Birkhoff's Theorem in Higher Derivative Theories of Gravity

In this paper we present a class of higher derivative theories of gravity which admit Birkhoff's theorem. In particular, we explicitly show that in this class of theories, although generically the field equations are of fourth order, under spherical (plane or hyperbolic) symmetry, all the field equations reduce to second order and have exactly the same or similar structure to those of Lovelock theories, depending on the spacetime dimensions and the order of the Lagrangian.Comment: 7 pages, no figures. v1: This version received an Honorable Mention from the Gravity Research Foundation - 2011 Awards for Essays on Gravitation. v2: Expanded version. To appear in CQ

Unifying Functional Interpretations: Past and Future

This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of functional interpretations, functional interpretations "with truth", and bounded functional interpretations. Our goal in the present paper is twofold: (1) to look back and single out the main lessons learnt so far, and (2) to look forward and list several open questions and possible directions for further research.Comment: 18 page

All the solutions of the form M2(warped)x\Sigma(d-2) for Lovelock gravity in vacuum in the Chern-Simons case

In this note we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean base manifold Sigma(d-2) of dimension d-2. We show that the solutions are naturally classified in terms of the equations that restrict the base manifold. According to the strength of such constraints we found the following branches in which Sigma(d-2) has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d-2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d-2, or finally a degenerate case in which the base manifold is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Phys.Rev. D76 (2007) 064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally we comment on how the inclusion of a non-vanishing torsion and matter fields may modify this analysis.Comment: 15 pages, no figure

Regularizing effect of absorption terms in singular problems

We prove existence of solutions to problems whose model is $$\begin{cases} \displaystyle -\Delta_p u + u^q = \frac{f}{u^\gamma} & \text{in}\ \Omega, \newline u\ge0 &\text{in}\ \Omega,\newline u=0 &\text{on}\ \partial\Omega, \end{cases}$$ where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge2$), $\Delta_p u$ is the $p$-laplacian operator for $1\le p 0$, $\gamma\ge 0$ and $f$ is a nonnegative function in $L^m(\Omega)$ for some $m\ge1$. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case $\gamma\le 1$. We also study uniqueness of these solutions as well as examples which show the optimality of the results. Finally, we find local $W^{1,p}$-solutions in case $\gamma>1$

Transient Absorption and Raman Spectroscopies in Organic Electronics

Raman spectroscopy has proved to be a very valuable tool for characterization in a large number of research fields, both biological, chemical and material sciences.[1] In the last decades, organic electronics has broken out as a real alternative to conventional electronics, based on inorganic materials. However, in order to advance significantly in this field of research is paramount the full characterization of electronic devices, going from the individual molecule to the system as a whole. Moreover, the study of photophysical and photochemical processes crosses the interest of many fields of research in physics, chemistry and biology. Among the experimental approaches developed for this purpose, the advent of ultrafast transient absorption spectroscopy has become a powerful and widely used method.[2,3] This pump-probe technique is a popular means of studying photophysics, because of its versatile time resolution and its ease of comparison with ground-state absorption spectra. In this communication, I will present the basic principles of transient absorption spectroscopy, along with some examples where its combination with Raman spectroscopy allows the great characterization of organic molecules with potential applications in organic electronics.[4,5] References [1] H. Schulz, M. Baranska, R. Baranski. Biopolymers 2005, 77, 212 - 221. [2] U. Megerle, I. Pugliesi, C. Schriever, C.F. Sailer, E. Riedle. Appl. Phys. B, 2009, 96, 215 - 231. [3] R. Berera, R. van Grondelle, J.T.M. Kennis. Photosynth. Res. 2009, 101, 105 - 118. [4] E. Anaya-Plaza, M. Moreno Oliva, A. Kunzmann, C. Romero-Nieto, R.D. Costa, A. de la Escosura, D.M. Guldi, T. Torres. Adv. Funct. Mater. 2015, 25, 7418 - 7427. [5] F. Liu, G.L. Espejo, S. Qiu, M. Moreno Oliva, J. Pina, J.S. Seixas de Melo, J. Casado, X. Zhu. J. Am. Chem. Soc. 2015, 137, 10357 - 10366.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech