Black holes in the generalized Proca theory

We investigate static and spherically symmetric black hole solutions in the generalized Proca theory which corresponds to the generalization of the shift-symmetric scalar–tensor Horndeski theory to the vector–tensor theory. Any solution obtained in this paper possesses a constant spacetime norm of the vector field, \(X:=-\frac{1}{2}g^{\mu \nu }A_\mu A_\nu =X_0=\mathrm{constant}\). The solutions in the theory with generalized quartic coupling \(G_4(X)\) generalize the stealth Schwarzschild and the Schwarzschild- (anti-) de Sitter solutions obtained in the theory with the nonminimal coupling to the Einstein tensor \(G^{\mu \nu } A_\mu A_\nu \). While in the vector–tensor theory with the coupling \(G^{\mu \nu }A_\mu A_\nu \) the electric charge does not explicitly affect the spacetime geometry, in more general cases with nonzero \(G_{4XX}(X_0)\ne 0\) this property does not hold in general. The solutions in the theory with generalized cubic coupling \(G_3(X)\) are given by the Schwarzschild- (anti-) de Sitter spacetime, where the dependence on \(G_3(X)\) does not appear in the metric function.     

(Ethylenediaminetetraacetic Acid)cerium(IV) [CeIV(EDTA)] Complexes with Dual Hydrophobic Binding Sites as Highly Efficient Catalysts for the Hydrolysis of Phosphodiesters

β‐Cyclodextrin (β‐CD) derivatives 1 with an amino group at C(6), C(3), or C(2) were homogeneously linked together by an ethylenediaminetetraacetic acid (EDTA) bridge (Scheme). Coordination of the linker to metal ions and cooperation of the dual cavities of 3 in binding hydrophobic guests were properly demonstrated by NMR techniques and a fluorescence‐based titration method, respectively. The hydrolysis of bis(4‐nitrophenyl) phosphate (BNPP) in the presence of Ce^IV complexes of β‐CD dimers 3 was tens of millionfold faster than that in the absence of the Ce^IV complexes. Hydrophobic binding of the β‐CD cavities was estimated to contribute to the catalysis by a factor of up to 520, and the type of modified sugar unit and the bridging positions influenced this cooperation between the β‐CD moieties and the catalytic metal center.     

Cyclodextrin as a Macrocyclic Monomer: Cationic Ring‐Opening Polymerization of O‐Permethylcyclodextrins

It has been disclosed for the first time that a cyclodextrin (CD) derivative is able to act as a macrocyclic monomer for ring‐opening polymerization to produce linear polyglucan. O‐Permethylated α‐, β‐, and γ‐CDs were found to be polymerizable with the aid of a cationic initiator, e.g., Et₃O⁺PF₆^– in dichloromethane. Interestingly, the more strained monomer (α‐ > β‐ > γ‐CD) was less reactive, which is ascribable to the characteristic shape of the CD molecule.     

Collective Hamiltonian for Multi-O(4) Model

The collective Hamiltonian up to the fourth order for multi-O(4) model is derived based on the self-consistent collective-coordinate (SCC) method,which is formulated in the framework of the time-dependent Hartree-Bogoliubov (TDHB) theory.The validity of the collective Hamiltonian is checked in the two special cases of the multi-O(4) modelthe case where the number of the shells is equal to one (a single j-shell case),and the case where the Hartree-Bogoliubov equilibrium point is spherical (the spherical case).The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.