1,721,109 research outputs found
New solutions of the Ermakov-Pinney equation in curved spacetime
No full textAn Ermakov–Pinney-like equation associated with the scalar wave equation in curved
space-time is here studied. The example of Schwarzschild space-time considered in
the present work shows that this equation can be viewed more as a “model equation,”
with interesting applications in black hole physics. Other applications studied involve
cosmological space-times (de Sitter) and pulse of plane gravitational waves: in all
these cases the evolution of the Ermakov–Pinney field seems to be consistent with
a rapid blow-up, unlike the Schwarzschild case where spatially damped oscillations
are allowed. Eventually, the phase function is also evaluated in many of the above
space-time models
Perturbative evaluation of the scalar two-point function in the cosmic microwave background power spectrum
No full textRecent work in the literature has found a suppression or, instead, an enhancement of the cosmic
microwave background power spectrum in quantum gravity, although the effect is too small to be observed
in both cases. The present paper studies in detail the equations recently proposed for a Born-Oppenheimer–
type analysis of the problem. By using a perturbative approach to the analysis of the nonlinear ordinary
differential equation obeyed by the two-point function for scalar fluctuations, we find various explicit forms
of such a two-point function, with the associated power spectrum. In particular, a new family of power
spectra is obtained and studied. The theoretical prediction of power enhancement at large scales is hence
confirmed
On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds
No full textWe study trapped surfaces from the point of view of local isometric embedding
into 3D Riemannian manifolds. When a two-surface is embedded into 3D
Euclidean space, the problem of finding all surfaces applicable upon it gives
rise to a non-linear partial differential equation of the Monge–Ampère type,
first discovered by Darboux, and later reformulated by Weingarten. Even
today, this problem remains very difficult, despite some remarkable results. We
find an original way of generalizing the Darboux technique, which leads to a
coupled set of six non-linear partial differential equations. For the 3-manifolds
occurring in Friedmann–(Lemaitre)–Robertson–Walker cosmologies, we
show that the local isometric embedding of trapped surfaces into them can
be proved by solving just one non-linear equation. Such an equation is here
solved for the three kinds of Friedmann model associated with positive, zero,
negative curvature of spatial sections, respectively
Investigating new forms of gravity-matter couplings in the gravitational field equations
No full textThis paper proposes a toy model where, in the Einstein equations, the right-hand side is modified
by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor
with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in
mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that
such a term yields a correction linear in ħ to the classical term that is instead just proportional to the energymomentum
tensor. One then obtains an effective energy-momentum tensor that consists of three
contributions: pure energy part, mechanical stress, and thermal part. The pure energy part has the
appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory
coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and
Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-
Robertson-Walker universe
A defect-correction algorithm for quadratic matrix equations, with applications to quasi-Toeplitz matrices
No full textA defect correction formula for quadratic matrix equations of the kind (Formula presented.) is presented. This formula, expressed by means of an invariant subspace of a suitable pencil, allows us to introduce a modification of the Structure-preserving Doubling Algorithm (SDA), that enables refining an initial approximation to the sought solution. This modification provides substantial advantages, in terms of convergence acceleration, in the solution of equations coming from stochastic models, by choosing a stochastic matrix as the initial approximation. An application to solving random walks in the quarter plane is shown, where the coefficients (Formula presented.) are quasi-Toeplitz matrices of infinite size
Fast discrete transforms by means of eigenpolynomials
No full textLet A = (aij) be an n x n matrix. Consider the discrete transform u + Au, and
associate with the jth column of A the eigenpolynomial aj(z) = cyzol aij xj. The properties of
eigenpolynomials play an important role in the case where A is a matrix of eigenvectors of a Toeplitz
matrix [1,2]. Here we consider the cases where A is the matrix defining the Discrete Fourier Transform
(DFT), the Discrete Hartley ‘Transform (DHT), the Discrete Sine Transform (DST) and the Discrete
Cosine ‘Dansform (DCT) in its two versions of (31 and (41. For each eigenpolynomial of each transform,
we explicitly determine all its zeros. We use eigenpolynomials as a unifying tool for describing the
Decimation In Frequency (DIF) versions of the main known algorithms for DFT. Moreover, by using
the information about the zeros of the eigenpolynomials we devise new algorithms for DFT, DHT,
DST and DCT, which reach or improve (in the case of DST and DCT) the record complexity bounds
without requiring the use of the algorithm for complex multiplication with three multiplications and
three additions [5] and of the implicit preconditioning
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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