Gravitation,thermodynamics, and the bound on viscosity

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, η/s = 1/4π. It was conjectured recently that all fluids conform to the lower bound η/s ≥ 1/4π. This conjectured bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.     

Analytic treatment of the network synchronization problem with time delays

Motivated by novel results in the theory of network synchronization, we analyze the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. We determine analytically the fundamental limit of synchronization efficiency in a noisy environment with uniform time delays. We show that the optimal efficiency of the network is achieved for λτ = π(3/2)/(2√π + 4) ≈ 0.738, where λ is the coupling strength (relaxation coefficient) and τ is the characteristic time delay in the communication between pairs of nodes. Our analysis reveals the underlying mechanism responsible for the trade-off phenomena observed in recent numerical simulations of network synchronization problems.     

Analytic study of self-gravitating polytropic spheres with light rings

Ultra-compact objects describe horizonless solutions of the Einstein field equations which, like black-hole spacetimes, possess null circular geodesics (closed light rings). We study analytically the physical properties of spherically symmetric ultra-compact isotropic fluid spheres with a polytropic equation of state. It is shown that these spatially regular horizonless spacetimes are generally characterized by two light rings \(\{r^{\text {inner}}_{\gamma },r^{\text {outer}}_{\gamma }\}\) with the property \(\mathcal{C}(r^{\text {inner}}_{\gamma })\le \mathcal{C}(r^{\text {outer}}_{\gamma })\), where \(\mathcal{C}\equiv m(r)/r\) is the dimensionless compactness parameter of the self-gravitating matter configurations. In particular, we prove that, while black-hole spacetimes are characterized by the lower bound \(\mathcal{C}(r^{\text {inner}}_{\gamma })\ge 1/3\), horizonless ultra-compact objects may be characterized by the opposite dimensionless relation \(\mathcal{C}(r^{\text {inner}}_{\gamma })\le 1/4\). Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotný et al. (Phys Rev D 95:043009, 2017).     

Quasinormal resonances of near-extremal Kerr–Newman black holes

We study analytically   the fundamental resonances of near-extremal, slowly rotating Kerr–Newman black holes. We find a simple analytic expression for these black-hole quasinormal frequencies in terms of the black-hole physical parameters: ω=mΩ−2iπTBH(l+1+n)$\omega =m\Omega -2i\pi T_{\mathrm{BH}}(l+1+n)$, where TBH$T_{\mathrm{BH}}$ and Ω are the temperature and angular velocity of the black hole. The mode parameters l and m   are the spheroidal harmonic index and the azimuthal harmonic index of a co-rotating mode, respectively. This analytical formula is valid in the regime ℑω?ℜω?M⁻¹$\Im \omega ?\Re \omega ?M^{\mathrm{-1}}$, where M is the black-hole mass.     

Return of the quantum cosmic censor

The influential theorems of Hawking and Penrose demonstrate that spacetime singularities are ubiquitous features of general relativity, Einstein's theory of gravity. The utility of classical general relativity in describing gravitational phenomena is maintained by the cosmic censorship principle. This conjecture, whose validity is still one of the most important open questions in general relativity, asserts that the undesirable spacetime singularities are always hidden inside of black holes. In this Letter we reanalyze extreme situations which have been considered as counterexamples to the cosmic censorship hypothesis. In particular, we consider the absorption of fermion particles by a spinning black hole. Ignoring quantum effects may lead one to conclude that an incident fermion wave may over spin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when quantum effects are properly taken into account, the integrity of the black-hole event horizon is irrefutable. This observation suggests that the cosmic censorship principle is intrinsically a quantum phenomena.     

On closures of orbits and arithmetic of quaternions

ForG=PGL₂(ℚ _p )×PGL₂ ℚ we study the closures of orbits under the maximal split Cartan subgroup ofG in homogeneous spacesΓ\G. We show that if a closure of an orbit contains a closed orbit then the orbit is either dense or closed. We show the relation of this to divisibility properties of integral quaternions and other lattices. Sponsored in part by the Edmund Landau Center for Research in Mathematical Analysis supported by the Minerva Foundation (Germany). Research at MSRI supported by NSF grant DMS8505550.     

Reactions in dry media: reactions of cholesterol and cholestanes on silica bound ferric chloride : Cholestane—diacholestene rearrangement

Reaction of cholesterol with silica bound FeCl₃ resulted in a mixture of 3β-cholesteryl chloride and dicholesteryl ether.5-Cholestene and hydroxy- and halogeno-substituted cholestane derivatives gave on heating at 100° with this reagent a 1:1 mixture of 20-epimeric diacholestenes. The 20(R)-isomer gave with meta-chloroperbenzoic acid 20(R)-α-epoxide, while the 20(S)-gave a mixture of 20(S)-α- and 20(S)-β-epoxides.5α,6β-Dihydrocholestane reacted with the FeCl₃/SiO₂ under milder conditions (50°) to give 6β-hydroxy-20(R)-diacholestene, which was converted to the 20(R)-diacholestene.     

Protein synthesis by solid-phase chemical ligation using a safety catch linker

The native chemical ligation reaction has been used extensively for the synthesis of the large polypeptides that correspond to folded proteins and domains. The efficiency of the synthesis of the target protein is highly dependent on the number of peptide segments in the synthesis. Assembly of proteins from multiple components requires repeated purification and lyophilization steps that give rise to considerable handling losses. In principle, performing the ligation reactions on a solid support would eliminate these inefficient steps and increase the yield of the protein assembly. A new strategy is described for the assembly of large polypeptides on a solid support that utilizes a highly stable safety catch acid-labile linker. This amide generating linker is compatible with a wide range of N-terminal protecting groups and ligation chemistries. The utility of the methodology is demonstrated by a three-segment synthesis of vMIP I, a chemokine that contains all 20 natural amino acids and has two disulfide bonds. The crude polypeptide product was recovered quantitatively from the solid support and purified in 20%-recovered yield. This strategy should facilitate the synthesis of large polypeptides and should find useful applications in the assembly of protein libraries.     

Chemical Synthesis of Proteins with Non‐Strategically Placed Cysteines Using Selenazolidine and Selective Deselenization

Although native chemical ligation has enabled the synthesis of hundreds of proteins, not all proteins are accessible through typical ligation conditions. The challenging protein, 125‐residue human phosphohistidine phosphatase 1 (PHPT1), has three cysteines near the C‐terminus, which are not strategically placed for ligation. Herein, we report the first sequential native chemical ligation/deselenization reaction. PHPT1 was prepared from three unprotected peptide segments using two ligation reactions at cysteine and alanine junctions. Selenazolidine was utilized as a masked precursor for N‐terminal selenocysteine in the middle segment, and, following ligation, deselenization provided the native alanine residue. This approach was used to synthesize both the wild‐type PHPT1 and an analogue in which the active‐site histidine was substituted with the unnatural and isosteric amino acid β‐thienyl‐l ‐alanine. The activity of both proteins was studied and compared, providing insights into the enzyme active site.