arXiv subjects

N. Sanchez

Publications and source records attributed to N. Sanchez.

At least 37 records · Page 2Linked to original sources

arXiv2001

String Driven Cosmology and its Predictions

We present a minimal model for the Universe evolution fully extracted from effective String Theory. This model is by its construction close to the standard cosmological evolution, and it is driven selfconsistently by the evolution of the string equation of state itself. The inflationary String Driven stage is able to reach enough inflation, describing a Big Bang like evolution for the metric. By linking this model to a minimal but well established observational information, (the transition times of the different cosmological epochs), we prove that it gives realistic predictions on early and current energy density and its results are compatible with General Relativity. Interestingly enough, the predicted current energy density is found Omega = 1 and a lower limit Omega \geq 4/9 is also found. The energy density at the exit of the inflationary stage also gives | Omega |_{inf}=1. This result shows an agreement with General Relativity (spatially flat metric gives critical energy density) within an inequivalent Non-Einstenian context (string low energy effective equations). The order of magnitude of the energy density-dilaton coupled term at the beginning of the radiation dominated stage agrees with the GUT scale. The predicted graviton spectrum is computed and analyzed without any free parameters. Peaks and asymptotic behaviours of the spectrum are a direct consequence of the dilaton involved and not only of the scale factor evolution. Drastic changes are found at high frequencies: the dilaton produces an increasing spectrum (in no string cosmologies the spectrum is decreasing). Without solving the known problems about higher order corrections and graceful exit of inflation, we find this model closer to the observational Universe than the current available string cosmology scenarii.

hep-th↗

arXiv2000

Self-gravitating fluid dynamics, unstabilities and solitons

This work studies the hydrodynamics of self-gravitating compressible isothermal fluids. We show that the hydrodynamic evolution equations in absence of viscosity are scale covariant. We study the evolution of the time dependent fluctuations around singular and regular isothermal spheres. We linearize the fluid equations around such stationary solutions and apply Laplace transform to solve them. We find that the system is stable below a critical size (X ~ 9.0 in dimensionless variables) and unstable above; this size is the same critical size found in the study of the thermodynamical stability in the canonical ensemble and associated to a center-to-border density ratio of 32.1 . We prove that the value of this critical size is independent of the Reynolds number of the system. Furthermore, we give a detailed description of the series of successive dynamical instabilities that appear at higher and higher sizes following the geometric progression X_n ~ 10.7^n. We turn then to study exact solutions of the hydrodynamic equations without viscosity and we provide analytic and numerical axisymmetric soliton-type solutions. The stability of exact solutions corresponding to a collapsing filament is studied by computing linear fluctuations. Radial fluctuations growing faster than the background are found for all sizes of the system. However, a critical size (X ~ 4.5) appears, separating a weakly from a strongly unstable regime.

astro-ph↗

arXiv2000

New dual relations between quantum field theory and string regimes in curved backgrounds

A {\cal R} "dual" transform is introduced which relates Quantum Field Theory and String regimes, both in a curved background with D-non compact dimensions. This operation maps the characteristic length of one regime into the other (and, as a consequence, mass domains as well). The {\cal R}-transform is not an assumed or {\it a priori} imposed symmetry but is revealed by the QFT and String dynamics in curved backgrounds. The Hawking-Gibbons temperature and the string maximal or critical temperature are {\cal R}-mapped one into the other. If back reaction of quantum matter is included, Quantum Field Theory and String phases appear, and {\cal R}-relations between them manifest as well. These {\cal R}-transformations are explicitly shown in two relevant examples: Black Hole and de Sitter space times.

hep-th↗

arXiv1999

Minimal String Driven Cosmology and its Predictions

We present a minimal model for the Universe evolution fully extracted from effective String Theory. By linking this model with a minimal but well established observational information, we prove that it gives realistic predictions on early and current energy density and its results are compatible with General Relativity. Interestingly enough, the predicted current energy density is found $Ω= 1$ and in anycase with lower limit $Ω\geq {4/9}$. On the other hand, the energy density at the exit of inflationary stage gives also $Ω|_{inf}=1$. This result shows an agreement with General Relativity (spatially flat metric gives critical energy density) within an unequivalent Non-Einstenian context (string low energy effective equations). The order of magnitude of the energy density-dilaton coupled term at the beginning of radiation dominated stage agrees with GUT scale. Without solving the known problems about higher order corrections and graceful exit of inflation, we find this model closer to the observational Universe properties than the current available string cosmology scenarii. At a more fundamental level, this model is by its construction close to the standard cosmological evolution, and it is driven selfconsistently by the evolution of the string equation of state itself. The inflationary String Driven stage is able to reach an enough amount of inflation, describing a Big Bang like evolution for the metric.

hep-th↗

arXiv1999

Linking a Minimal Theoretical Model of Scale Factor Evolution with Observational Universe Information

We study several approaches for constructing a minimal model of Universe evolution by matching different stages of scale factor laws. We discuss the continuity in the transitions among the stages and the time variables involved. We develop a way to modelize these transitions without loss of observational predictability. The key is the scale factor and its connection with minimal but well stablished observational information (transition times and expansion ratii). This construction is clearly useful in metric perturbations type computations, but it can be applied in whatever subject dealing with a cosmology involving different evolution stages.

gr-qc↗

arXiv1999

The Primordial Gravitational Wave Background in String Cosmology

We find the spectrum P(w)dw of the gravitational wave background produced in the early universe in string theory. We work in the framework of String Driven Cosmology, whose scale factors are computed with the low-energy effective string equations as well as selfconsistent solutions of General Relativity with a gas of strings as source. The scale factor evolution is described by an early string driven inflationary stage with an instantaneous transition to a radiation dominated stage and successive matter dominated stage. This is an expanding string cosmology always running on positive proper cosmic time. A careful treatment of the scale factor evolution and involved transitions is made. A full prediction on the power spectrum of gravitational waves without any free-parameters is given. We study and show explicitly the effect of the dilaton field, characteristic to this kind of cosmologies. We compute the spectrum for the same evolution description with three differents approachs. Some features of gravitational wave spectra, as peaks and asymptotic behaviours, are found direct consequences of the dilaton involved and not only of the scale factor evolution. A comparative analysis of different treatments, solutions and compatibility with observational bounds or detection perspectives is made.

hep-th↗

arXiv1999

Non-Singular String-Cosmologies From Exact Conformal Field Theories

Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular spacetimes with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. We analyse these cosmologies in detail with respect to the behaviour of the scale factors, the scalar curvature and the string-coupling. The sign of the scalar curvature is changed by the quantum corrections in oscillating cosmologies and evolves with time in the non-oscillating cases. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation.

hep-th↗

arXiv1999

Hawking Radiation in String Theory and the String Phase of Black Holes

The quantum string emission by Black Holes is computed in the framework of the `string analogue model' (or thermodynamical approach), which is well suited to combine QFT and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures). The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S in the black hole background. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to T_S, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic `minimal' black hole of mass M_{\min} or radius r_{\min} (inversely proportional to T_S) and string temperature T_S. The semiclassical QFT black hole (of mass M and temperature T_H) and the string black hole (of mass M_{min} and temperature T_S) are mapped one into another by a `Dual' transform which links classical/QFT and quantum string regimes. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations with mass M_+ (radius r_+) and temperature T_+) is computed. Both, the QFT and string black hole regimes are well defined and bounded: r_{min} leq r_+ \leq r_S, M_{min} \leq M_+ \leq M, T_H \leq T_+ \leq T_S. The string `minimal' black hole has a life time tau_{min} \simeq \frac{k_B c}{G \hbar} T^{-3}_S.

