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The discovery of ultra-high energy gamma-ray sources (detected at energies $\geq$ 100 TeV) thanks to highly sensitive observatories such as the High Altitude Water Cherenkov (HAWC) Observatory, the Tibet AS-gamma Experiment, and the Large High Altitude Air Shower Observatory (LHAASO), marked the beginning of the sub--PeV and PeV era in gamma-ray astrophysics (energies $\sim$ 0.1 to 100 PeV). This new astrophysics is closely related to the emerging topic of PeVatrons, in which HAWC has played a remarkable role and will continue to contribute discoveries and relevant studies thanks to the better data provided by the installed outriggers. In this paper, we present a brief overview of the PeVatrons and the HAWC observatory., Comment: Accepted for publication in the book of contributions of the TMEX-2023: Theory meets experiments, January 5-11, 2023, Vietnam. DOI in formality

We present a short overview of the TeV-Halos objects as a discovery and a relevant contribution of the High Altitude Water \v{C}erenkov (HAWC) observatory to TeV astrophysics. We discuss history, discovery, knowledge, and the next step through a new and more detailed analysis than the original study in 2017. TeV-Halos will contribute to resolving the problem of the local positron excess observed on the Earth. To clarify the latter, understanding the diffusion process is mandatory., Comment: Work presented in the 21st International Symposium on Very High Energy Cosmic Ray Interactions(ISVHECRI 2022) as part of the Ph. D. Thesis of Ramiro Torres-Escobedo (SJTU, Shanghai, China). Accepted for publication in SciPost Physics Proceedings (ISSN 2666-4003). 11 pages, 3 Figures. Short overview of HAWC and TeV Halos objects until 2022

The High-Altitude Water Cherenkov (HAWC) observatory is a second-generation continuously operated, wide field-of-view, TeV gamma-ray observatory. The HAWC observatory and its analysis techniques build on experience of the Milagro experiment in using ground-based water Cherenkov detectors for gamma-ray astronomy. HAWC is located on the Sierra Negra volcano in M\'exico at an elevation of 4100 meters above sea level. The completed HAWC observatory principal detector (HAWC) consists of 300 closely spaced water Cherenkov detectors, each equipped with four photomultiplier tubes to provide timing and charge information to reconstruct the extensive air shower energy and arrival direction. The HAWC observatory has been optimized to observe transient and steady emission from sources of gamma rays within an energy range from several hundred GeV to several hundred TeV. However, most of the air showers detected are initiated by cosmic rays, allowing studies of cosmic rays also to be performed. This paper describes the characteristics of the HAWC main array and its hardware., Comment: Accepted for publications in Nuclear Inst. and Methods in Physics Research, A (2023) 168253 ( https://www.sciencedirect.com/science/article/abs/pii/S0168900223002437 ); 39 pages, 14 Figures

We give new definitions of null infinity and black hole in terms of causal boundaries, applicable to any strongly causal spacetime $(M,g)$. These are meant to extend the standard ones given in terms of conformal boundaries, and use the new definitions to prove a classic result in black hole theory for this more general context: if the null infinity is regular (i.e. well behaved in a suitable sense) and $(M,g)$ obeys the null convergence condition, then any closed trapped surface in $(M,g)$ has to be inside the black hole region. As an illustration of this general construction, we apply it to the class of generalized plane waves, where the conformal null infinity is not always well-defined. In particular, it is shown that (generalized) black hole regions do not exist in a large family of these spacetimes., Comment: 32 pages, 4 figures. Included new reference

In this paper a systematic study of the causal structure and global causality properties of multiwarped spacetimes is developed. This analysis is used to make a detailed description of the causal boundary of these spacetimes. Some applications of our results in examples of physical interest, for instance, in the context of Maldacena's conjecture, are considered., Comment: 37 pages, 1 figure

List of proceedings from the HAWC Collaboration presented at the 35th International Cosmic Ray Conference, 12 July - 20 July 2017, Bexco, Busan, Korea., Comment: List of proceedings from the HAWC Collaboration presented at ICRC2017. Corrected typos in the index of the previous version. Follow the "HTML" link to access the list

