Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

This thesis Entitled Studies on Quasinormal modes and Late-time tails black hole spacetimes. In this thesis, the signature of these new theories are probed on the evolution of field perturbations on the black hole spacetimes in the theory. Chapter 1 gives a general introduction to black holes and its perturbation formalism. Various concepts in the area covered by the thesis are also elucidated in this chapter. Chapter 2 describes the evolution of massive, charged scalar field perturbations around a Reissner-Nordstrom black hole surrounded by a static and spherically symmetric quintessence. Chapter 3 comprises the evolution of massless scalar, electromagnetic and gravitational fields around spherically symmetric black hole whose asymptotes are defined by the quintessence, with special interest on the late-time behavior. Chapter 4 examines the evolution of Dirac field around a Schwarzschild black hole surrounded by quintessence. Detailed numerical simulations are done to analyze the nature of field on different surfaces of constant radius . Chapter 5is dedicated to the study of the evolution of massless fields around the black hole geometry in the HL gravity.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

"Vegeu el resum a l'inici del document del fitxer adjunt."

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Intensity correlation function of dye lasers: Short-time behavior

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

Understanding and Managing the Late Time of Ratooning Effect on Cane Yield

Each year growers are faced with the decision of when to harvest individual blocks of sugarcane throughout the harvest season. This decision influences the yield of the current crop and can affect the yield in the following season. Growers must therefore decide which blocks to harvest early and which to harvest later in the harvest season. Usually, the latest harvested cane is the lowest yielding the following year (the �late harvest� effect). Block productivity data from Tully were used to determine the effects of harvest timing on cane yield of the current and subsequent crop. The results are tabulated to provide a ready reference to these time of harvest effects on the current and future crop in either a single year or over the full crop cycle for the Tully district.

Searching for swept-up hydrogen and helium in the late-time spectra of 11 nearby Type Ia supernovae

The direct detection of a stellar system that explodes as a Type Ia supernova (SN Ia) has not yet been successful. Various indirect methods have been used to investigate SN Ia progenitor systems but none have produced conclusive results. A prediction of single-degenerate models is that H- (or He-) rich material from the envelope of the companion star should be swept up by the SN ejecta in the explosion. Seven SNe Ia have been analysed to date looking for signs of H-rich material in their late-time spectra and none were detected. We present results from new late-time spectra of 11 SNe Ia obtained at the Very Large Telescope using XShooter and FORS2. We present the tentative detection of Hα emission for SN 2013ct, corresponding to ∼0.007 M_⊙ of stripped/ablated companion star material (under the assumptions of the spectral modelling). This mass is significantly lower than expected for single-degenerate scenarios, suggesting that >0.1 M_⊙ of H-rich is present but not observed. We do not detect Hα emission in the other 10 SNe Ia. This brings the total sample of normal SNe Ia with non-detections (<0.001–0.058 M_⊙) of H-rich material to 17 events. The simplest explanation for these non-detections is that these objects did not result from the explosion of a CO white dwarf accreting matter from a H-rich companion star via Roche lobe overflow or symbiotic channels. However, further spectral modelling is needed to confirm this. We also find no evidence of He-emission features, but models with He-rich companion stars are not available to place mass limits.

Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

Black hole's response to external perturbations will carry significant information about these exotic objects. Its response, shortly after the initial `kick', is known to be ruled by the damped oscillation of the perturbating eld, called quasinormal modes(QNMs), followed by the tails of decay and is the characteristic of the background black hole spacetime. In the last three decades, several shortcomings came out in the Einstein's General Theory of Relativity(GTR). Such issues come, especially, from observational cosmology and quantum eld theory. In the rst case, for example, the observed accelerated expansion of the universe and the hypothesized mysterious dark energy still lack a satisfactory explanation. Secondly, GTR is a classical theory which does not work as a fundamental theory, when one wants to achieve a full quantum description of gravity. Due to these facts modi cation to GTR or alternative theories for gravity have been considered. Two potential approaches towards these problems are the quintessence model for dark energy and Ho rava-Lifshitz(HL) gravity. Quintessence is a dynamical model of dark energy which is often realized by scalar eld mechanism. HL gravity is the recently proposed theory of gravity, which is renormalizable in power counting arguments. The two models are considered as a potential candidate in explaining these issues.

Perturbations of black p-branes

We consider black p-brane solutions of the low-energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a AdSd((p+2)) x Sd((8-p)) space which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a (p+1)-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.

Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena`s correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of d-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully d-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low- frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.

Quasinormal modes of brane-localized standard model fields in Gauss-Bonnet theory

We study the massless scalar, Dirac, and electromagnetic fields propagating on a 4D-brane, which is embedded in higher-dimensional Gauss-Bonnet space-time. We calculate, in the time domain, the fundamental quasinormal modes of a spherically symmetric black hole for such fields. Using WKB approximation we study quasinormal modes in the large multipole limit. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at an asymptotically late time.

Real-time fieldbus communications using Profibus networks

This paper provides a comprehensive study on how to use Profibus fieldbus networks to support real-time industrial communications, that is, on how to ensure the transmission of real-time messages within a maximum bound time. Profibus is base on a simplified timed token (TT) protocol, which is a well-proved solution for real-time communication systems. However, Profibus differs with respect to the TT protocol, thus preventing the application of the usual TT protocol real-time analysis. In fact, real-time solutions for networks based on the TT protocol rely on the possibility of allocating specific bandwidth for the real-time traffic. This means that a minimum amount of time is always available, at each token visit, to transmit real-time messages, transversely, with the Profibus protocol, in the worst case, only one real-time message is processed per token visit. The authors propose two approaches to guarantee the real-time behavior of the Profibus protocol: (1) an unconstrained low-priority traffic profile; and (2) a constrained low-priority traffic profile. The proposed analysis shows that the first profile is a suitable approach for more responsive systems (tighter deadlines), while the second allows for increased nonreal-time traffic throughput