hep-th↗

arXiv1998

Generation of gravitational waves by generic sources in de Sitter space-time

We study the generation of gravitational radiation by sources moving in the de Sitter background. Exploiting the maximal symmetry and the conformal flatness of de Sitter space-time we prove that the derivation of this gravitational radiation can be done along the same lines as in Minkowski space-time. A gauge is chosen in which all the physical and unphysical modes of the graviton are those of a minimally coupled massless scalar field in de Sitter space-time and a massless field in Minkowski space-time. The graviton retarded Green's function and the Schwinger commutator function are computed in this gauge using Quantum Field Theory techniques. We obtain closed formulae for the spectral decomposition in frequencies of the linaearized gravitational field produced by the source, in terms of a suitable spectral decomposition of the source energy-momentum tensor. This spectral decomposition is dictated by the free (sourceless) gravitational wave modes in the de Sitter background

astro-ph↗

arXiv1997

The Black Hole: Scatterer, Absorber and Emitter of Particles

Accurate and powerful computational methods developed by the author for the wave scattering by black holes allow to obtain the highly non trivial total absorption spectrum of the Black Hole. As well as partial wave phase shifts and cross sections (elastic and inelastic), the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The exact total absorption spectrum of waves by the Black Hole has as a function of frequency a remarkable oscillatory behaviour characteristic of a diffraction pattern. This is an unique distinctive feature of the black hole absorption, and due to its r = 0 singularity. Ordinary absorptive bodies and optical models do not present these features. The unitarity optical theorem is generalized to the Black Hole case explicitly showing that absorption ocurrs only at the origin. All these results allow to understand and reproduce the Black Hole absorption spectrum in terms of Fresnel-Kirchoff diffraction theory: by the interference of the absorbed rays arriving at the origin through different optical paths. These fundamental features of the Black Hole Absorption will be present for generic higher dimensional Black Hole backgrounds, and whatever the low energy effective theory they arise from. In recent and increasing litterature devoted to compute absorption cross sections (grey body factors) of black holes (whatever ordinary, stringy, D-braned), the fundamental remarkable features of the Black Hole Absorption spectrum are overlooked.

hep-th↗

arXiv1996

String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $τ$--coordinate is given by $X^0(σ, τ)=q(σ)τ^{1\over1+2β}+c^2B^0(σ, τ)+\cdots$, $B^0(σ,τ)=\sum_k b_k(σ)τ^k$ where $b_k(σ)$ are given by Eqs.\ (3.15), and $β$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\simη^β$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(η)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,ϕ,t)$ are $r=\sum_n A^1_{n}(σ)(-τ)^{2n/(D+1)}~,$ $ϕ=\sum_n A^3_{n}(σ)(-τ)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (σ)(-τ)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $τ$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-τ)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.

gr-qc↗

arXiv1996

Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes

We find that the fundamental quadratic form of classical string propagation in $2+1$ dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the $2+1$ black hole anti de Sitter spacetime), {\it all} three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the Sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multi-string solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the Sinh-Gordon equation, the Cosh-Gordon equation and the Liouville equation by higher dimensional generalizations.

hep-th↗

arXiv1995

New Classes of Exact Multi-String Solutions in Curved Spacetimes

We find new classes of {\it exact} string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as {\it multi-string} solutions, in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. In anti de Sitter spacetime, the solutions describe an {\it infinite} number of infinitely long stationary strings of equal energy but different pressures. In de Sitter spacetime, outside the horizon, they describe infinitely many {\it dynamical} strings infalling non-radially, scattering at the horizon and going back to spatial infinity in different directions. For special values of the constants of motion, there are families of solutions with {\it selected finite} numbers of different and independent strings. In black hole spacetimes (without cosmological constant), {\it no} multi-string solutions are found. In the Schwarzschild black hole, inside the horizon, we find one straight string infalling non-radially, with {\it indefinetely} growing size, into the $r=0$ singularity. In the $2+1$ black hole anti de Sitter background, the string stops at $r=0$ with {\it finite} length.