List of proceedings from the HAWC Collaboration presented at the 34th International Cosmic Ray Conference, 30 July - 6 August 2015, The Hague, The Netherlands., Comment: List of proceedings from the HAWC Collaboration presented at ICRC2015. Follow the "HTML" link to access the list

There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator $L$. As emphasized in a classical article by Geroch, Liang and Wald, some of them have the property, commonly regarded as a drawback, that there are points of the spacetime $M$ non $T_1$-separated from points of the boundary $\partial M$. Here we show that this problem can be solved from a general topological viewpoint. In particular, there is a canonical minimum refinement of the topology in the completion $\overline{M}$ which $T_2$-separates the spacetime $M$ and its boundary $\partial M$ ---no matter the type of completion one chooses. Moreover, we analyze the case of sequential spaces and show how the refined $T_2$-separating topology can be constructed from a modification $L^*$ of the original limit operator $L$. Finally, we particularize this procedure to the case of the causal boundary and show how the separability of $M$ and $\partial M$ can be introduced as an abstract axiom in its definition., Comment: 29 pages, 8 figures, latex

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified concusions may arise, showing that those conclusions will fail only in special cases, at least some of which may be described. These are the so-called rigidity theorems, and have many important examples in the especialized literature. In this paper, we prove rigidity results for generalized plane waves and certain globally hyperbolic spacetimes in the presence of maximal compact surfaces. Motivated by some general properties appearing in these proofs, we develop the theory of lightlike sets, entities similar to achronal sets, but more appropriate to deal with low-regularity null submanifolds., Comment: 23 pages

Recently, a new viewpoint on the classical c-boundary in Mathematical Relativity has been developed, the relations of this boundary with the conformal one and other classical boundaries have been analyzed, and its computation in some classes of spacetimes, as the standard stationary ones, has been carried out. In the present paper, we consider the notion of isocausality given by Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out isocausal comparisons with standard stationary spacetimes. As a consequence, the qualitative behavior of the c-boundary (at the three levels: point set, chronology and topology) of a wide class of spacetimes, is obtained., Comment: 44 pages, 5 Figures, latex. Version with minor changes and the inclusion of Figure 5

In this note we reduce the problem of geodesic connectedness in a wide class of G\"odel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former., Comment: 14 pages

We construct an example which shows that two isocausal spacetimes, in the sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also suggests that isocausality can be useful for the understanding and computation of the c-boundary., Comment: Minor modifications, including the title, which matches now with the published version. 12 pages, 3 figures

Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = R x M, suggests a natural compactification $M_B$ associated to any Riemannian metric on M or, more generally, to any Finslerian one. The corresponding boundary $\partial_B M$ is constructed in terms of Busemann-type functions. Roughly, $\partial_B M$ represents the set of all the directions in M including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary $\partial_B M$ is related to two classical boundaries: the Cauchy boundary and the Gromov boundary. Our aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification $M_B$, relating it with the previous two completions, and (3) to give a full description of the causal boundary $\partial V$ of any standard conformally stationary spacetime., Comment: Final version with minor modifications, to appear in Memoirs of the American Mathematical Society. 80 pages, 10 figures, latex

In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf map. The utility of this method is illustrated by providing marginally trapped surfaces crossing expanding and collapsing regions of a closed FLRW spacetime. The approach introduced in this paper is also extended to twisted spaces., Comment: 20 pages

