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One of the theoretical motivations behind the belief that black holes as described by general relativity exist in nature is that it is hard to find matter configurations that mimic their properties, especially their compactness. One of the classic results that goes in this direction is the so-called Buchdahl limit: a bound for the maximum compactness that, under a few assumptions, static fluid spheres in hydrostatic equilibrium can possibly have. We highlight two of the main assumptions that could be violated in physically realistic situations: i) isotropy and ii) an outward-decreasing monotonicity of the density profile, which, as we discuss in detail, can be understood as a form of energy condition. We construct a pair of toy models that exemplify how the Buchdahl limit can be overcome if any of these two assumptions is individually relaxed. In particular, we show that relaxing the monotonicity assumption alone yields a new, less restrictive compactness limit as long as the energy density is not allowed to become negative. If negative energies are permitted, the compactness of these toy models can be as close to the black hole limit as desired. We also discuss how these toy models represent some of the main features of realistic systems, and how they could be extended to find more refined models., Comment: 37 pages, 7 figures

BabyIAXO is the intermediate stage of the International Axion Observatory (IAXO) to be hosted at DESY. Its primary goal is the detection of solar axions following the axion helioscope technique. Axions are converted into photons in a large magnet that is pointing to the sun. The resulting X-rays are focused by appropriate X-ray optics and detected by sensitive low-background detectors placed at the focal spot. The aim of this article is to provide an accurate quantitative description of the different components (such as the magnet, optics, and X-ray detectors) involved in the detection of axions. Our efforts have focused on developing robust and integrated software tools to model these helioscope components, enabling future assessments of modifications or upgrades to any part of the IAXO axion helioscope and evaluating the potential impact on the experiment's sensitivity. In this manuscript, we demonstrate the application of these tools by presenting a precise signal calculation and response analysis of BabyIAXO's sensitivity to the axion-photon coupling. Though focusing on the Primakoff solar flux component, our virtual helioscope model can be used to test different production mechanisms, allowing for direct comparisons within a unified framework., Comment: 36 pages, 18 figures, 4 tables, Submitted to JHEP

The development of Internet of Things (IoT) technologies has led to the widespread adoption of monitoring networks for a wide variety of applications, such as smart cities, environmental monitoring, and precision agriculture. A major research focus in recent years has been the development of graph-based techniques to improve the quality of data from sensor networks, a key aspect for the use of sensed data in decision-making processes, digital twins, and other applications. Emphasis has been placed on the development of machine learning and signal processing techniques over graphs, taking advantage of the benefits provided by the use of structured data through a graph topology. Many technologies such as the graph signal processing (GSP) or the successful graph neural networks (GNNs) have been used for data quality enhancement tasks. In this survey, we focus on graph-based models for data quality control in monitoring sensor networks. Furthermore, we delve into the technical details that are commonly leveraged for providing powerful graph-based solutions for data quality tasks in sensor networks, including missing value imputation, outlier detection, or virtual sensing. To conclude, we have identified future trends and challenges such as graph-based models for digital twins or model transferability and generalization., Comment: Paper submitted to Journal of Network and Computer Applications

Fine-tuning foundation models via reinforcement learning (RL) has proven promising for aligning to downstream objectives. In the case of diffusion models (DMs), though RL training improves alignment from early timesteps, critical issues such as training instability and mode collapse arise. We address these drawbacks by exploiting the hierarchical nature of DMs: we train them dynamically at each epoch with a tailored RL method, allowing for continual evaluation and step-by-step refinement of the model performance (or alignment). Furthermore, we find that not every denoising step needs to be fine-tuned to align DMs to downstream tasks. Consequently, in addition to clipping, we regularise model parameters at distinct learning phases via a sliding-window approach. Our approach, termed Hierarchical Reward Fine-tuning (HRF), is validated on the Denoising Diffusion Policy Optimisation method, where we show that models trained with HRF achieve better preservation of diversity in downstream tasks, thus enhancing the fine-tuning robustness and at uncompromising mean rewards.

