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General relativity provides us with some solutions for rotating black holes. However, there are some problems associated with them: the appearance of singularities, the possibility of violations of the cosmic censorship conjecture, the existence of regions where the mass acts repulsively, and the violation of causality. Many authors consider that these problems reveal the existence of certain limits in the applicability of general relativity. For instance, it is believed that the same existence of singularities in the classical black hole solutions is a weakness of the theory and that a full quantum gravity theory would provide us with singularity-free black hole models. In this paper, the generic properties of the interiors of singularity-free rotating black holes are analyzed. Remarkably, it is shown that they are devoid of any of the aforementioned problems of the classical solutions., Peer Reviewed, Postprint (author's final draft)

The collapse of astrophysically significant bodies generates, under suitable conditions, black holes. Since one expects the generator of the black hole to be a rotating body, the black hole will also rotate. The existence of inner singularities in classical solutions for rotating black holes and the fact that General Relativity is incompatible with Quantum Mechanics lead us to seek for alternative regular models for rotating black holes. The interest in singularity-free rotating black holes has grown significantly in recent years, as shown by the increase in the number of published papers devoted to it. Undoubtedly, the latest observational developments (LIGO, the Event Horizon Telescope or, in the near future, the LISA project) and the possibility to probe our theoretical predictions have reatly contributed to awaken the interest. This text discusses the general characteristics of regular rotating black holes. These include the conditions needed to guarantee the absence of singularities and the consequences that such conditions entail for the violation of the energy conditions in black hole models. It is argued that regular rotating black holes do not require an extension through their inner disk, contrary to classical rotating black holes. In this way, the problems with negative-mass interpretations and causality violations appearing in classical solutions could be avoided. It has been included a discussion on the maximal extension and the usual global causal structure expected for these spacetimes. The different methods for obtaining regular rotating black holes are treated, including the use of the generalized Newman-Janis algorithm as an alibi to derive regular rotating black holes from regular spherically symmetric static ones. The text also provides an introduction to the thermodynamics and phenomenology of rotating black holes., Peer Reviewed, Postprint (author's final draft)

A two scalar field model that incorporates the Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. We define the scale invariant couplings of the scalar fields to the different measures through exponential potentials. Spontaneous breaking of scale invariance takes place when integrating the fields that define the measures. When going to the Einstein frame we obtain: (i) An effective potential for the scalar fields with three flat regions which allows for a unified description of both early universe inflation (in the higher energy density flat region) as well as of present dark energy epoch which can be realized with a double phase, i.e., in two flat regions. (ii) In the slow roll inflation, only one field combination the ``dilaton", which transforms under scale transformations, has non trivial dynamics, the orthogonal one, which is scale invariant remains constant. The corresponding perturbations of the dilaton are calculated. (iii) For a reasonable choice of the parameters the present model perturbations conforms to the Planck Collaboration data. (iv) In the late universe we define scale invariant couplings of Dark Matter to the dilaton.(v) We calculate the evolution of the late universe under these conditions with the realization of two different possible realizations of $\Lambda$CDM type scenarios depending of the flat region in the late universe. These two phases could appear at different times in the history of the universe.(vi) From the Planck data, we find the constraints on the parameters during the inflationary epoch and these values are used to obtain constraints relevant to the present epoch., Comment: 19 pages and 2 figures. arXiv admin note: text overlap with arXiv:1408.5344

Jornada de benvinguda ETSAB. Curs 2019-20. Acte de benvinguda on els responsables de les diferents assignatures donen el seu punt de vista sobre la catedral de Notre Dame de Paris., Jornada de benvinguda ETSAB. Curs 2019-20. Acte de benvinguda on els responsables de les diferents assignatures donen el seu punt de vista sobre la catedral de Notre Dame de Paris.

The final publication is available at Springer via 10.1007/s10714-017-2236-5, We add a prescription to the Newman–Janis algorithm in order to use it as a means of finding new extended rotating black hole spacetimes from static spherically symmetric ones. Then, we apply the procedure to a quantum improved black hole spacetime coming from Quantum Einstein Gravity in order to get the maximally extended spacetime corresponding to a non-singular rotating black hole. We rigourously check for the existence of scalar curvature singularities in the quantum improved rotating spacetime and we show that it is devoid of them. We also analyze the horizons and causal structure of the rotating black hole and provide Penrose diagrams for the maximally extended spacetime., Peer Reviewed, Postprint (author's final draft)

