Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version

Classical and quantum: a conflict of interest

We highlight three conflicts between quantum theory and classical general relativity, which make it implausible that a quantum theory of gravity can be arrived at by quantising classical gravity. These conflicts are: quantum nonlocality and space-time structure; the problem of time in quantum theory; and the quantum measurement problem. We explain how these three aspects bear on each other, and how they point towards an underlying noncommutative geometry of space-time.Comment: 15 pages. Published in `Gravity and the quantum' [Essays in honour of Thanu Padmanabhan on the occasion of his sixtieth birthday] Eds. Jasjeet Singh Bagla and Sunu Engineer (Springer, 2017

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

P-odd and CP-odd Four-Quark Contributions to Neutron EDM

In a class of beyond-standard-model theories, CP-odd observables, such as the neutron electric dipole moment, receive significant contributions from flavor-neutral P-odd and CP-odd four-quark operators. However, considerable uncertainties exist in the hadronic matrix elements of these operators strongly affecting the experimental constraints on CP-violating parameters in the theories. Here we study their hadronic matrix elements in combined chiral perturbation theory and nucleon models. We first classify the operators in chiral representations and present the leading-order QCD evolutions. We then match the four-quark operators to the corresponding ones in chiral hadronic theory, finding symmetry relations among the matrix elements. Although this makes lattice QCD calculations feasible, we choose to estimate the non-perturbative matching coefficients in simple quark models. We finally compare the results for the neutron electric dipole moment and P-odd and CP-odd pion-nucleon couplings with the previous studies using naive factorization and QCD sum rules. Our study shall provide valuable insights on the present hadronic physics uncertainties in these observables.Comment: 40 pages, 7 figures. This is the final version. A discussion of the uncertainty of the calculation is adde

Order and Stochastic Dynamics in Drosophila Planar Cell Polarity

Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model

Proof over promise: towards a more inclusive ranking of Dutch academics in Economics & Business

The Dutch Economics top-40, based on publications in ISI listed journals, is - to the best of our knowledge - the oldest ranking of individual academics in Economics and is well accepted in the Dutch academic community. However, this ranking is based on publication volume, rather than on the actual impact of the publications in question. This paper therefore uses two relatively new metrics, the citations per author per year (CAY) metric and the individual annual h-index (hIa) to provide two alternative, citation-based, rankings of Dutch academics in Economics & Business. As a data source, we use Google Scholar instead of ISI to provide a more comprehensive measure of impact, including citations to and from publications in non-ISI listed journals, books, working and conference papers. The resulting rankings are shown to be substantially different from the original ranking based on publications. Just like other research metrics, the CAY or hIa-index should never be used as the sole criterion to evaluate academics. However, we do argue that the hIa-index and the related citations per author per year metric provide an important additional perspective over and above a ranking based on publications in high impact journals alone. Citation-based rankings are also shown to inject a higher level of diversity in terms of age, gender, discipline and academic affiliation and thus appear to be more inclusive of a wider range of scholarship

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Incidence of re-amputation following partial first ray amputation associated with diabetes mellitus and peripheral sensory neuropathy: a systematic review.

Diabetes mellitus with peripheral sensory neuropathy frequently results in forefoot ulceration. Ulceration at the first ray level tends to be recalcitrant to local wound care modalities and off-loading techniques. If healing does occur, ulcer recurrence is common. When infection develops, partial first ray amputation in an effort to preserve maximum foot length is often performed. However, the survivorship of partial first ray amputations in this patient population and associated re-amputation rate remain unknown. Therefore, in an effort to determine the actual re-amputation rate following any form of partial first ray amputation in patients with diabetes mellitus and peripheral neuropathy, the authors conducted a systematic review. Only studies involving any form of partial first ray amputation associated with diabetes mellitus and peripheral sensory neuropathy but without critical limb ischemia were included. Our search yielded a total of 24 references with 5 (20.8%) meeting our inclusion criteria involving 435 partial first ray amputations. The weighted mean age of patients was 59 years and the weighted mean follow-up was 26 months. The initial amputation level included the proximal phalanx base 167 (38.4%) times; first metatarsal head resection 96 (22.1%) times; first metatarsal-phalangeal joint disarticulation 53 (12.2%) times; first metatarsal mid-shaft 39 (9%) times; hallux fillet flap 32 (7.4%) times; first metatarsal base 29 (6.7%) times; and partial hallux 19 (4.4%) times. The incidence of re-amputation was 19.8% (86/435). The end stage, most proximal level, following re-amputation was an additional digit 32 (37.2%) times; transmetatarsal 28 (32.6%) times; below-knee 25 (29.1%) times; and LisFranc 1 (1.2%) time. The results of our systematic review reveal that one out of every five patients undergoing any version of a partial first ray amputation will eventually require more proximal re-amputation. These results reveal that partial first ray amputation for patients with diabetes and peripheral sensory neuropathy may not represent a durable, functional, or predictable foot-sparing amputation and that a more proximal amputation, such as a balanced transmetatarsal amputation, as the index amputation may be more beneficial to the patient. However, this remains a matter for conjecture due to the limited data available and, therefore, additional prospective investigations are warranted

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201