On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

This paper is the third part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first part of this series we established the well posedness of the characteristic problem, whereas in the second part we studied the stability of the radius function at the Cauchy horizon. In this third and final paper we show that, depending on the decay rate of the initial data, mass inflation may or may not occur. When the mass is controlled, it is possible to obtain continuous extensions of the metric across the Cauchy horizon with square integrable Christoffel symbols. Under slightly stronger conditions, we can bound the gradient of the scalar field. This allows the construction of (non-isometric) extensions of the maximal development which are classical solutions of the Einstein equations. Our results provide evidence against the validity of the strong cosmic censorship conjecture when $\Lambda>0$.Comment: 48 pages, 5 figures; v2: some presentation changes, mostly in the Introduction; v3: substantial changes in Section 5; v4: expanded Introduction; some presentation changes; matches final published versio

On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon

This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first paper of this sequence, we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos on the stability of the radius function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed by Dafermos, focusing on the level sets of the radius function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper, we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.Comment: 44 pages, 13 figures; v2: a few small changes; v3: a paragraph was added in the Introduction, minor clarifications were made thoughout, the list of references was expanded, matches final published versio

Implementation of Compressed Sensing in Telecardiology Sensor Networks

Mobile solutions for patient cardiac monitoring are viewed with growing interest, and improvements on current implementations are frequently reported, with wireless, and in particular, wearable devices promising to achieve ubiquity. However, due to unavoidable power consumption limitations, the amount of data acquired, processed, and transmitted needs to be diminished, which is counterproductive, regarding the quality of the information produced. Compressed sensing implementation in wireless sensor networks (WSNs) promises to bring gains not only in power savings to the devices, but also with minor impact in signal quality. Several cardiac signals have a sparse representation in some wavelet transformations. The compressed sensing paradigm states that signals can be recovered from a few projections into another basis, incoherent with the first. This paper evaluates the compressed sensing paradigm impact in a cardiac monitoring WSN, discussing the implications in data reliability, energy management, and the improvements accomplished by in-network processing

Water Quality Monitoring and Associated Distributed Measurement Systems: An Overview

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Underwater Acoustic Source Localization and Sounds Classification in Distributed Measurement Networks

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Wireless sensor network-based solution for environmental monitoring: water quality assessment case study

The challenges of climate change, population growth, demographic change, urbanization and resource depletion mean that the world’s great cities need to adapt to survive and thrive over the coming decades. Slashing greenhouse gas emissions to prevent catastrophic climate change, while maintaining or increasing quality of life, can be a costly and dif cult process. Two factors that directly affect the life quality in the XXI century cities are the water and air quality that can be monitored using the combination of low cost sensing modules, machine to machine (M2M) and internet of things (IoT) technologies. In this context, this study presents a wireless sensor network architecture that combines low cost sensing nodes and a low cost multi- parameters sensing probe for reliable monitoring of water quality parameters of surface waters (lakes, estuaries and rivers) in urban areas. A particular attention is dedicated to the design of the conductivity, temperature and turbidity signal conditioning circuits, highlighting important issues related to linearisation, measuring dynamic range and low-cost implementation by using commercial off-the-shelf components and devices. Several issues related to the wireless sensor network implementation are included in this study, as well as several simulation and experimental results.info:eu-repo/semantics/publishedVersio