7,889 research outputs found
Quantum cosmology of quadratic f(R) theories with a FRW metric
We study the quantum cosmology of a quadratic theory with a FRW
metric, via one of its equivalent Horndeski type actions, where the dynamics of
the scalar field is induced. The classical equations of motion and the
Weeler-deWitt equation, in their exact versions, are solved numerically. From
the choice of a free parameter in the action follow two cases, inflation + exit
and inflation alone. The numerical solution of the Wheeler-DeWitt equation
depends strongly on the boundary conditions, which can be chosen so that the
resulting wave function of the universe seems to be normalizable and consistent
with hermitian operators.Comment: 6 pages, 4 figure
Hodge polynomials of the moduli spaces of pairs
Let be a smooth projective curve of genus over the complex
numbers. A holomorphic pair on is a couple , where is a
holomorphic bundle over of rank and degree , and is
a holomorphic section. In this paper, we determine the Hodge polynomials of the
moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We
also deal with the case in which has fixed determinant.Comment: 23 pages, typos added, minor change
Examples of signature (2,2) manifolds with commuting curvature operators
We exhibit Walker manifolds of signature (2,2) with various commutativity
properties for the Ricci operator, the skew-symmetric curvature operator, and
the Jacobi operator. If the Walker metric is a Riemannian extension of an
underlying affine structure A, these properties are related to the Ricci tensor
of A
AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
We study black hole solutions in extended gravities with higher-order
curvature terms, including conformal and Einstein-Weyl gravities. In addition
to the usual AdS vacuum, the theories admit Lifshitz and Schr\"odinger vacua.
The AdS black hole in conformal gravity contains an additional parameter over
and above the mass, which may be interpreted as a massive spin-2 hair. By
considering the first law of thermodynamics, we find that it is necessary to
introduce an associated additional intensive/extensive pair of thermodynamic
quantities. We also obtain new Liftshitz black holes in conformal gravity and
study their thermodynamics. We use a numerical approach to demonstrate that AdS
black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl
gravity. We also demonstrate the existence of asymptotically Lifshitz black
holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary
of the parameter ranges for the AdS black holes. Outside the range, the
solutions develop naked singularities. The asymptotically AdS and Lifshitz
black holes provide an interesting phase transition, in the corresponding
boundary field theory, from a relativistic Lorentzian system to a
non-relativistic Lifshitz system.Comment: typos corrected, references adde
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