The notion of causal boundary $\partial M$ for a strongly causal spacetime $M$ has been a controversial topic along last decades: on one hand, some attempted definitions were not fully consistent, on the other, there were simple examples where an open conformal embedding $i:M\hookarrow M_{0}$ could be defined, but the corresponding conformal boundary $\partial_{i}M$ disagreed drastically with the causal one. Nevertheless, the recent progress in this topic suggests a definitive option for $\partial M$, which is developed here in detail. Our study has two parts: (I) To give general arguments on a boundary in order to ensure that it is admissible as a causal boundary at the three natural levels, i.e., as a point set, as a chronological space and as a topological space. Then, the essential uniqueness of our choice is stressed, and the relatively few admissible alternatives are discussed. (II) To analyze the role of the conformal boundary $\partial_{i}M$. We show that, in general, $\partial_{i}M$ may present a very undesirable structure. Nevertheless, it is well-behaved under certain general assumptions, and its accessible part $\partial_{i}^{*}M$ agrees with the causal boundary. This study justifies both boundaries. On one hand, the conformal boundary $\partial_{i}^{*}M$, which cannot be defined for a general spacetime but is easily computed in particular examples, appears now as a special case of the causal boundary. On the other, the new redefinition of the causal boundary not only is free of inconsistencies and applicable to any strongly causal spacetime, but also recovers the expected structure in the cases where a natural conformal boundary is available. The cases of globally hyperbolic spacetimes and asymptotically conformally flat ends are especially studied., Comment: Revisded version, including the correction of Appendix 3.6 (51 pages, 13 figures). To appear in Adv. Th. Math. Phys

The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is particularized for two important families of spacetimes, conformal to the previous ones: (standard) static spacetimes and Generalized Robertson-Walker spacetimes. As consequence, it is shown that this new approach essentially reproduces the structure of the conformal boundary for multiple classical spacetimes: Reissner-Nordstrom (including Schwarzschild), Anti-de Sitter, Taub and standard cosmological models as de Sitter and Einstein Universe., Comment: 21 pages, 7 figures

A complete study of the structure of Ricci collineations for type B warped spacetimes is carried out. This study can be used as a method to obtain these symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and plane and spherical symmetric spacetimes are considered specifically., Comment: 18 pages. Version accepted for publication in JMP

Let $M = M_0 \times \R^2$ be a pp--wave type spacetime endowed with the metric $<\cdot,\cdot>_z = <\cdot,\cdot>_x + 2 du dv + H(x,u) du^2$, where $(M_0, <\cdot,\cdot>_x) $ is any Riemannian manifold and $H(x,u)$ an arbitrary function. We show that the behaviour of $H(x,u)$ at spatial infinity determines the causality of $M$, say: (a) if $-H(x,u)$ behaves subquadratically (i.e, essentially $-H(x,u) \leq R_1(u) |x|^{2-\epsilon} $ for some $\epsilon >0$ and large distance $|x|$ to a fixed point) and the spatial part $(M_0, <\cdot,\cdot>_x) $ is complete, then the spacetime $M$ is globally hyperbolic, (b) if $-H(x,u)$ grows at most quadratically (i.e, $-H(x,u) \leq R_1(u) |x|^{2}$ for large $|x|$) then it is strongly causal and (c) $M$ is always causal, but there are non-distinguishing examples (and thus, non-strongly causal), even when $-H(x,u) \leq R_1(u) |x|^{2+\epsilon} $, for small $\epsilon >0$. Therefore, the classical model $M_0 = \R^2$, $H(x,u) = \sum_{i,j} h_{ij}(u) x_i x_j (\not\equiv 0)$, which is known to be strongly causal but not globally hyperbolic, lies in the critical quadratic situation with complete $M_0$. This must be taken into account for realistic applications. In fact, we argue that $-H$ will be subquadratic (and the spacetime globally hyperbolic) if $M$ is asymptotically flat. The relation of these results with the notion of astigmatic conjugacy and the existence of conjugate points is also discussed., Comment: Version improved with further discussions and a new section; 21 pages, Latex

A general class of Lorentzian metrics, $M_0 x R^2$, $ds^2 = <.,.> + 2 du dv + H(x,u) du^2$, with $(M_0, <.,.>$ any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity, causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of $H(x,u)$ with $x$ at infinity determines many properties of geodesics. Essentially, a subquadratic growth of $H$ ensures geodesic completeness and connectedness, while the critical situation appears when $H(x,u)$ behaves in some direction as $|x|^2$, as in the classical model of exact gravitational waves, Comment: Final version with minor errata corrected. 19 pages, Latex. To appear in Gen. Relat. Gravit. (2003)

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence condition are also found., Comment: 31 pages and 2 figures