No-hair theorems are uniqueness results constraining the form of the metric of black holes in general relativity. These theorems are typically formulated under idealized assumptions, involving a mixture of local (regularity of the horizon) and global aspects (vacuum spacetime and asymptotic flatness). This limits their applicability to astrophysical scenarios of interest such as binary black holes and accreting systems, as well as their extension to horizonless objects. A previous result due to G\"urlebeck constrains the asymptotic multipolar structure of static spacetimes containing black holes surrounded by matter although not revealing the possible structure of the metric itself. In this work, we disentangle some of these assumptions in the static and axisymmetric case. Specifically: i) we show that only a one-parameter family of black-hole geometries is compatible with a given external gravitational field, ii) we also analyze the case in which the central object is close to forming an event horizon but is still horizonless and show that the deviations from the natural black-hole shape have to die off as one approaches the black hole limit under the physical principle that curvatures are bounded., Comment: 53 pages, 17 figures

Ocean mesoscale variability, a key component of the climate system, influences ocean circulation and heat, gas, carbon and nutrient distribution. Trends on Eddy Kinetic Energy (EKE), a metric measuring its intensity, are investigated using two products constructed from 30 years of altimetric observations. Statistically significant positive trends in globally-averaged EKE reveal a strengthening of 1-3% per decade. Regions of intense mesoscale activity become more energetic than other areas. Robust positive EKE trends are observed in the Kuroshio Extension and the Gulf Stream, with remarkable EKE increases of ~50% and ~20%, respectively, over the last decade. Our study opens a new question into how the observed Gulf Stream strengthening impacts the AMOC, and challenges existing climate models emphasizing the necessity for improved small-scale ocean process representation.

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

This article reviews different microwave technologies used in dark matter axion detection experiments with resonant cavities. The general concepts of the experiment are presented and ways to optimize the design parameters of microwave resonators are discussed. Additionally, different frequency tuning systems are described. Finally, research lines where microwave engineering can contribute to this kind of axion detection are presented.

We describe the results of a haloscope axion search performed with an 11.7 T dipole magnet at CERN. The search used a custom-made radio-frequency cavity coated with high-temperature superconducting tape. A set of 27 h of data at a resonant frequency of around 8.84 GHz was analysed. In the range of axion mass 36.5676 $\mu$eV to 36.5699 $\mu$eV, corresponding to a width of 554 kHz, no signal excess hinting at an axion-like particle was found. Correspondingly, in this mass range, a limit on the axion to photon coupling-strength was set in the range between g$_{a\gamma}\gtrsim$ 6.2e-13 GeV$^{-1}$ and g$_{a\gamma}\gtrsim$ 1.54e-13 GeV$^{-1}$ with a 95% confidence level., Comment: 19 pages, 8 figures

Thanks to technologies such as virtual network function the Fifth Generation (5G) of mobile networks dynamically allocate resources to different types of users in an on-demand fashion. Virtualization extends up to the 5G core, where software-defined networks and network slicing implement a customizable environment. These technologies can be controlled via application programming interfaces and web technologies, inheriting hence their security risks and settings. An attacker exploiting vulnerable implementations of the 5G core may gain privileged control of the network assets and disrupt its availability. However, there is currently no security assessment of the web security of the 5G core network. In this paper, we present the first security assessment of the 5G core from a web security perspective. We use the STRIDE threat modeling approach to define a complete list of possible threat vectors and associated attacks. Thanks to a suite of security testing tools, we cover all of these threats and test the security of the 5G core. In particular, we test the three most relevant open-source 5G core implementations, i.e., Open5GS, Free5Gc, and OpenAirInterface. Our analysis shows that all these cores are vulnerable to at least two of our identified attack vectors, demanding increased security measures in the development of future 5G core networks.

Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to relational hypergraphs, where the task of link prediction is over $k$-ary relations, which is substantially harder than link prediction with knowledge graphs. In this paper, we propose a framework for link prediction with relational hypergraphs, unlocking applications of graph neural networks to fully relational structures. Theoretically, we conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms and also via logical expressiveness. Empirically, we validate the power of the proposed model architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction, and lead to state-of-the-art results for transductive link prediction.

The axion haloscope is the currently most sensitive method to probe the vanishingly small coupling of this prominent Dark Matter candidate to photons. To scan a sizeable axion Dark Matter parameter space, the cavities that make up the haloscope need to be tuned efficiently. In this article, we describe a novel technique to tune axion haloscopes around $8.4$ GHz in a purely mechanical manner without the use of dielectrics. We achieve tuning by introducing a gap along the cavity geometry. Losses are added due to the leaking of the field out of the structure only if the gap becomes too large concerning the total width. A tuning range of around $600$ MHz is achieved, depending on the environmental conditions. We present the results of a corresponding prototype and outline prospects to further develop this technique.

We present the results of a systematic search of the Transiting Exoplanet Survey Satellite (TESS) 2-min cadence data for new rapidly oscillating Ap (roAp) stars observed during the Cycle 2 phase of its mission. We find seven new roAp stars previously unreported as such and present the analysis of a further 25 roAp stars that are already known. Three of the new stars show multiperiodic pulsations, while all new members are rotationally variable stars, leading to almost 70 per cent (22) of the roAp stars presented being $\alpha^2$ CVn-type variable stars. We show that targeted observations of known chemically peculiar stars are likely to overlook many new roAp stars, and demonstrate that multi-epoch observations are necessary to see pulsational behaviour changes. We find a lack of roAp stars close to the blue edge of the theoretical roAp instability strip, and reaffirm that mode instability is observed more frequently with precise, space-based observations. In addition to the Cycle 2 observations, we analyse TESS data for all known roAp stars. This amounts to 18 further roAp stars observed by TESS. Finally, we list six known roAp stars that TESS is yet to observe. We deduce that the incidence of roAp stars amongst the Ap star population is just 5.5 per cent, raising fundamental questions about the conditions required to excite pulsations in Ap stars. This work, coupled with our previous work on roAp stars in Cycle 1 observations, presents the most comprehensive, homogeneous study of the roAp stars in the TESS nominal mission, with a collection of 112 confirmed roAp stars in total., Comment: Accepted for publication in MNRAS. 32 Pages, 2 Tables, 77 Figures

Spatial statistics is traditionally based on stationary models on $\mathbb{R^d}$ like Mat\'ern fields. The adaptation of traditional spatial statistical methods, originally designed for stationary models in Euclidean spaces, to effectively model phenomena on linear networks such as stream systems and urban road networks is challenging. The current study aims to analyze the incidence of traffic accidents on road networks using three different methodologies and compare the model performance for each methodology. Initially, we analyzed the application of spatial triangulation precisely on road networks instead of traditional continuous regions. However, this approach posed challenges in areas with complex boundaries, leading to the emergence of artificial spatial dependencies. To address this, we applied an alternative computational method to construct nonstationary barrier models. Finally, we explored a recently proposed class of Gaussian processes on compact metric graphs, the Whittle-Mat\'ern fields, defined by a fractional SPDE on the metric graph. The latter fields are a natural extension of Gaussian fields with Mat\'ern covariance functions on Euclidean domains to non-Euclidean metric graph settings. A ten-year period (2010-2019) of daily traffic-accident records from Barcelona, Spain have been used to evaluate the three models referred above. While comparing model performance we observed that the Whittle-Mat\'ern fields defined directly on the network outperformed the network triangulation and barrier models. Due to their flexibility, the Whittle-Mat\'ern fields can be applied to a wide range of environmental problems on linear networks such as spatio-temporal modeling of water contamination in stream networks or modeling air quality or accidents on urban road networks., Comment: 24 pages, 9 figures

