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WORMHOLES IN 5D MODELS // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 109-112

We consider our world as a brane embedded in the 5D space-time which is a solution of the 5D Einstein equations with Л-term. We do not solve the modied Einstein equations on the brane, instead of this we use exact solution of 5D Einstein equations. The energy-momentum tensor appears as the Israel jump condition on the brane. This tensor at the innity gives positive tension in one side of the wormhole and negative tension in the second part of the wormhole space-time. In the case of the AdS5 model without Randall-Sundrum asymptotic we found the wormhole metric which satises the energy conditions.

Keywords: wormhole, Randall-Sundrum model, multidimensional theory, energy conditions

THE CASIMIR ENERGY FOR TWO AND THREE LAYER OF GRAPHENS // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 135-138

The Casimir energy of system of parallel conductive planes with constant conductivity is considered. General form of the Casimir energy for two and three planes is obtained. For the case of equal interplane distances the energy is proportional to inverse third power of distance. For small conductivity the energy does not depend on the Planck constant and velocity of light. The Casimir energy of planes with ideal conductivity is the sum of the Casimir energy of the neighboring planes.

Keywords: Casimir energy, zeta-function, zero point energy, graphene