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

On the Relationship Between Ultrasonic and Micro-Structural Properties of Imperfect Interfaces in Layered Solids

The interaction of ultrasonic waves with interfaces formed by two non-conforming, rough surfaces in contact has been the subject of numerous investigations [1–10]. The motivations behind these studies have been various: from the assessment of the real area of contact between two rough surfaces [1], to the modeling of crack closure near the tip of a fatigue crack [4]; from the identification of the nature of interfacial imperfections in kissing and partial bonds [6], to the generation of ultrasonic waves [8]. In most of these studies, the characterization of the interfacial properties has been attempted by studying the reflection of longitudinal and shears waves at normal incidence. Only recently, the problem concerning the interaction of ultrasonic waves with realistic complex systems such as that formed by two neighboring imperfect interfaces has been addressed. Lavrentyev and Rokhlin [9, 10] used ultrasonic spectroscopy to evaluate the interfacial conditions from the spectra of longitudinal and shear waves reflected normally from the interfaces

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

Champions, converts, doubters, and defectors: the impact of shifting perceptions on momentum for change

Maintaining momentum is a key influence on the ultimate success of large-scale change. In this paper, we develop theory to explain how stable vs. shifting change-supportive perceptions over time differentially influence the perceived momentum associated with goal-directed change (i.e., change-based momentum). We use cross-level polynomial regression and data obtained early and one year later within an organization implementing a lean manufacturing transformation to model changes in individual perceptions. Results suggest that momentum perceptions are higher for “Champions” (stable and high perceptions over time) as compared to “Converts” (increasing perceptions over time), but momentum perceptions are lower for “Defectors” (decreasing perceptions over time) as compared to “Doubters” (stable and low perceptions over time). We find that even if participants converge upon change-supportive perceptions later in the change process, early divergent perceptions influence subsequent momentum for the change. These findings highlight the important role of temporal shifts in perceptions for organizational change processes

A Gammaherpesviral Internal Repeat Contributes to Latency Amplification

BACKGROUND: Gammaherpesviruses cause important infections of humans, in particular in immunocompromised patients. The genomes of gammaherpesviruses contain variable numbers of internal repeats whose precise role for in vivo pathogenesis is not well understood. METHODOLOGY/PRINCIPAL FINDINGS: We used infection of laboratory mice with murine gammaherpesvirus 68 (MHV-68) to explore the biological role of the 40 bp internal repeat of MHV-68. We constructed several mutant viruses partially or completely lacking this repeat. Both in vitro and in vivo, the loss of the repeat did not substantially affect lytic replication of the mutant viruses. However, the extent of splenomegaly, which is associated with the establishment of latency, and the number of ex vivo reactivating and genome positive splenocytes were reduced. Since the 40 bp repeat is part of the hypothetical open reading frame (ORF) M6, it might function as part of M6 or as an independent structure. To differentiate between these two possibilities, we constructed an N-terminal M6STOP mutant, leaving the repeat structure intact but rendering ORF M6 unfunctional. Disruption of ORF M6 did neither affect lytic nor latent infection. In contrast to the situation in lytically infected NIH3T3 cells, the expression of the latency-associated genes K3 and ORF72 was reduced in the latently infected murine B cell line Ag8 in the absence of the 40 bp repeat. CONCLUSIONS/SIGNIFICANCE: These data suggest that the 40 bp repeat contributes to latency amplification and might be involved in the regulation of viral gene expression

Weinberg like sum rules revisited

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We summarize the status of these sum rules and analyze their overall agreement with phenomenological Lagrangians, low-energy relations, parity doubling, hadron string models, and experimental data.Comment: 31 pages, noticed misprints are corrected, references are added, and other minor corrections are mad