Large entropy production inside black holes: a simple model

Particles dropped into a rotating black hole can collide near the inner horizon with enormous energies. The entropy produced by these collisions can be several times larger than the increase in the horizon entropy due to the addition of the particles. In this paper entropy is produced by releasing large numbers of neutrons near the outer horizon of a rotating black hole such that they collide near the inner horizon at energies similar to those achieved at the Relativistic Heavy Ion Collider. The increase in horizon entropy is approximately 80 per dropped neutron pair, while the entropy produced in the collisions is 160 per neutron pair. The collision entropy is produced inside the horizon, so this excess entropy production does not violate Bousso's bound limiting the entropy that can go through the black hole's horizon. The generalized laws of black hole thermodynamics are obeyed. No individual observer inside the black hole sees a violation of the second law of thermodynamicsComment: 10 page

The interior structure of rotating black holes 1. Concise derivation

This paper presents a concise derivation of a new set of solutions for the interior structure of accreting, rotating black holes. The solutions are conformally stationary, axisymmetric, and conformally separable. Hyper-relativistic counter-streaming between freely-falling collisionless ingoing and outgoing streams leads to mass inflation at the inner horizon, followed by collapse. The solutions fail at an exponentially tiny radius, where the rotational motion of the streams becomes comparable to their radial motion. The papers provide a fully nonlinear, dynamical solution for the interior structure of a rotating black hole from just above the inner horizon inward, down to a tiny scale.Comment: Version 1: 8 pages, 3 figures. Version 2: Extensively revised to emphasize the derivation of the solution rather than the solution itself. 11 pages, 4 figures. Version 3: Minor changes to match published version. Mathematica notebook available at http://jila.colorado.edu/~ajsh/rotatinginflationary/rotatinginflationary.n

Walking on common ground: a cross-disciplinary scoping review on the clinical utility of digital mobility outcomes

Physical mobility is essential to health, and patients often rate it as a high-priority clinical outcome. Digital mobility outcomes (DMOs), such as real-world gait speed or step count, show promise as clinical measures in many medical conditions. However, current research is nascent and fragmented by discipline. This scoping review maps existing evidence on the clinical utility of DMOs, identifying commonalities across traditional disciplinary divides. In November 2019, 11 databases were searched for records investigating the validity and responsiveness of 34 DMOs in four diverse medical conditions (Parkinson's disease, multiple sclerosis, chronic obstructive pulmonary disease, hip fracture). Searches yielded 19,672 unique records. After screening, 855 records representing 775 studies were included and charted in systematic maps. Studies frequently investigated gait speed (70.4% of studies), step length (30.7%), cadence (21.4%), and daily step count (20.7%). They studied differences between healthy and pathological gait (36.4%), associations between DMOs and clinical measures (48.8%) or outcomes (4.3%), and responsiveness to interventions (26.8%). Gait speed, step length, cadence, step time and step count exhibited consistent evidence of validity and responsiveness in multiple conditions, although the evidence was inconsistent or lacking for other DMOs. If DMOs are to be adopted as mainstream tools, further work is needed to establish their predictive validity, responsiveness, and ecological validity. Cross-disciplinary efforts to align methodology and validate DMOs may facilitate their adoption into clinical practice

Entropy creation inside black holes points to observer complementarity

Heating processes inside large black holes can produce tremendous amounts of entropy. Locality requires that this entropy adds on space-like surfaces, but the resulting entropy (10^10 times the Bekenstein-Hawking entropy in an example presented in the companion paper) exceeds the maximum entropy that can be accommodated by the black hole's degrees of freedom. Observer complementarity, which proposes a proliferation of non-local identifications inside the black hole, allows the entropy to be accommodated as long as individual observers inside the black hole see less than the Bekenstein-Hawking entropy. In the specific model considered with huge entropy production, we show that individual observers do see less than the Bekenstein-Hawking entropy, offering strong support for observer complementarity.Comment: 13 pages. This is a companion paper to arXiv:0801.4415; Added reference

