We present here a detailed derivation of an explicit spin-dependent expression for the bending angle of light as it traverses in the equatorial plane of a spinning black hole. We show that the deflection produced in the presence of the black hole angular momentum explicitly depends on whether the motion of the light ray is in the direction, or opposite to the spin. Compared to the zero-spin Schwarzschild case, the bending angle is greater for direct orbits, and smaller for retrograde orbits, confirming our physical intuition about the loss of left-right symmetry from a lensing perspective. In addition, we show that for higher spins, the effect is more pronounced resulting in tighter winding of direct orbits with respect to the axis of rotation, and a higher degree of unwinding of retro orbits. A direct consequence of this effect is a shift in image positions in strong gravitational lensing.
The Shevaroy Hills of northern Tamil Nadu, southern India, expose the highest-grade granulites of a prograde amphibolite facies to granulite facies deep-crustal section of Late Archaean age. These highly oxidized quartzofeldspathic garnet charnockites generally show minor high-TiO 2 biotite and amphibole as the only hydrous minerals and are greatly depleted in the incompatible elements Rb and Th. Peak metamorphic temperatures (garnet-orthopyroxene) and pressures (garnet-orthopyroxene-plagioclasequartz) are near 750°C and 8 kbar, respectively. Pervasive veinlets of K-feldspar exist throughout dominant plagioclase in each sample and show clean contact with orthopyroxene. They are suggested to have been produced by a low H 2 O activity, migrating fluid phase under granulite facies conditions, most likely a concentrated chloride/carbonate brine with high alkali mobility accompanied by an immiscible CO 2 -rich fluid. Silicate, oxide and sulphide mineral assemblages record high oxygen fugacity. Pyroxenes in the felsic rocks have high Mg/(Mg+Fe) (0.5-0.7). The major oxide mineral is ilmenite with up to 60 mole per cent exsolved hematite. Utilizing three independent oxygen barometers (ferrosilite-magnetite-quartz, ferrosilite-hematite-quartz and magnetite-hematite) in conjunction with garnet-orthopyroxene exchange temperatures, samples with XIlm Hm >0.1 yield a consistent oxygen fugacity about two log units above fayalite stability. Less oxidized samples (XIlm Hm <0.1) show some scatter with indications of having equilibrated under more reducing conditions. Temperature-f (O 2 ) arrays result in self consistent conditions ranging from 660°C and 10−16 bar to 820°C and 10−11.5 bar. These trends are confirmed by calculations based on the assemblage clinopyroxene-orthopyroxene-magnetite-ilmenite using the QUIlF program. In the most oxidized granulite samples (XIlm Hm >0.4) pyrite is the dominant sulphide and pyrrhotite is absent. Pyrite grains in these samples have marginal alteration to magnetite along the rims, signifying a hightemperature oxidation event. Moderately oxidized samples (0.1
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.