Quantum Mechanics on Periodic and Non-Periodic Lattices and Almost Unitary Schwinger Operators

In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations between these algebras and show that the almost unitary Schwinger operators are equivalent to the Schwinger algebra. We introduce new representations for MN(C) in terms of these algebras

Cosmological isotropic matter-energy generalizations of Schwarzschild and Kerr metrics

We present a time dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state parameter. In the second part, we generalize the rotating black hole solution to an expanding universe. We derive from the proposed metric the special solutions of the field equations for the dust approximation and the dark energy solution. We show that the presence of a rotating black hole does not modify the scale factor $b(t)=t^{2/3}$ law for dust, nor $b(t)=e^{\lambda\hspace{1mm}t}$ and $p=-\rho$ for dark energy.Comment: 12 pages, accepted version for publication in Int.J.Mod.Phys.

The Scalar Mode of Gravity

We consider the scalar mode of gravity as expressed by a conformal factor of the metric and present a model motivated by the Jordan-Brans-Dicke action. We obtain a Lagrangian density in Minkowski space which exhibits a massive particle and an expanding space-time.Comment: 7 pages; typos correcte

The Atmosphere of a Black Hole

We present a static, isotropic fluid solution around a black hole and its effects on the field equations and the horizon. We offer the solutions, their descriptions and we comment on their shortcomings. We derive from the proposed metric the density, the pressure, the equation of state, the temperature near and far of the black hole and the equation of state parameter. We show that for a special case, when $r\rightarrow\ 0$ the solution behaves as $p=\frac{\rho}{3}$, the equation of state for radiation and for $r\rightarrow\infty$ we observe that $p=0$, the equation of state for dust.Comment: 7 page