We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying periodic architected metamaterials. Such theory results in fourth-order governing partial differential equations, and the periodicity conditions involve continuity across the periodic boundary of primal fields (displacement and electric potential) and their normal derivatives, continuity of the corresponding dual generalized forces (tractions, double tractions, surface charge density and double surface charge density). Rather than imposing these conditions numerically as explicit constraints, we develop an approximation space which fulfils generalized periodicity by construction. Our method naturally allows us to impose general macroscopic fields (strains/stresses and electric fields/electric displacements) along arbitrary directions, enabling the characterization of the material anisotropy. We apply the proposed method to study periodic architected metamaterials with apparent piezoelectricity. We first verify the method by directly comparing the results with a large periodic structure, then apply it to evaluate the anisotropic apparently piezoelectricity of a geometrically polarized 2D lattice, and finally demonstrate the application of the method in a 3D architected metamaterial.

In this work, we focus on the period-luminosity relation (PLR) of $\delta$ Sct stars, in which mode excitation and selection mechanisms are still poorly constrained, and whose structure and oscillations are affected by rotation. We review the PLRs in the recent literature, and add a new inference from a large sample of $\delta$ Sct. We highlight the difficulty in identifying the fundamental mode and show that rotation-induced surface effects can impact the measured luminosities, explaining the broadening of the PLR. We derive a tight relation between the low-order large separation and the fundamental radial mode frequency (F0) that holds for rotating stars, thus paving the way towards mode identification. We show that the PLRs we obtain for different samples are compatible with each other and with the recent literature, and with most observed $\delta$ Sct stars when taking rotation effects into account. We also find that the highest-amplitude peak in the frequency spectrum corresponds to the fundamental mode in most $\delta$ Sct, thus shedding some light on their elusive mode selection mechanism., Comment: 10 pages, 5 figures, 1 table, IAU conference proceeding

We present the BioImage$.$IO Chatbot, an AI assistant powered by Large Language Models and supported by a community-driven knowledge base and toolset. This chatbot is designed to cater to a wide range of user needs through a flexible extension mechanism that spans from information retrieval to AI-enhanced analysis and microscopy control. Embracing open-source principles, the chatbot is designed to evolve through community contributions. By simplifying navigation through the intricate bioimaging landscape, the BioImage$.$IO Chatbot empowers life sciences to progress by leveraging the collective expertise and innovation of its users., Comment: 15 pages, 2 figures

The backreaction of quantum fields in their vacuum state results in equilibrium structures that surpass the Buchdahl compactness limit. Such backreaction is encapsulated in the vacuum expectation value of the renormalized stress-energy tensor (RSET). In previous works we presented analytic approximations to the RSET, obtained by dimensional reduction, available in spherical symmetry, and showed that the backreaction-generated solutions described ultracompact fluid spheres with a negative mass interior. Here, we derive a novel approximation to the RSET that does not rely on dimensional reduction, but rather on a reduction of the differential order. This approximation also leads to regular stars surpassing the Buchdahl limit. We conclude that this is a consequence of the negative energies associated with the Boulware vacuum which, for sufficiently compact fluid spheres, make the Misner-Sharp mass negative near the centre of spherical symmetry. Our analysis provides further cumulative evidence that quantum vacuum polarization is capable of producing new forms of stellar equilibrium with robust properties accross different analytical approximations to the RSET., Comment: 15 pages, 5 figures. Added a new figure, an appendix, and improved the main text. To appear in Phys. Rev. D

The formal XAI community has studied a plethora of interpretability queries aiming to understand the classifications made by decision trees. However, a more uniform understanding of what questions we can hope to answer about these models, traditionally deemed to be easily interpretable, has remained elusive. In an initial attempt to understand uniform languages for interpretability, Arenas et al. (2021) proposed FOIL, a logic for explaining black-box ML models, and showed that it can express a variety of interpretability queries. However, we show that FOIL is limited in two important senses: (i) it is not expressive enough to capture some crucial queries, and (ii) its model agnostic nature results in a high computational complexity for decision trees. In this paper, we carefully craft two fragments of first-order logic that allow for efficiently interpreting decision trees: Q-DT-FOIL and its optimization variant OPT-DT-FOIL. We show that our proposed logics can express not only a variety of interpretability queries considered by previous literature, but also elegantly allows users to specify different objectives the sought explanations should optimize for. Using finite model-theoretic techniques, we show that the different ingredients of Q-DT-FOIL are necessary for its expressiveness, and yet that queries in Q-DT-FOIL can be evaluated with a polynomial number of queries to a SAT solver, as well as their optimization versions in OPT-DT-FOIL. Besides our theoretical results, we provide a SAT-based implementation of the evaluation for OPT-DT-FOIL that is performant on industry-size decision trees.

The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high interpretability. These models utilize trained architectures to execute atomic queries and integrate modules that mimic symbolic query operators. However, most neuro-symbolic query processors are constrained to tree-like graph pattern queries. These queries admit a bottom-up execution with constant values or anchors at the leaves and the target variable at the root. While expressive, tree-like queries fail to capture critical properties in knowledge graphs, such as the existence of multiple edges between entities or the presence of triangles. We introduce a framework for answering arbitrary graph pattern queries over incomplete knowledge graphs, encompassing both cyclic queries and tree-like queries with existentially quantified leaves. These classes of queries are vital for practical applications but are beyond the scope of most current neuro-symbolic models. Our approach employs an approximation scheme that facilitates acyclic traversals for cyclic patterns, thereby embedding additional symbolic bias into the query execution process. Our experimental evaluation demonstrates that our framework performs competitively on three datasets, effectively handling cyclic queries through our approximation strategy. Additionally, it maintains the performance of existing neuro-symbolic models on anchored tree-like queries and extends their capabilities to queries with existentially quantified variables.

We contribute to the study of formal languages that can be recognized by transformer encoders. We focus on two self-attention mechanisms: (1) UHAT (Unique Hard Attention Transformers) and (2) AHAT (Average Hard Attention Transformers). UHAT encoders are known to recognize only languages inside the circuit complexity class ${\sf AC}^0$, i.e., accepted by a family of poly-sized and depth-bounded boolean circuits with unbounded fan-ins. On the other hand, AHAT encoders can recognize languages outside ${\sf AC}^0$), but their expressive power still lies within the bigger circuit complexity class ${\sf TC}^0$, i.e., ${\sf AC}^0$-circuits extended by majority gates. We first show a negative result that there is an ${\sf AC}^0$-language that cannot be recognized by an UHAT encoder. On the positive side, we show that UHAT encoders can recognize a rich fragment of ${\sf AC}^0$-languages, namely, all languages definable in first-order logic with arbitrary unary numerical predicates. This logic, includes, for example, all regular languages from ${\sf AC}^0$. We then show that AHAT encoders can recognize all languages of our logic even when we enrich it with counting terms. We apply these results to derive new results on the expressive power of UHAT and AHAT up to permutation of letters (a.k.a. Parikh images).

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the $k$-dimensional Weisfeiler-Leman ($k$WL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the $k$WL test. A central focus of research in this field revolves around determining the least dimensionality $k$, for which $k$WL can discern graphs with different number of occurrences of a pattern graph $P$. We refer to such a least $k$ as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern $P$. We additionally demonstrate that in cases where the $k$WL test distinguishes between graphs with varying occurrences of a pattern $P$, the exact number of occurrences of $P$ can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern $P$, answering an open question from previous work.

