On Spin Dependence of Relativistic Acoustic Geometry

This work makes the first ever attempt to understand the influence of the black hole background space-time in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, the role of the spin angular momentum of the astrophysical black hole (the Kerr parameter $a$ -- a representative feature of the background black hole metric) in estimating the value of the acoustic surface gravity (the representative feature of the corresponding analogue space time) has been investigated for axially symmetric inflow of hydrodynamic fluid onto a rotating black hole. Since almost all astrophysical black holes are supposed to posses some degree of intrinsic rotation, the influence of the Kerr parameter on classical analogue models is very important to understand. For certain values of the initial boundary conditions describing the aforementioned flow, more than one acoustic horizons, namely two black hole type and one white hole type, may form, where the surface gravity may become formally infinite at the acoustic white hole. The connection between the corresponding analogue Hawking temperature with astrophysically relevant observables associated with the spectral signature has been discussed.Comment: 22 pages, 11 figures, Comments welcom

Air oxygenation chemistry of 4-TBC catalyzed by chloro bridged dinuclear copper(ii) complexes of pyrazole based tridentate ligands: synthesis, structure, magnetic and computational studies.

Four dinuclear bis(μ-Cl) bridged copper(ii) complexes, [Cu(2)(μ-Cl)(2)(L(X))(2)](ClO(4))(2) (L(X) = N,N-bis[(3,5-dimethylpyrazole-1-yl)-methyl]benzylamine with X = H(1), OMe(2), Me(3) and Cl(4)), have been synthesized and characterized by the single crystal X-ray diffraction method. In these complexes, each copper(ii) center is penta-coordinated with square-pyramidal geometry. In addition to the tridentate L(X) ligand, a chloride ion occupies the last position of the square plane. This chloride ion is also bonded to the neighboring Cu(ii) site in its axial position forming an SP-I dinuclear Cu(ii) unit that exhibits small intramolecular ferromagnetic interactions and supported by DFT calculations. The complexes 1-3 exhibit methylmonooxygenase (pMMO) behaviour and oxidise 4-tert-butylcatechol (4-TBCH(2)) with molecular oxygen in MeOH or MeCN to 4-tert-butyl-benzoquinone (4-TBQ), 5-methoxy-4-tert-butyl-benzoquinone (5-MeO-4-TBQ) as the major products along with 6,6'-Bu(t)-biphenyl-3,4,3',4'-tetraol and others as minor products. These are further confirmed by ESI- and FAB-mass analyses. A tentative catalytic cycle has been framed based on the mass spectral analysis of the products and DFT calculations on individual intermediates that are energetically feasible