Unitarity and the Hilbert space of quantum gravity

Under the premises that physics is unitary and black hole evaporation is complete (no remnants, no topology change), there must exist a one-to-one correspondence between states on future null and timelike infinity and on any earlier spacelike Cauchy surface (e.g., slices preceding the formation of the hole). We show that these requirements exclude a large set of semiclassical spacetime configurations from the Hilbert space of quantum gravity. In particular, the highest entropy configurations, which account for almost all of the volume of semiclassical phase space, would not have quantum counterparts, i.e. would not correspond to allowed states in a quantum theory of gravity.Comment: 7 pages, 3 figures, revtex; minor changes in v2 (version published in Class. Quant. Grav.

Stable quantum systems in anti-de Sitter space: Causality, independence and spectral properties

If a state is passive for uniformly accelerated observers in n-dimensional anti-de Sitter space-time (i.e. cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a "geodesic causal structure" on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded spacetime regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space-time localization. Examples are provided of models satisfying the hypotheses of these theorems.Comment: 27 pages, 1 figure: dedicated to Jacques Bros on the occasion of his 70th birthday. Revised version: typos corrected; as to appear in J. Math. Phy

On multi-graviton and multi-gravitino gauge theories

This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime dimensions. General possibilities for multiplication rules and coupling constants are simultaneously accommodated by regarding the set of fields equivalently as a single algebra-valued spin-2 field and single algebra-valued spin-3/2 field, where the underlying algebra is factorized into a field-coupling part and an internal multiplication part. The condition that there exist a gauge invariant Lagrangian (to within a divergence) for these algebra-valued fields is used to derive determining equations whose solutions give all allowed deformation terms, yielding nonlinear field equations and nonabelian gauge symmetries, together with all allowed formal multiplication rules as needed in the Lagrangian for demonstration of invariance under the gauge symmetries and for derivation of the field equations. In the case of spin-2 fields alone, the main result of this analysis is that all deformations (without any higher derivatives than appear in the linear theory) are equivalent to an algebra-valued Einstein gravity theory. By a systematic examination of factorizations of the algebra, a novel type of nonlinear gauge theory of two or more spin-2 fields is found, where the coupling for the fields is based on structure constants of an anticommutative, anti-associative algebra, and with formal multiplication rules that make the fields anticommuting (while products obey anti-associativity). Supersymmetric extensions of these results are obtained in the more general case when spin-3/2 fields are included.Comment: 33 pages (latex

The Effect of Inefficient Accretion on Planetary Differentiation

Pairwise collisions between terrestrial embryos are the dominant means of accretion during the last stage of planet formation. Hence, their realistic treatment in N-body studies is critical to accurately model the formation of terrestrial planets and to develop interpretations of telescopic and spacecraft observations. In this work, we compare the effects of two collision prescriptions on the core-mantle differentiation of terrestrial planets: a model in which collisions are always completely accretionary (``perfect merging'') and a more realistic model based on neural networks that has been trained on hydrodynamical simulations of giant impacts. The latter model is able to predict the loss of mass due to imperfect accretion and the evolution of non-accreted projectiles in hit-and-run collisions. We find that the results of the neural-network model feature a wider range of final core mass fractions and metal-silicate equilibration pressures, temperatures, and oxygen fugacities than the assumption of perfect merging. When used to model collisions in N-body studies of terrestrial planet formation, the two models provide similar answers for planets more massive than 0.1 Earth's masses. For less massive final bodies, however, the inefficient-accretion model predicts a higher degree of compositional diversity. This phenomenon is not reflected in planet formation models of the solar system that use perfect merging to determine collisional outcomes. Our findings confirm the role of giant impacts as important drivers of planetary diversity and encourage a realistic implementation of inefficient accretion in future accretion studies.Comment: 21 pages, 2 tables, 7 figures. Published open access on PSJ: https://iopscience.iop.org/article/10.3847/PSJ/abf0a

Hamiltonian thermodynamics of a Lovelock black hole

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kucha\v{r}-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonical ensemble. Whenever the partition function is dominated by a Euclidean black hole solution, the entropy is given by the Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low temperature limit the system exhibits a dominant classical solution that has no counterpart in Einstein's theory. The asymptotically flat space limit of the partition function does not exist. The results indicate qualitative robustness of the thermodynamics of five-dimensional Einstein theory upon the addition of a nontrivial Lovelock term.Comment: 22 pages, REVTeX v3.