Haloscopes, microwave resonant cavities utilized in detecting dark matter axions within powerful static magnetic fields, are pivotal in modern astrophysical research. This paper delves into the realm of cylindrical geometries, investigating techniques to augment volume and enhance compatibility with dipole or solenoid magnets. The study explores volume constraints in two categories of haloscope designs: those reliant on single cavities and those employing multicavities. In both categories, strategies to increase the expanse of elongated structures are elucidated. For multicavities, the optimization of space within magnets is explored through 1D configurations. Three subcavity stacking approaches are investigated, while the foray into 2D and 3D geometries lays the groundwork for future topological developments. The results underscore the efficacy of these methods, revealing substantial room for progress in cylindrical haloscope design. Notably, an elongated single cavity design attains a three-order magnitude increase in volume compared to a WC-109 standard waveguide-based single cavity. Diverse prototypes featuring single cavities, 1D, 2D, and 3D multicavities highlight the feasibility of leveraging these geometries to magnify the volume of tangible haloscope implementations.

Task-based programming models have proven to be a robust and versatile way to approach development of applications for distributed environments. They provide natural programming patterns with high performance. However, execution on this paradigm can be very sensitive to granularity --i.e., the quantity and execution length of tasks. Granularity is often linked with the block size of the data, and finding the optimal block size has several challenges, as it requires inner knowledge of the computing environment. Our proposal is to supplement the task-based programming model with a new mechanism --our SplIter proposal. At its core, the SplIter provides a transparent way to split a collection into partitions (logical groups of blocks, obtained without any transfers nor data rearrangement), which can then be iterated. Tasks are linked to those partitions, which means that SplIter breaks the dependency between block size and task granularity. The evaluation shows that the SplIter is able to achieve performance improvements of over one order of magnitude when compared to the baseline, and it is either competitive or strictly better (depending on application characteristics) to the competitor alternative. We have chosen different applications covering a wide variety of scenarios; those applications are representatives of a broader set of applications and domains. The changes required in the source code of a task-based application are minimal, preserving the high programmability of the programming model. Two different state-of-the-art task-based frameworks have been evaluated for all the applications: COMPSs and Dask, showing that the SplIter can be effectively used within different frameworks.

Standard General Relativity assumes that, in the absence of classical matter sources, spacetime is empty. This chapter considers and analyses the new behaviours of the gravitational field that appear when one substitutes this emptiness by a reactive vacuum, stemming in particular from the idea of vacuum provided by quantum field theory. We restrict our study to spherically symmetric configurations, and take a simple free quantum scalar field as a proxy to more complicated formulations. Our analysis is split into a study of static and of dynamical configurations. Under the assumption of staticity, we find and describe the different asymptotically flat self-consistent solutions that appear when using a vacuum Renormalised Stress-Energy Tensor (RSET) as an additional source in the Einstein equations. Of particular interest is the discovery that, as opposed to standard general relativity, the new theory naturally contains static ultracompact stellar configurations which could observationally be mistaken for black holes (BHs). Then, in our study of dynamical configurations, we investigate the possibility of these same vacuum effects changing the internal gravitational processes after an initial gravitational collapse in a way which shows a path towards forming the aforementioned ultracompact configurations. This has lead us to analyse several dynamical situations seldom contemplated in the literature. Of special relevance, we find that the inner horizon that all realistic BHs should contain could inflate outwards quickly enough to meet the outer one before any appreciable Hawking evaporation has taken place., Comment: 64 pages, 9 figures. Invited chapter to appear in the volume "New Frontiers in Gravitational Collapse and Spacetime Singularities" (Eds. P. S. Joshi and D. Malafarina, Springer Series in Astrophysics and Cosmology)

In a work by Visser, Bassett and Liberati (VBL) [Nucl. Phys. B (Proc. Suppl.) 88, 267 (2000)] a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald [Class. Quantum Grav. 17, 4999, (2000)] who argued that this relation is gauge dependent and therefore lacks physical significance. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation provides an explanation of why gravity is attractive in all standard weak-field situations., Comment: 33 pages, no figures