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

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

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

Performance of the CMS Cathode Strip Chambers with Cosmic Rays

The Cathode Strip Chambers (CSCs) constitute the primary muon tracking device in the CMS endcaps. Their performance has been evaluated using data taken during a cosmic ray run in fall 2008. Measured noise levels are low, with the number of noisy channels well below 1%. Coordinate resolution was measured for all types of chambers, and fall in the range 47 microns to 243 microns. The efficiencies for local charged track triggers, for hit and for segments reconstruction were measured, and are above 99%. The timing resolution per layer is approximately 5 ns

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

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

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Applying Bayesian model averaging for uncertainty estimation of input data in energy modelling

Background Energy scenarios that are used for policy advice have ecological and social impact on society. Policy measures that are based on modelling exercises may lead to far reaching financial and ecological consequences. The purpose of this study is to raise awareness that energy modelling results are accompanied with uncertainties that should be addressed explicitly. Methods With view to existing approaches of uncertainty assessment in energy economics and climate science, relevant requirements for an uncertainty assessment are defined. An uncertainty assessment should be explicit, independent of the assessor&#8217;s expertise, applicable to different models, including subjective quantitative and statistical quantitative aspects, intuitively understandable and be reproducible. Bayesian model averaging for input variables of energy models is discussed as method that satisfies these requirements. A definition of uncertainty based on posterior model probabilities of input variables to energy models is presented. Results The main findings are that (1) expert elicitation as predominant assessment method does not satisfy all requirements, (2) Bayesian model averaging for input variable modelling meets the requirements and allows evaluating a vast amount of potentially relevant influences on input variables and (3) posterior model probabilities of input variable models can be translated in uncertainty associated with the input variable. Conclusions An uncertainty assessment of energy scenarios is relevant if policy measures are (partially) based on modelling exercises. Potential implications of these findings include that energy scenarios could be associated with uncertainty that is presently neither assessed explicitly nor communicated adequately