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SUMMARY:Vacuum polarization of a quantized scalar field in the thermal sta
te in a long throat
DTSTART;VALUE=DATE-TIME:20181024T135500Z
DTEND;VALUE=DATE-TIME:20181024T141500Z
DTSTAMP;VALUE=DATE-TIME:20230128T135427Z
UID:indico-contribution-1070@cern.ch
DESCRIPTION:Speakers: Arkadiy Popov ()\nThe study of vacuum polarization e
ffects in strong gravitational fields is a pertinent issue since such effe
cts may play a role in the cosmological scenario and the construction of a
self-consistent model of black hole evaporation. These effects can be tak
en into account by solving the semiclassical backreaction equations \n \n
$ G^{\\mu}_{\\nu}=8 \\pi \\langle T^{\\mu}_{\\nu} \\rangle\, \\qquad \\qqu
ad \\qquad \\qquad (1)$ \n \nwhere $\\langle T^{\\mu}_{\\nu} \\rangle$ is
the expectation value of the stress-energy tensor operator for the quantiz
ed fields.\n \nThe main difficulty in the theory of semiclassical gravity
is that the vacuum polarization effects are determined by the topological
and geometrical properties of spacetime as a whole or by the choice of qua
ntum state in which the expectation values are taken. It means that calcul
ation of the functional dependence of $\\langle T^{\\mu}_{\\nu} \\rangle_{
ren}$ on the metric tensor in an arbitrary spacetime presents formidable d
ifficulty. Only in some spacetimes with high degrees of symmetry for the c
onformally invariant fields $\\langle T_{\\mu \\nu} \\rangle_{ren}$ can be
computed and equations of the theory of semiclassical gravity can be solv
ed exactly. Let us stress that the single parameter of length dimensionali
ty in problem (1) is the Planck length $l_{\\small PL}$. This implies that
the characteristic scale $l$ of the spacetime curvature (which correspond
s to the solution of equations (1) can differ from ${l_{ \\small PL}}$ onl
y if there is a large dimensionless parameter. As an example of such a par
ameter one can consider a number of fields the polarization of which is a
source of spacetime curvature (*it is assumed\, of course\, that the chara
cteristic scale of change of the background gravitational field is suffici
ently greater than $l_{\\small PL}$ so that the very notion of a classical
spacetime still has some meaning*). In the case of massive field\, the ex
istence of an additional parameter $1/m$ does not increase the characteris
tic scale of the spacetime curvature $l$ which is described by the solutio
n of equations (1) (*the characteristic scale of the components $G^{\\mu}_
{\\nu}$ on the left-hand side of equations (1) is $1/l^2$\, on the right-h
and side - ${l_{\\small PL}}^2/(m^2 l^6)$)*. For the massless quantized f
ields such a parameter can be the coupling constants of field to the curva
ture of spacetime [1]. Another possibility of introducing an additional pa
rameter in the problem (1) is to consider the non-zero temperature of quan
tum state for the quantized field. It is known (see\, e.g.\, [2]) that in
the high-temperature limit (when $T \\gg 1/l\, T$ being a temperature of t
hermal state) $\\langle T^{\\mu}_{\\nu} \\rangle$ for such a thermal state
is proportional to the fourth power of the temperature $T$.\n\nIn this wo
rk an analytical approximation of ${\\langle \\varphi^2 \\rangle}$ for a q
uantized scalar field in a thermal state at arbitrary temperature is consi
dered. The scalar field is assumed to be both massive and massless\, with
an arbitrary coupling $\\xi$ to the scalar curvature\, and in a thermal st
ate at an arbitrary temperature $T$. The gravitational background is assum
ed to be static spherically symmetric and slowly varying. We have shown th
at in such spacetime the effect of vacuum polarization of a quantized scal
ar field in the thermal state does not depend on temperature and condition
s at infinity. This implies that in considered situation ${\\langle \\varp
hi^2 \\rangle}$ is a local quantity for any finite mass $m$ of the quantiz
ed field\, including $m = 0$.\n \n**References** \n\n[1] A.A. Popov\, *Cla
ss. Quantum Grav.* **22**\, 5223 (2005).\n\n[2] N. Nakazawa and T. Fukuyam
a\, *Nucl. Phys. B* **252**\, 621 (1985).\n\n[3] A.A. Popov\, *Phys. Rev D
.* **94**\, 124033 (2016).\n\nhttps://indico.particle.mephi.ru/event/22/co
ntributions/1070/
LOCATION:Hotel Intourist Kolomenskoye 4* Petrovskiy-1 hall
URL:https://indico.particle.mephi.ru/event/22/contributions/1070/
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