hep-th↗

arXiv1995

The Effect of Spatial Curvature on the Classical and Quantum Strings

We study the effects of the spatial curvature on the classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson-Walker spacetimes with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the {\it back-reaction} effect of these strings on the spacetime: the self-consistent solution to the Einstein equations is a spatially closed $(K>0)$ spacetime with a selected value of the curvature index $K$ (the scale f* is normalized to unity). No self-consistent solutions with $K\leq 0$ exist. We semi-classically quantize the circular strings and find the mass $m$ in each case. For $K>0,$ the very massive strings, oscillating on the full hypersphere, have $m^2\sim K n^2\;\;(n\in N_0)$ {\it independent} of $α'$ and the level spacing {\it grows} with $n,$ while the strings oscillating on one hemisphere (without crossing the equator) have $m^2α'\sim n$ and a {\it finite} number of states $N\sim 1/(Kα').$ For $K<0,$ there are infinitely many string states with masses $m\log m\sim n,$ that is, the level spacing grows {\it slower} than $n.$ The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.

hep-th↗

arXiv1994

Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

We compute the {\it exact} equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form $P=(γ-1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $γ$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(πHα'),\;C$ being the Casimir operator, $C=-L_{μν}L^{μν},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find $α'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),$ and a {\it finite} number of states $N_{\mbox{dS}}\approx 0.17/(H^2α')$ in de Sitter spacetime; $m^2_{\mbox{AdS}}\approx 4H^2n^2$ (large $n\in N_0$) and $N_{\mbox{AdS}}=\infty$ in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.

hep-th↗

arXiv1994

Mass Spectrum of Strings in Anti de Sitter Spacetime

We perform string quantization in anti de Sitter (AdS) spacetime. The string motion is stable, oscillatory in time with real frequencies $ω_n= \sqrt{n^2+m^2α'^2H^2}$ and the string size and energy are bounded. The string fluctuations around the center of mass are well behaved. We find the mass formula which is also well behaved in all regimes. There is an {\it infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS) there is a {\it finite} number of states only). The critical dimension at which the graviton appears is $D=25,$ as in de Sitter space. A cosmological constant $Λ\neq 0$ (whatever its sign) introduces a {\it fine structure} effect (splitting of levels) in the mass spectrum at all states beyond the graviton. The high mass spectrum changes drastically with respect to flat Minkowski spacetime. For $Λ<0,$ we find $ \sim \midΛ\mid N^2,$ {\it independent} of $α',$ and the level spacing {\it grows} with the eigenvalue of the number operator, $N.$ The density of states $ρ(m)$ grows like $\mbox{Exp}[(m/\sqrt{\midΛ\mid}\;)^{1/2}]$ (instead of $ρ(m)\sim\mbox{Exp}[m\sqrt{α'}]$ as in Minkowski space), thus {\it discarding} the existence of a critical string temperature. For the sake of completeness, we also study the quantum strings in the black string background, where strings behave, in many respects, as in the ordinary black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat Minkowski space.

hep-th↗

arXiv1994

Strings Propagating in the 2+1 Dimensional Black Hole Anti de Sitter Spacetime

We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at $r=0.$ We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at $r=0.$ We find the exact general solution for the circular string motion in all these backgrounds, it is given closely and completely in terms of elliptic functions. For the non-rotating black hole backgrounds the circular strings have a maximal bounded size $r_m,$ they contract and collapse into $r=0.$ No indefinitely growing strings, neither multi-string solutions are present in these backgrounds. In rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the presence of angular momentum prevents the string from collapsing into $r=0.$ The circular string motion is also completely solved in the black hole de Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS spacetime), in which expanding unbounded strings and multi-string solutions appear.

hep-th↗

arXiv1993

Exact String Solutions in 2+1-Dimensional De Sitter Spacetime

Exact and explicit string solutions in de Sitter spacetime are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat spacetime analogy appears: starting with a single world-sheet, several (here two) strings emerge. One string is stable and the other (unstable) grows as the universe grows. Their invariant size and energy either grow as the expansion factor or tend to constant. Moreover, strings can expand (contract) for large (small) universe radius with a different rate than the universe.

hep-th↗