paradox and black-hole entropy

In statistical mechanics Gibbs' paradox is avoided if the particles of a gas are assumed to be indistinguishable. The resulting entropy then agrees with the empirically tested thermodynamic entropy up to a term proportional to the logarithm of the particle number. We discuss here how analogous situations arise in the statistical foundation of black-hole entropy. Depending on the underlying approach to quantum gravity, the fundamental objects to be counted have to be assumed indistinguishable or not in order to arrive at the Bekenstein--Hawking entropy. We also show that the logarithmic corrections to this entropy, including their signs, can be understood along the lines of standard statistical mechanics. We illustrate the general concepts within the area quantization model of Bekenstein and Mukhanov.Comment: Contribution to Mashhoon festschrift, 13 pages, 4 figure

Weighing the Light Gravitino Mass with Weak Lensing Surveys

We explore the discovery potential of light gravitino mass m_{3/2} by combining future cosmology surveys and collider experiments. The former probe the imprint of light gravitinos in the cosmic matter density field, whereas the latter search signatures of a supersymmetry breaking mechanism. Free-streaming of light gravitinos suppresses the density fluctuations at galactic and sub-galactic length scales, where weak gravitational lensing can be used as a powerful probe. We perform numerical simulations of structure formation to quantify the effect. We then run realistic ray-tracing simulations of gravitational lensing to measure the cosmic shear in models with light gravitino. We forecast the possible reach of future wide-field surveys by Fisher analysis; the light gravitino mass can be determined with an accuracy of m_{3/2}=4\pm 1 eV by a combination of the Hyper Suprime Cam survey and cosmic microwave background anisotropy data obtained by Planck satellite. The corresponding accuracy to be obtained by the future Large Synoptic Survey Telescope is \delta m_{3/2}=0.6 eV. Data from experiments at Large Hadron Collider at 14 TeV will provide constraint at m_{3/2} \simeq 5 eV in the minimal framework of gauge-mediated supersymmetry breaking (GMSB) model. We conclude that a large class of the GMSB model can be tested by combining the cosmological observations and the collider experiments.Comment: 22 pages, 9 figure