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The hypergeneralized Heun equation in quantum field theory in curved space-times

100%
Batic D., Sandoval M.
Open Physics
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2010
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vol. 8
|
issue 3
490-497
EN
We show for the first time the role played by the hypergeneralized Heun equation (HHE) in the context of quantum field theory in curved space-times. More precisely, we find suitable transformations relating the separated radial and angular parts of a massive Dirac equation in the Kerr-Newman-deSitter metric to a HHE.
2
Content available remote

Electrovac universes with a cosmological constant

100%
Posada-Aguirre N., Batic D.
Open Physics
|
2014
|
vol. 12
|
issue 5
297-304
EN
We present the extension of the Einstein-Maxwell system called electrovac universes by introducing a cosmological constant Λ. In the absence of the Λ term, the crucial equation in solving the Einstein-Maxwell system is the Laplace equation. The cosmological constant modifies this equation to become in a nonlinear partial differential equation which takes the form ΔU =2ΛU 3. We offer special solutions of this equation.
3
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Velocity and velocity bounds in static spherically symmetric metrics

81%
Arraut I., Batic D., Nowakowski M.
Open Physics
|
2011
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vol. 9
|
issue 4
926-938
EN
We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.
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