A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no figure

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

G\"odel Incompleteness and the Black Hole Information Paradox

Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization is to identify the G\"odel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement

Gravitational and Yang-Mills instantons in holographic RG flows

We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\times S^3/\mathbb{Z}_N$ and $AdS_3\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by a vacuum expectation value of a marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\times S^5/\mathbb{Z}_N$ and $AdS_5\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theory in the IR, with gauge group $USp(n)$. The corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/\mathbb{Z}_2$, respectively. We also explore more general RG flows, in which both the UV and IR CFTs are N=2 quiver gauge theories and the corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/(\mathbb{Z}_M\times \mathbb{Z}_2)$. Finally, we discuss the matching between the geometric and field theoretic pictures of the flows.Comment: 32 pages, 3 figures, typoe corrected and a reference adde

The Spectrometer/Telescope for Imaging X-rays (STIX)

Aims. The Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter is a hard X-ray imaging spectrometer, which covers the energy range from 4 to 150 keV. STIX observes hard X-ray bremsstrahlung emissions from solar flares and therefore provides diagnostics of the hottest (⪆10 MK) flare plasma while quantifying the location, spectrum, and energy content of flare-accelerated nonthermal electrons. Methods. To accomplish this, STIX applies an indirect bigrid Fourier imaging technique using a set of tungsten grids (at pitches from 0.038 to 1 mm) in front of 32 coarsely pixelated CdTe detectors to provide information on angular scales from 7 to 180 arcsec with 1 keV energy resolution (at 6 keV). The imaging concept of STIX has intrinsically low telemetry and it is therefore well-suited to the limited resources available to the Solar Orbiter payload. To further reduce the downlinked data volume, STIX data are binned on board into 32 selectable energy bins and dynamically-adjusted time bins with a typical duration of 1 s during flares. Results. Through hard X-ray diagnostics, STIX provides critical information for understanding the acceleration of electrons at the Sun and their transport into interplanetary space and for determining the magnetic connection of Solar Orbiter back to the Sun. In this way, STIX serves to link Solar Orbiter’s remote and in-situ measurements

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

STIX X-ray microflare observations during the Solar Orbiter commissioning phase

Context. The Spectrometer/Telescope for Imaging X-rays (STIX) is the hard X-ray instrument onboard Solar Orbiter designed to observe solar flares over a broad range of flare sizes. Aims. We report the first STIX observations of solar microflares recorded during the instrument commissioning phase in order to investigate the STIX performance at its detection limit. Methods. STIX uses hard X-ray imaging spectroscopy in the range between 4-150 keV to diagnose the hottest flare plasma and related nonthermal electrons. This first result paper focuses on the temporal and spectral evolution of STIX microflares occuring in the Active Region (AR) AR12765 in June 2020, and compares the STIX measurements with Earth-orbiting observatories such as the X-ray Sensor of the Geostationary Operational Environmental Satellite (GOES/XRS), the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, and the X-ray Telescope of the Hinode mission. Results. For the observed microflares of the GOES A and B class, the STIX peak time at lowest energies is located in the impulsive phase of the flares, well before the GOES peak time. Such a behavior can either be explained by the higher sensitivity of STIX to higher temperatures compared to GOES, or due to the existence of a nonthermal component reaching down to low energies. The interpretation is inconclusive due to limited counting statistics for all but the largest flare in our sample. For this largest flare, the low-energy peak time is clearly due to thermal emission, and the nonthermal component seen at higher energies occurs even earlier. This suggests that the classic thermal explanation might also be favored for the majority of the smaller flares. In combination with EUV and soft X-ray observations, STIX corroborates earlier findings that an isothermal assumption is of limited validity. Future diagnostic efforts should focus on multi-wavelength studies to derive differential emission measure distributions over a wide range of temperatures to accurately describe the energetics of solar flares. Conclusions. Commissioning observations confirm that STIX is working as designed. As a rule of thumb, STIX detects flares as small as the GOES A class. For flares above the GOES B class, detailed spectral and imaging analyses can be performed

Models and data analysis tools for the Solar Orbiter mission

Context. The Solar Orbiter spacecraft will be equipped with a wide range of remote-sensing (RS) and in situ (IS) instruments to record novel and unprecedented measurements of the solar atmosphere and the inner heliosphere. To take full advantage of these new datasets, tools and techniques must be developed to ease multi-instrument and multi-spacecraft studies. In particular the currently inaccessible low solar corona below two solar radii can only be observed remotely. Furthermore techniques must be used to retrieve coronal plasma properties in time and in three dimensional (3D) space. Solar Orbiter will run complex observation campaigns that provide interesting opportunities to maximise the likelihood of linking IS data to their source region near the Sun. Several RS instruments can be directed to specific targets situated on the solar disk just days before data acquisition. To compare IS and RS, data we must improve our understanding of how heliospheric probes magnetically connect to the solar disk.Aims. The aim of the present paper is to briefly review how the current modelling of the Sun and its atmosphere can support Solar Orbiter science. We describe the results of a community-led effort by European Space Agency's Modelling and Data Analysis Working Group (MADAWG) to develop different models, tools, and techniques deemed necessary to test different theories for the physical processes that may occur in the solar plasma. The focus here is on the large scales and little is described with regards to kinetic processes. To exploit future IS and RS data fully, many techniques have been adapted to model the evolving 3D solar magneto-plasma from the solar interior to the solar wind. A particular focus in the paper is placed on techniques that can estimate how Solar Orbiter will connect magnetically through the complex coronal magnetic fields to various photospheric and coronal features in support of spacecraft operations and future scientific studies.Methods. Recent missions such as STEREO, provided great opportunities for RS, IS, and multi-spacecraft studies. We summarise the achievements and highlight the challenges faced during these investigations, many of which motivated the Solar Orbiter mission. We present the new tools and techniques developed by the MADAWG to support the science operations and the analysis of the data from the many instruments on Solar Orbiter.Results. This article reviews current modelling and tool developments that ease the comparison of model results with RS and IS data made available by current and upcoming missions. It also describes the modelling strategy to support the science operations and subsequent exploitation of Solar Orbiter data in order to maximise the scientific output of the mission.Conclusions. The on-going community effort presented in this paper has provided new models and tools necessary to support mission operations as well as the science exploitation of the Solar Orbiter data. The tools and techniques will no doubt evolve significantly as we refine our procedure and methodology during the first year of operations of this highly promising mission.Peer reviewe

The Solar Orbiter Science Activity Plan: translating solar and heliospheric physics questions into action

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate?; (2) How do solar transients drive heliospheric variability?; (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere?; (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission’s science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit’s science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans, resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime. This allows for all four mission goals to be addressed. In this paper, we introduce Solar Orbiter’s SAP through a series of examples and the strategy being followed