Quantum gravitational effects in black hole spacetimes with a cosmological constant ¿ are considered. The effective quantum spacetimes for the black holes are constructed by taking into account the renormalization group improvement of classical solutions obtained in the framework of unimodular gravity (a theory which is identical to general relativity at a classical level). This allows us to avoid the usual divergences associated with the presence of a running ¿. The horizons and causal structure of the improved black holes are discussed, taking into account the current observational bounds for the cosmological constant. It is shown that the resulting effective quantum black hole spacetimes are always devoid of singularities., Peer Reviewed, Postprint (author's final draft)

The final publication is available at Springer via 10.1007/s10714-016-2166-7, Different proposals for regular rotating black hole spacetimes have appeared recently in the literature. However, a rigorous analysis and proof of the regularity of this kind of spacetimes is still lacking. In this note we analyze rotating Kerr-like black hole spacetimes and find the necessary and sufficient conditions for the regularity of all their second order scalar invariants polynomial in the Riemann tensor. We also show that the regularity is linked to a violation of the weak energy conditions around the core of the rotating black hole., Peer Reviewed, Postprint (author's final draft)

Descripció del recurs: 17 de març de 2017, En aquest llibre s’ofereix una introducció moderna al càlcul estructural. Es pretén que les noves generacions d’arquitectes coneguin des dels primers cursos, d’una banda, els fonaments de la ciència que són aplicables a les estructures i, de l’altra, els rudiments de les aplicacions del càlcul estructural. Seguint aquesta filosofia, el llibre cobreix l’espai conceptual existent entre els models de la matèria més utilitzats en la tecnologia de les estructures i els primers resultats de l’anàlisi d’estructures complexes. Així doncs, s’hi tracten des dels models de partícula puntual, sòlid rígid o sòlid elàstic, passant per les lleis de Newton i Hooke, fins als diagrames d’esforços axials, tallants i moments flectors dels pòrtics i la deformada a estima de bigues i pòrtics. L’enfocament del llibre es basa en l’exposició dels fonaments físics i la seva aplicació a la pràctica arquitectònica. Per tant, s’hi pot trobar una bona quantitat d’exemples d’interès arquitectònic resolts., 1

The main singularity theorems are reviewed, and a detailed development of the required mathematical tools in their proofs is performed. Also, the plausibility and applicability of the assumptions of the theorems to realistic spacetimes and how the results might change if other assumptions were made are discussed. Finally, some examples to illustrate a range of cases regarding the fulfillment of the hypothesis of the theorems are provided and analyzed. The stress is put in how regular spacetimes succeed in avoiding the hypothesis in singularity theorems and which consequences this has on them., En este trabajo se revisan los principales teoremas de singularidad, juntamente con los desarrollos matemáticos necessarios para sus demostraciones. Además, se discute la plausibilidad y aplicabilidad de las hipótesis de los teoremas a espacio-tiempos realistas y cómo pueden cambiar sus resultados si se hacen otras suposiciones. Finalmente, se muestran y se analizan algunos ejemplos para ilustrar un rango de casos en relación al cumplimiento de las hipótesis de los teoremas. El énfasis recae en cómo los espacio-tiempos regulares evitan las hipótesis de los teoremas y las consecuencias que esto comporta., En aquest treball es revisan els principals teoremes de singularitat, juntament amb els desenvolupaments matemàtics necessaris per les seves demostracions. A més, es discuteix la plausibilitat i aplicabilitat de les hipòtesis dels teoremes a espai-temps realistes i com poden canvien els seus resultats si es fan altres suposicions. Finalment, es mostren i s'analitzen alguns exemples per il·lustrar un rang de casos en relació al compliment de les hipòtesis dels teoremes. L'énfasi recau en com els espai-temps regulars eviten les hipòtesis del teoremes i les conseqüències que això comporta.

We provide a general formalism that allows to analyze the phenomenon of tunneling in arbitrary spacetimes. We show that a flux of particles produced by tunneling through general marginally trapped surfaces may be perceived by some privileged observers. We discuss how this particle perception can be related to Hawking/Unruh radiation in specific cases. Our approach naturally leads to an expression for the effective surface gravity of marginally trapped surfaces. The procedure is applicable to general astrophysical and cosmological dynamical situations. Some practical examples for known and new cases are provided., Peer Reviewed, Postprint (author’s final draft)

