Effective gravity and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">OSp</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>,</mml:mo><mml:mn>4</mml:mn><mml:mn /><mml:mo>)</mml:mo><mml:mn /></mml:math>-invariant matter

Attention has been recently called upon the fact that the weak and null energy conditions and the second law of thermodynamics are violated in wormhole solutions of Einstein's theory with classical, nonminimally coupled, scalar fields as material source. It is shown that the discussion is only meaningful when ambiguities in the definitions of stress-energy tensor and energy density of a nonminimally coupled scalar are resolved. The three possible approaches are discussed with emphasis on the positivity of the respective energy densities and covariant conservation laws. The root of the ambiguities is traced to the energy localization problem for the gravitational field.

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Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-brane geometry

Bellucci

Saharian

Vardanyan³

2016

Phys. Rev. D

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We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field in the region between two co-dimension one branes on the background of locally AdS spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to Aharonov-Bohm type effect on the vacuum currents. There exists a range in the space of the Robin coefficients for separate branes where the vacuum state becomes unstable. Compared to the case of the standard AdS bulk, in models with compact dimensions the stability condition imposed on the parameters is less restrictive. The current density has nonzero components along compact dimensions only. These components are decomposed into the brane-free and brane-induced contributions. Different representations are provided for the latter well suited for the investigation of the near-brane, near-AdS boundary and near-AdS horizon asymptotics. The component along a given compact dimension is a periodic function of the gauge field flux, enclosed by that dimension, with the period of the flux quantum. An important feature, that distinguishes the current density from the expectation values of the field squared and energy-momentum tensor, is its finiteness on the branes. In particular, for Dirichlet boundary condition the current density vanishes on the branes. We show that, depending on the constants in the boundary conditions, the presence of the branes may either increase or decrease the current density compared with that for the brane-free geometry. Applications are given to the Randall-Sundrum 2-brane model with extra compact dimensions. In particular, we estimate the effects of the hidden brane on the current density on the visible brane.

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Effective gravity andOSp(N,4)-invariant matter

Cited by 3 publications

References 46 publications

Scalar gravitational waves and Einstein frame

Scalar gravitational waves and Einstein frame

Energy conditions and classical scalar fields

Hadamard function and the vacuum currents in braneworlds with compact dimensions: Two-brane geometry

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