831 research outputs found
One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly
The one-loop partition function for a charged self-interacting Bose gas at
finite temperature in D-dimensional spacetime is evaluated within a path
integral approach making use of zeta-function regularization. For D even, a new
additional vacuum term ---overlooked in all previous treatments and coming from
the multiplicative anomaly related to functional determinants-- is found and
its dependence on the mass and chemical potential is obtained. The presence of
the new term is shown to be crucial for having the factorization invariance of
the regularized partition function. In the non interacting case, the
relativistic Bose-Einstein condensation is revisited. By means of a suitable
charge renormalization, for D=4 the symmetry breaking phase is shown to be
unaffected by the new term, which, however, gives actually rise to a non
vanishing new contribution in the unbroken phase.Comment: 25 pages, RevTex, a new Section and several explanations added
concering the non-commutative residue and the physical discussio
Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories
A fundamental criterion of viability of any gravity theory is existence of a
stable ground-state solution being either Minkowski, dS or AdS space. Stability
of the ground state is independent of which frame is physical. In general, a
given theory has multiple ground states and splits into independent physical
sectors. All metric gravity theories with the Lagrangian being a function of
Ricci tensor are dynamically equivalent to Einstein gravity with a source and
this allows us to study the stability problem using methods developed in GR. We
apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians
the stability criterion works simply and effectively whenever the curvature of
the ground state is determined. An infinite number of gravity theories have a
stable ground state and further viability criteria are necessary.Comment: A modified and expanded version of a second part of the paper which
previously appeared as gr-qc/0702097v1. The first, modified part is now
published as gr-qc/0702097v2 and as a separate paper in Class. Qu. Grav. The
present paper matches the published versio
Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
We derive the equilibrium hydrostatic equation of a spherical star for any
gravitational Lagrangian density of the form . The Palatini
variational principle for the Helmholtz Lagrangian in the Einstein gauge is
used to obtain the field equations in this gauge. The equilibrium hydrostatic
equation is obtained and is used to study the Newtonian limit for
. The same procedure is carried out for the more
generally case giving a good
Newtonian limit.Comment: Revised version, to appear in Classical and Quantum Gravity
One-loop f(R) gravity in de Sitter universe
Motivated by the dark energy issue, the one-loop quantization approach for a
family of relativistic cosmological theories is discussed in some detail.
Specifically, general gravity at the one-loop level in a de Sitter
universe is investigated, extending a similar program developed for the case of
pure Einstein gravity. Using generalized zeta regularization, the one-loop
effective action is explicitly obtained off-shell, what allows to study in
detail the possibility of (de)stabilization of the de Sitter background by
quantum effects. The one-loop effective action maybe useful also for the study
of constant curvature black hole nucleation rate and it provides the plausible
way of resolving the cosmological constant problem.Comment: 25 pages, Latex file. Discussion enlarged, new references added.
Version accepted in JCA
On thermodynamics second law in the modified Gauss Bonnet gravity
The second law and the generalized second law of thermodynamics in cosmology
in the framework of the modified Gauss-Bonnet theory of gravity are
investigated. The conditions upon which these laws hold are derived and
discussed.Comment: 9pages, typos corrected, references adde
Tunnelling Methods and Hawking's radiation: achievements and prospects
The aim of this work is to review the tunnelling method as an alternative
description of the quantum radiation from black holes and cosmological
horizons. The method is first formulated and discussed for the case of
stationary black holes, then a foundation is provided in terms of analytic
continuation throughout complex space-time. The two principal implementations
of the tunnelling approach, which are the null geodesic method and the
Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The
Hamilton-Jacobi method is then extended to cover spherically symmetric
dynamical black holes, cosmological horizons and naked singularities. Prospects
and achievements are discussed in the conclusions.Comment: Topical Review commissioned and accepted for publication by
"Classical and Quantum Gravity". 101 pages; 6 figure
Oscillations of the F(R) dark energy in the accelerating universe
Oscillations of the dark energy around the phantom divide line,
, both during the matter era and also in the de Sitter epoch
are investigated. The analysis during the de Sitter epoch is revisited by
expanding the modified equations of motion around the de Sitter solution. Then,
during the matter epoch, the time dependence of the dark energy perturbations
is discussed by using two different local expansions. For high values of the
red shift, the matter epoch is a stable point of the theory, giving the
possibility to expand the -functions in terms of the dark energy
perturbations. In the late-time matter era, the realistic case is considered
where dark energy tends to a constant. The results obtained are confirmed by
precise numerical computation on a specific model of exponential gravity. A
novel and very detailed discussion is provided on the critical points in the
matter era and on the relation of the oscillations with possible singularities.Comment: 23 pages, 11 figures, version to appear in EPJ
Spectral analysis and zeta determinant on the deformed spheres
We consider a class of singular Riemannian manifolds, the deformed spheres
, defined as the classical spheres with a one parameter family of
singular Riemannian structures, that reduces for to the classical metric.
After giving explicit formulas for the eigenvalues and eigenfunctions of the
metric Laplacian , we study the associated zeta functions
. We introduce a general method to deal with some
classes of simple and double abstract zeta functions, generalizing the ones
appearing in . An application of this method allows to
obtain the main zeta invariants for these zeta functions in all dimensions, and
in particular and . We give
explicit formulas for the zeta regularized determinant in the low dimensional
cases, , thus generalizing a result of Dowker \cite{Dow1}, and we
compute the first coefficients in the expansion of these determinants in powers
of the deformation parameter .Comment: 1 figur
Compactifying the state space for alternative theories of gravity
In this paper we address important issues surrounding the choice of variables
when performing a dynamical systems analysis of alternative theories of
gravity. We discuss the advantages and disadvantages of compactifying the state
space, and illustrate this using two examples. We first show how to define a
compact state space for the class of LRS Bianchi type I models in -gravity
and compare to a non--compact expansion--normalised approach. In the second
example we consider the flat Friedmann matter subspace of the previous example,
and compare the compact analysis to studies where non-compact
non--expansion--normalised variables were used. In both examples we comment on
the existence of bouncing or recollapsing orbits as well as the existence of
static models.Comment: 18 pages, revised to match published versio
Applications of the Mellin-Barnes integral representation
We apply the Mellin-Barnes integral representation to several situations of
interest in mathematical-physics. At the purely mathematical level, we derive
useful asymptotic expansions of different zeta-functions and partition
functions. These results are then employed in different topics of quantum field
theory, which include the high-temperature expansion of the free energy of a
scalar field in ultrastatic curved spacetime, the asymptotics of the -brane
density of states, and an explicit approach to the asymptotics of the
determinants that appear in string theory.Comment: 20 pages, LaTe
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