This is an author created, un copyedited version of an article accepted for publication in Classical and quantum gravity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0264-9381/32/18/189501., We correct some computations presented in section 4.2 of the article (Class. Quantum Grav. {\bf 32} (2015) 085004), concerning the Kerr-Vaidya space-time. The correct, new results, do support the claims in the paper., Peer Reviewed, Postprint (author's final draft)

Based on a previously found general class of quantum improved exact solutions composed of non-interacting (dust) particles, we model the gravitational collapse of stars. As the modeled star collapses a closed apparent 3-horizon is generated due to the consideration of quantum effects. The effect of the subsequent emission of Hawking radiation related to this horizon is taken into consideration. Our computations lead us to argue that a total evaporation could be reached. The inferred global picture of the spacetime corresponding to gravitational collapse is devoid of both event horizons and shell-focusing singularities. As a consequence, there is no information paradox and no need of firewalls., Peer Reviewed, Postprint (published version)

A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities. (C) 2014 The Author. Published by Elsevier B.V., Peer Reviewed, Postprint (published version)

We model the gravitational collapse of heavy massive shells including its main quantum corrections. Among these corrections, quantum improvements coming from Quantum Einstein Gravity are taken into account, which provides us with an effective quantum spacetime. Likewise, we consider dynamical Hawking radiation by modeling its back-reaction once the horizons have been generated. Our results point towards a picture of gravitational collapse in which the collapsing shell reaches a minimum non-zero radius (whose value depends on the shell initial conditions) with its mass only slightly reduced. Then, there is always a rebound after which most (or all) of the mass evaporates in the form of Hawking radiation. Since the mass never concentrates in a single point, no singularity appears., Peer Reviewed, Postprint (author’s final draft)

Preprint of an article published in International journal of modern physics D, 22, 13, 2013, 1350086-1 - 1350086-15 10.1142/S0218271813500867 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijmpd, It has been postulated that black holes could be created in particle collisions within the range of the available energies for nowadays colliders (LHC). In this paper we analyze the evaporation of a type of black holes that are candidates for this specific behaviour, namely, small black holes on a brane in a world with large extra-dimensions. We examine their evolution under the assumption that energy conservation is satisfied during the process and compare it with the standard evaporation approach. We claim that, rather than undergoing a quick total evaporation, black holes become quasi-stable. We comment on the (absence of) implications for safety of this result. We also discuss how the presence of black holes together with the correctness of the energy conservation approach might be experimentally verified., Preprint

It is argued that primordial black holes with initial masses satisfying M<1015 g, instead of having explode, might currently be in a quasistable phase contributing to a tiny fraction of the measured dark matter. This statement is based on a computation of black hole evaporation in which energy conservation is taken into account that shows that the backreaction to Hawking radiation favors the quasistabilization of the black hole. The result is specifically shown for general spherically symmetric quantum black holes described by an effective metric independently of the specific framework from which it is derived. The quintessential primordial black hole is fully analyzed as an example., Peer Reviewed, Postprint (published version)

Published in Physics letters B by ELSEVIER. The original publication is available at http://www.sciencedirect.com/science/article/pii/S0370269313005066, Different approaches to quantum gravity conclude that black holes may possess an inner horizon, in addition to the (quantum corrected) outer ‘Schwarzschild’ horizon. In this paper we assume the existence of this inner horizon and explain the physical process that might lead to the tunneling of particles through it. It is shown that the tunneling would produce a flux of particles with a spectrum that deviates from the pure thermal one. Under the appropriate approximation the extremely high temperature of this horizon is calculated for an improved quantum black hole. It is argued that the flux of particles tunneled through the horizons affects the dynamics of the black hole interior leading to an endogenous instability., Preprint

Preprint of an article published in International journal of modern physics D, 23, 1, 2013, 1450009-1 - 1450009-15 10.1142/S0218271814500096 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijmpd, We claim that imposing energy conservation to the emission of Hawking radiation and to the modeling of black hole (BH) evaporation might prevent BH explosions as well as violations of the third law of BH thermodynamics. This is specifically shown for the general class of spherically symmetric quantum BHs described by an effective quantum vacuum invariant under boosts in the radial direction. No assumptions are made with regard to the specific framework from which the quantum BHs are derived., Preprint

The causal character of singularities is often studied in relation to the existence of naked singularities and the subsequent possible violation of the cosmic censorship conjecture. Generally, one constructs a model in the framework of general relativity described in some specific coordinates and finds an ad hoc procedure to analyze the character of the singularity. In this paper, we show that the causal character of the zero-areal-radius (R = 0) singularity in spherically symmetric models is related to some specific invariants. In this way, if some assumptions are satisfied, one can ascertain the causal character of the singularity algorithmically through the computation of these invariants and, therefore, independent of the coordinates used in the model., Peer Reviewed, Preprint

