Separability and radial asymptotic behaviour of the Dirac equation and integral spectral representation for the Dirac propagator in the 5D Myers-Perry geometry in Eddington-Finkelstein-type coordinates

We analytically extend the 5D Myers-Perry metric through the event and Cauchy horizons by defining Eddington-Finkelstein-type coordinates. We then use the orthonormal frame formalism to formulate and perform separation of variables on the massive Dirac equation, and analyse the asymptotic behaviour at the horizons and at infinity of the solutions to the radial ODE thus obtained, as was done by R\"oken in the Kerr geometry. Using the essential self-adjointness result of Finster and R\"oken and Stone's formula, we obtain an integral spectral representation of the Dirac propagator in terms of resolvents of the Dirac Hamiltonian, which can in turn be expressed in terms of Green's functions of the radial ODE.Comment: 22 page

Local Dirac energy decay in the 5D Myers-Perry geometry using an integral spectral representation for the Dirac propagator

We consider the massive Dirac equation in the exterior region of the 5-dimensional Myers-Perry black hole. Using the resulting ODEs obtained from the separation of variables of the Dirac equation, we construct an integral spectral representation for the solution of the Cauchy problem with compactly supported smooth initial data. We then prove that the probability of presence of a Dirac particle to be in any compact region of space decays to zero as $t\to\infty$, in analogy with the case of the Dirac operator in the Kerr-Newman geometry.Comment: 13 pages, fixed typographic error

Classification of superpotentials for cohomogeneity one Ricci solitons

We classify superpotentials for the Hamiltonian system corresponding to the cohomogeneity one gradient Ricci soliton equations. Aside from recovering known examples of superpotentials for steady solitons, we find a new superpotential on a specific case of the B\'erard-Bergery-Calabi ansatz. The latter is used to obtain an explicit formula for a steady complete soliton with an equidistant family of hypersurfaces given by circle bundles over $S^2\times S^2$. There are no superpotentials in the non-steady case in dimensions greater than 2, even if polynomial coefficients are allowed. We also briefly discuss generalised first integrals and the limitations of some known methods of finding them.Comment: 28 page

The dependence of the IR-radio correlation on the metallicity

We have compiled a sample of 26 metal-poor galaxies with 12 + log(O/H) < 8.1 with both infrared continuum and 1.4 GHz radio continuum data. By comparing to galaxies at higher metallicity, we have investigated the dependence on the metallicity of the IR-radio relationship at 24 um, 70 um, 100 um and 160 um bands as well as the integrated FIR luminosity. It is found that metal-poor galaxies have on average lower qIR than metal-rich ones with larger offsets at longer IR wavelengths, from -0.06 dex in q24um to -0.6 dex in q160um. The qIR of all galaxies as a whole at 160 um show positive trends with the metallicity and IR-to-FUV ratio, and negative trends with the IR color, while those at lower IR wavelengths show weaker correlations. We proposed a mechanism that invokes combined effects of low obscured-SFR/total-SFR fraction and warm dust temperature at low metallicity to interpret the above behavior of qIR, with the former reducing the IR radiation and the latter further reducing the IR emission at longer IR wavelength. Other mechanisms that are related to the radio emission including the enhanced magnetic field strength and increased thermal radio contribution are unable to reconcile the IR-wavelength-dependent differences of qIR between metal-poor and metal- rich galaxies. In contrast to qIR, the mean total-SFR/radio ratio of metal-poor galaxies is the same as the metal-rich one, indicating the 1.4 GHz radio emission is still an effective tracer of SFRs at low metallicity.Comment: 25 pages, 11 figures, 4 tables. ApJ in pres

2-Methyl-2,4-di-4-pyridyl-2,3-dihydro-1H-1,5-benzodiazepine acetic acid solvate

In the title compound, C20H18N4·CH3COOH, the benzene ring forms dihedral angles of 81.34 (11) and 54.32 (11)° with the two pyridine rings. In the crystal, inter­molecular O—H⋯N hydrogen bonding links one 1,5-benzodiazepine mol­ecule and one acetic acid solvent mol­ecule into a dimer. These dimers, related by translation along the b axis, are further linked into chains via weak inter­molecular N—H⋯N hydrogen bonds