18 research outputs found
Product Einstein Manifolds, Zeta-Function Regularization and the Multiplicative Anomaly
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and of the multiplicative anomaly is derived
Quantum generation of Schwarzschild-de Sitter (Nariai) black holes in effective dilaton-Maxwell gravity
Dilaton coupled electromagnetic field is essential element of low-energy
string effective action or it may be considered as result of spherical
compactification of Maxwell theory in higher dimensions. The large and
large curvature effective action for dilaton coupled vectors is calculated.
Adding such quantum correction to classical dilaton gravity action we show that
effective dilaton-Maxwell gravity under consideration may generate
Schwarzschild-de Sitter black holes (SdS BHs) with constant dilaton as
solutions of the theory. That suggests a mechanism (alternative to BHs
production) for quantum generation of SdS BHs in early universe (actually, for
quantum creation of inflationary Universe) due to back-reaction of dilaton
coupled matter. The possibility of proliferation of anti-de Sitter space is
briefly discussed.Comment: LaTeX file, 11 page
Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
The thermodynamic properties of the (2+1)-dimensional non-rotating black hole
of Ba\~nados, Teitelboim and Zanelli are discussed. The first quantum
correction to the Bekenstein-Hawking entropy is evaluated within the on-shell
Euclidean formalism, making use of the related Chern-Simons representation of
the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum
correction are dealt with a renormalization of the Newton constant. It is
argued that the quantum correction due to the gravitational field shrinks the
effective radius of a hole and becomes more and more important as soon as the
evaporation process goes on, while the area law is not violated.Comment: 14 pages, Latex, one new reference adde
Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume
The one-loop effective action for a massive self-interacting scalar field is
investigated in -dimensional ultrastatic space-time ,
being a non-compact hyperbolic manifold with finite volume. Making
use of the Selberg trace formula, the -function related to the small
disturbance operator is constructed. For an arbitrary gravitational coupling,
it is found that has a simple pole at . The one-loop effective
action is analysed by means of proper-time regularisations and the one-loop
divergences are explicitly found. It is pointed out that, in this special case,
also -function regularisation requires a divergent counterterm, which
however is not necessary in the free massless conformal invariant coupling
case. Finite temperature effects are studied and the high-temperature expansion
is presented. A possible application to the problem of the divergences of the
entanglement entropy for a free massless scalar field in a Rindler-like
space-time is briefly discussed.Comment: 13 pages, LaTex. The contribution of hyperbolic elements has been
added. Other minor corrections and reference