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Register a new userVacuum polarization on the brane
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Added by
Elizabeth Winstanley
Publication date
2015
fields
Physics
and research's language is
English
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We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.
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Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.
In this paper we attempt to examine the possibility of construction of a traversable wormhole on the Randall-Sundrum braneworld with ordinary matter employing the Kuchowicz potential as one of the metric potentials. In this scenario, the wormhole shape function is obtained and studied, along with validity of Null Energy Condition (NEC) and the junction conditions at the surface of the wormhole are used to obtain a few of the model parameters. The investigation, besides giving an estimate for the bulk equation of state parameter, draws important constraints on the brane tension which is a novel attempt in this aspect and very interestingly the constraints imposed by a physically plausible traversable wormhole is in high confirmity with those drawn from more general space-times or space-time independent situations involved in fundamental physics. Also, we go on to claim that the possible existence of a wormhole may very well indicate that we live on a three-brane universe.
The shear dynamics in Bianchi I cosmological model on the brane with a perfect fluid (the equation of state is $p=(gamma-1) mu$) is studied. It is shown that for $1 < gamma < 2$ the shear parameter has maximum at some moment during a transition period from nonstandard to standard cosmology. An exact formula for the matter density $mu$ in the epoch of maximum shear parameter as a function of the equation of state is obtained.
We present the vacuum polarisation of a massless, conformally coupled scalar field on the brane for a Schwarzschild-Tangherlini black hole in a bulk of zero to seven additional dimensions.
In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the $O(4)$ Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses $m geq 0$ of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Motolla-Allen $alpha$-vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless $m=0$ and the conformally coupled massless $m=m_c$ cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen $alpha$-vacua even for $m>0$.
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