Solution of the Dirac equation in the rotating Bertotti-Robinson spacetime

The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The set of equations representing the Dirac equation in the Newman-Penrose formalism is decoupled into an axial and angular part. The axial equation, which is independent of mass, is solved exactly in terms of hypergeometric functions. The angular equation is considered both for massless (neutrino) and massive spin-(1/2) particles. For the neutrinos, it is shown that the angular equation admits an exact solution in terms of the confluent Heun equation. In the existence of mass, the angular equation does not allow an analytical solution, however, it is expressible as a set of first order differential equations apt for numerical study.Comment: 17 pages, no figure. Appeared in JMP (May, 2008

Dilatonic interpolation between Reissner-Nordstrom and Bertotti-Robinson spacetimes with physical consequences

We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordstr\"om spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable. In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.Comment: 27 pages, 4 figures, to appear in CQG

Formation of the sural nerve in foetal cadavers

The purpose of this study was to provide a morphologic description and assessmenton the formation level of the sural nerve (SN) and its components. Alsowe aimed to reveal histological features of the SN components. An anatomicalstudy of the formation of the SN was carried out on 100 limbs from 50 embalmedfoetuses. The results showed that the SN was formed by the union ofthe medial sural cutaneous nerve (MSCN) and the peroneal communicatingbranch (PCB) in 71% of the cases (Type A); the MSCN and PCB are branches ofthe tibial and common peroneal nerve (CPN) or lateral sural cutaneous nerves(LSCN), respectively. Formation level of the SN was at the distal third of the legin 43% of the cases, at the middle third of the leg in 46% of the cases, and atthe upper third of the leg in 11% of the cases. The PCB originated in the CPN in68% and the PCB originated in the LSCN in 3% of the cases. The SN wasformed only by the MSCN in 20% of the cases (Type B). Type C was divided intofour subgroups: in the first group the PCB and fibres of the posterior femoralcutaneous nerve joined the MSCN in 4% of cases; in the second group theMSCN, PCB, and sciatic nerve did not unite and coursed separately in 1% ofcases; in the third group the SN arose directly from the sciatic nerve alone andthe MSCN made a little contribution in 2% of cases; and in the fourth groupthe PCB, fibres of the sciatic nerve, and the MSCN formed the SN in 1% of thecases. The SN was formed only by the PCB in 1% of the cases (Type D). Distancesof the formation level of the SN to the intercondylar line and the lateralmalleolus were measured and also noted. A detailed knowledge of the anatomyof the SN and its contributing nerves are important in many interventionalprocedures

Exponential corrected thermodynamics of Born-Infeld BTZ black holes in massive gravity

It is known that entropy of black hole gets correction at quantum level. Universally, these corrections are logarithmic and exponential in nature. We analyze the impacts of these quantum corrections on thermodynamics of Born-Infeld BTZ black hole in massive gravity by considering both such kinds of correction. We do comparative analysis of corrected thermodynamics with their equilibrium values. Here, we find that the exponential correction yields to the second point of the first order phase transition. Also, quantum correction effects significantly on the Helmholtz free energy of larger black holes. We study the equation of state for the exponential corrected black hole to obtain a leading order virial expansion.Comment: 16 pages, 4 figure