La motivació dels estudiants a les aules és un tema que preocupa a tots els professors de l’ensenyament. L’ideal seria que es pogués respondre a la pregunta “com es pot fer perquè els alumnes estiguin interessats a les aules?” Aquesta resposta encara no s’ha trobat, i tot apunta a que no sigui una resposta fàcil. En aquest treball es defineix un concepte clau dins el que és la motivació: la motivació intrínseca. Aquest tipus de motivació és la que fa que la gent faci activitats “perquè vol” i no perquè hi ha algun element extern que la força a fer-ho. A la definició es tracta de descriure, segons diferents autors, els components en que es pot dividir aquesta motivació. Al treball també es destaquen dos aspectes que controlen la motivació dels alumnes: el valor que donen als seus objectius i les atribucions causals que realitzen d’allò que perceben. Es proposen algunes actuacions a l’aula encarades a aprofitar aquests aspectes. S’ha fet també un breu estudi sobre dos tipus d’activitats de tipus no estàndard per a realitzar a l’aula. Per una banda, els problemes contextualitzats en les quals es basa la teoria de l’Educació Matemàtica Realista de l’escola Freudenthal, dels quals a la secció final del treball es porta una activitat concreta a l’aula, i d’altra banda, l’aprenentatge per projectes. A més, s’analitzen dues classes de matemàtiques a aules reals, identificant els elements de motivació utilitzats per professors diferents. Per últim, es descriu una activitat concreta que s’ha portat a l’aula: “L’aritmètica del rellotge”. És, com s’ha dit, del tipus “problema contextualitzat”. S’ha fet un petit anàlisi de l’actuació i de la valoració de l’activitat per part dels alumnes mitjançant una enquesta que han respost a l’aula.

El treball fi de màster pretén aportar una visió general, i alhora determinar el context educatiu actual en què es troben els països d’Espanya i del Regne Unit per mitjà de la comparativa d’alguns dels seus aspectes més rellevants. S’ha tractat d’abordar en un inici tot aquell element més extern que configura en sí el marc educatiu d’ambdós països com ara legislació educativa vigent, avaluació del sistema, calendari i horari escolar, estructura del sistema educatiu etc. Tot seguit s’ha aprofundit en aspectes més interns com són l’estudi del currículum i de la metodologia emprada en respecte a la matèria de matemàtiques, i sempre en base a l’etapa d’educació secundària obligatòria. A continuació s’ha observat ambdós països des de una tercera posició, totalment externa, com són les proves PISA, a partir de les quals s’han donat diverses dades en quant a l’educació com per exemple la despesa pública en educació, ràtio d’alumnes per professorat, formació acadèmica de la població etc. Per concloure, i dins l’apartat de conclusions, s’ha reflexionat de tot el que s’ha observat al llarg del treball, sobretot amb l’objectiu de respondre la hipòtesi inicialment formulada, i a més de donar una opinió personal sobre l’ús del mètode comparatiu com a mitjà d’explicar els resultats obtinguts en educació. Per realitzar el treball de fi de màster s’ha utilitzat informació extreta de documents oficials com són la llei orgànica d’educació, o el National Curriculum; també de dades estadístiques com les que ofereix l’Eurostat o el INE; així com d’articles, notícies i vídeos, amb el fi de servir de base de tota conclusió generada en el treball.

Many models in which the object under study loses all its mass have appeared in the literature. No doubt, the most eminent examples are the models for evaporating black holes and for evaporating stars. Here we describe a semiclassical study of these evaporating models centered on the evaporating event itself. We pay special attention to the evaporating models as a means of avoiding singularities during the collapse. In case of any pre-existing non-spacelike curvature singularity, we show that these models tend to evaporate it., Peer Reviewed, Postprint (published version)

Postprint (published version)

Postprint (published version)

A general class of quantum improved stellar models with interiors composed of non-interacting (dust) particles is obtained and analyzed in a framework compatible with asymptotic safety. First, the effective exterior, based on the Quantum Einstein Gravity approach to asymptotic safety is presented and, second, its effective compatible dust interiors are deduced. The resulting stellar models appear to be devoid of shell-focusing singularities. (C) 2014 The Author. Published by Elsevier B.V., Peer Reviewed, Postprint (published version)