Environment-mediated structure, surface redox activity and reactivity of ceria nanoparticles

Nanomaterials, with potential application as bio-medicinal agents, exploit the chemical properties of a solid, with the ability to be transported (like a molecule) to a variety of bodily compartments. However, the chemical environment can change significantly the structure and hence properties of a nanomaterial. Accordingly, its surface reactivity is critically dependent upon the nature of the (biological) environment in which it resides. Here, we use Molecular Dynamics (MD) simulation, Density Functional Theory (DFT) and aberration corrected TEM to predict and rationalise differences in structure and hence surface reactivity of ceria nanoparticles in different environments. In particular we calculate reactivity 'fingerprints' for unreduced and reduced ceria nanoparticles immersed in water and in vacuum. Our simulations predict higher activities of ceria nanoparticles, towards oxygen release, when immersed in water because the water quenches the coordinative unsaturation of surface ions. Conversely, in vacuum, surface ions relax into the body of the nanoparticle to relieve coordinative unsaturation, which increases the energy barriers associated with oxygen release. Our simulations also reveal that reduced ceria nanoparticles are more active towards surface oxygen release compared to unreduced nanoceria. In parallel, experiment is used to explore the activities of ceria nanoparticles that have suffered a change in environment. In particular, we compare the ability of ceria nanoparticles, in an aqueous environment, to scavenge superoxide radicals compared to the same batch of nanoparticles, which have first been dried and then rehydrated. The latter show a distinct reduction in activity, which we correlate to a change in the redox chemistry associated with moving between different environments. The reactivity of ceria nanoparticles is therefore not only environment dependent, but is also influenced by the transport pathway or history required to reach the particular environment in which its reactivity is to be exploited. © 2013 The Royal Society of Chemistry

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

Laminin and α-Dystroglycan Mediate Acetylcholine Receptor Aggregation via a MuSK-Independent Pathway

Specific isoforms of laminin (LN) are concentrated at neuromuscular junctions (NMJs) where they may participate in synaptic organization or function. In myotubes from C2 cells, LN is concentrated within the majority of spontaneous acetylcholine receptor (AChR) aggregates. Neural agrin substantially increases this colocalization, suggesting that agrin can recruit LN into AChR aggregates. Addition of LN to C2 myotubes induces a more than twofold increase in the number of AChR aggregates. These aggregates have a larger size and are more dense than are those induced by agrin, suggesting that LN is involved in the growth and/or stabilization of AChR aggregates. Consistent with this hypothesis, an antiserum to LN reduces the size of individual AChR aggregates but increases their number. In C2 myotubes, extracellular matrix receptors containing the integrin beta1 subunit are poorly colocalized with AChR aggregates, suggesting that integrins may not be involved in LN-induced aggregation. In contrast, almost all AChR aggregates are associated with dystroglycan immunoreactivity, and monoclonal antibody (mAb) IIH6 against alpha-dystroglycan (alpha-DG), a LN and agrin receptor, causes a concentration-dependent inhibition of LN-induced aggregation. Moreover, S27 cells, which lack a functional alpha-DG, and two C2-derived cell lines expressing antisense DG mRNA fail to aggregate AChRs in response to LN. Finally, LN-induced AChR aggregation does not involve the phosphorylation of the muscle-specific tyrosine kinase receptor (MuSK) or the AChR beta subunit. We hypothesize that the interaction of LN with alpha-DG contributes to the growth and/or stabilization of AChR microaggregates into macroaggregates at the developing NMJ via a MuSK-independent mechanism