Walking-related digital mobility outcomes as clinical trial endpoint measures: protocol for a scoping review

Introduction Advances in wearable sensor technology now enable frequent, objective monitoring of real-world walking. Walking-related digital mobility outcomes (DMOs), such as real-world walking speed, have the potential to be more sensitive to mobility changes than traditional clinical assessments. However, it is not yet clear which DMOs are most suitable for formal validation. In this review, we will explore the evidence on discriminant ability, construct validity, prognostic value and responsiveness of walking-related DMOs in four disease areas: Parkinson’s disease, multiple sclerosis, chronic obstructive pulmonary disease and proximal femoral fracture. Methods and analysis Arksey and O’Malley’s methodological framework for scoping reviews will guide study conduct. We will search seven databases (Medline, CINAHL, Scopus, Web of Science, EMBASE, IEEE Digital Library and Cochrane Library) and grey literature for studies which (1) measure differences in DMOs between healthy and pathological walking, (2) assess relationships between DMOs and traditional clinical measures, (3) assess the prognostic value of DMOs and (4) use DMOs as endpoints in interventional clinical trials. Two reviewers will screen each abstract and full-text manuscript according to predefined eligibility criteria. We will then chart extracted data, map the literature, perform a narrative synthesis and identify gaps. Ethics and dissemination As this review is limited to publicly available materials, it does not require ethical approval. This work is part of Mobilise-D, an Innovative Medicines Initiative Joint Undertaking which aims to deliver, validate and obtain regulatory approval for DMOs. Results will be shared with the scientific community and general public in cooperation with the Mobilise-D communication team. Registration Study materials and updates will be made available through the Center for Open Science’s OSFRegistry (https://osf.io/k7395)

Connecting real-world digital mobility assessment to clinical outcomes for regulatory and clinical endorsement–the Mobilise-D study protocol

Background: The development of optimal strategies to treat impaired mobility related to ageing and chronic disease requires better ways to detect and measure it. Digital health technology, including body worn sensors, has the potential to directly and accurately capture real-world mobility. Mobilise-D consists of 34 partners from 13 countries who are working together to jointly develop and implement a digital mobility assessment solution to demonstrate that real-world digital mobility outcomes have the potential to provide a better, safer, and quicker way to assess, monitor, and predict the efficacy of new interventions on impaired mobility. The overarching objective of the study is to establish the clinical validity of digital outcomes in patient populations impacted by mobility challenges, and to support engagement with regulatory and health technology agencies towards acceptance of digital mobility assessment in regulatory and health technology assessment decisions. Methods/design: The Mobilise-D clinical validation study is a longitudinal observational cohort study that will recruit 2400 participants from four clinical cohorts. The populations of the Innovative Medicine Initiative-Joint Undertaking represent neurodegenerative conditions (Parkinson’s Disease), respiratory disease (Chronic Obstructive Pulmonary Disease), neuro-inflammatory disorder (Multiple Sclerosis), fall-related injuries, osteoporosis, sarcopenia, and frailty (Proximal Femoral Fracture). In total, 17 clinical sites in ten countries will recruit participants who will be evaluated every six months over a period of two years. A wide range of core and cohort specific outcome measures will be collected, spanning patient-reported, observer-reported, and clinician-reported outcomes as well as performance-based outcomes (physical measures and cognitive/mental measures). Daily-living mobility and physical capacity will be assessed directly using a wearable device. These four clinical cohorts were chosen to obtain generalizable clinical findings, including diverse clinical, cultural, geographical, and age representation. The disease cohorts include a broad and heterogeneous range of subject characteristics with varying chronic care needs, and represent different trajectories of mobility disability. Discussion: The results of Mobilise-D will provide longitudinal data on the use of digital mobility outcomes to identify, stratify, and monitor disability. This will support the development of widespread, cost-effective access to optimal clinical mobility management through personalised healthcare. Further, Mobilise-D will provide evidence-based, direct measures which can be endorsed by regulatory agencies and health technology assessment bodies to quantify the impact of disease-modifying interventions on mobility. Trial registration: ISRCTN12051706