Causal Spacetime Research Articles

Overcharging an accelerating Reissner-Nordström-anti-de Sitter black hole with test field and particle

Accelerating black holes have been widely studied in the context of black hole thermodynamics, holographic gravity theories, and in the description of black holes at the center of galaxies. As a fundamental assumption to ensure spacetime causality, we investigate the weak cosmic censorship conjecture (WCCC) in the accelerating Reissner-Nordström-Anti-de Sitter (RN-AdS) spacetime through the scattering of a charged field and the absorption of a charged particle. For the scattering of a charged scalar field, both near-extremal and extremal accelerating RN-AdS black holes cannot be overcharged, thereby upholding the validity of the WCCC. In the case of the absorption of a test charged particle, the results demonstrate that the event horizon of the extremal accelerating RN-AdS black hole cannot be destroyed, while the event horizon of the near-extremal black hole can be overcharged if the test particle satisfies certain conditions. The above results suggest that, in the case of test particles, second-order effects like self-force and self-energy should be further considered.

A note on null distance and causality encoding *

Under natural conditions, the null distance introduced by Sormani and Vega (2016 Class. Quantum Grav. 33 085001) is a metric space distance function on spacetime, which, in a certain precise sense, can encode the causality of spacetime. The null distance function requires the choice of a time function. The purpose of this note is to observe that the causality assumptions related to such a choice in results used to establish global encoding of causality, due to Sakovich and Sormani (2023 J. Math. Phys. 64 012502) and to Burtscher and García-Heveling (2022 arXiv:2209.15610 [math.DG]), can be weakened.

Causal structure of spacetime and Scott topology

In this paper we establish the spacetime manifold as a partially ordered set via the casual structure. We show that these partially ordered sets are naturally continuous as a suitable way below relation can be established via the chronological order. We further consider those classes of spacetimes on which a lattice structure can be endowed by physically defining the joins and meets. By considering the physical properties of null geodesics on the spacetime manifold we show that these lattices are necessarily distributive. These lattices are then continuous as a result of the equivalence between the way below relation and chronology. This enables us to define the Scott topology on the spacetime manifold and describe it on an equal footing as any other continuous lattice. We further show that the Scott topology is a proper subset of Alexandroff topology, which must be the manifold topology for the strongly causal spacetimes, (and hence a coarser topology than Alexandroff). In the process we find some interesting results on the sobriety of these manifolds. We prove that they are necessarily not sober under the Scott topology but regain their sobriety under Alexandroff topology. We also define a dual Scott topology on these manifolds by endowing them with bicontinuous poset structure and show that the join of the Scott topology with the dual is the Alexandroff topology. We also discuss the previous works done in this topic and how the present work generalises those results to some extent.

Overspinning a rotating black hole in semiclassical gravity with type-A trace anomaly

Recently, Fernandes discovered an analytic solution for rotating black holes in semiclassical gravity induced by the trace anomaly. These solutions exhibit some distinctive characteristics, including a non-spherically symmetric event horizon, the absence of circularity conditions, and violations of the Kerr bound. As a crucial assumption to uphold causality in spacetime, we investigate the validity of the weak cosmic censorship conjecture (WCCC) within this class of solutions with type-A trace anomaly by introducing a test particle on the equatorial plane. Our study reveals three distinct mechanisms that can potentially destroy the event horizon, leading to a violation of the WCCC. Our findings indicate that, with the exception of extremal Kerr, static extremal, and static singular black holes, the WCCC may be violated under the first-order perturbation of the test particle. These results suggest the need for further exploration of modifications to the behavior of the test particle under quantum effects in order to address the violation of the WCCC in this system.

Space-Time Causality Analysis of Regional Impacts of ENSO on Terrestrial and Oceanic Precipitation

Future changes are expected in precipitation under climate change, therefore, changes are projected in the oceanic and terrestrial components. However, it remains poorly elucidated how the El Niño–Southern Oscillation (ENSO) can influence these changes. Therefore, we aimed to perform a space-time causality analysis of regional ENSO impacts on terrestrial and oceanic precipitation by using the Granger causality method as a function of eight temporal lags (lags 1–8). The monthly values of total precipitation obtained using the Lagrangian approach and their respective terrestrial (PLT) and oceanic (PLO) components were used. The analysis was performed for the two regions of western North America (WNA) and eastern South America (ESA) with strong ENSO signals. For the WNA region in winter, the maximum Granger causality was observed in the component of oceanic origin for temporal lags 1 and 2 (3 and 6 months), with a predominance of both positive and negative ENSO conditions. For the ESA region, it was verified that the causality of the ENSO index was maximum for PLT. Temporal lags 2–5 (6–15 months) stood out in winter when there was a marked region of the Granger causality over the La Plata Basin. In autumn, for lags 1–4 (3–12 months), the Granger causality values were predominant in the southern and western areas of ESA and showed a tendency to move northward with an increased temporal lag. Finally, it was shown that high correlation values did not imply the causality of the relationship between the ENSO index and precipitation in the two regions.

Gluing constructions for Lorentzian length spaces.

We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT(k) spaces, which roughly states that gluing is compatible with upper curvature bounds. Due to the absence of a notion of spacelike distance in Lorentzian pre-length spaces we can only formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.

Charged BTZ black holes cannot be destroyed via the new version of the gedanken experiment

The singularity at the center of charged Bañados–Teitelboim–Zanelli (BTZ) black holes is called a conical singularity. Unlike the canonical singularity in typical black holes, a conical singularity does not destroy the causality of spacetime. Due to the special property of the conical singularity, we examine the weak cosmic censorship conjecture (WCCC) using the new version of the gedanken experiment proposed by Sorce and Wald. A perturbation process wherein the spherically symmetric matter fields pass through the event horizon and fall into the black holes is considered. Assuming that the cosmological constant is obtained by the matter fields, it therefore can be seen as a dynamical variable during the process. From this perspective, according to the stability condition and the null energy condition, the first- and second-order perturbation inequalities are derived. Based on the first-order optimal condition and the second-order perturbation inequality, we show that the nearly extremal charged BTZ black hole cannot be destroyed in the above perturbation process. The result also implies that even if the singularity at the center of the black hole is conical, it still should be surrounded by the event horizon and hidden inside the black hole.

OntoTouTra: Tourist Traceability Ontology Based on Big Data Analytics

Tourist traceability is the analysis of the set of actions, procedures, and technical measures that allows us to identify and record the space–time causality of the tourist’s touring, from the beginning to the end of the chain of the tourist product. Besides, the traceability of tourists has implications for infrastructure, transport, products, marketing, the commercial viability of the industry, and the management of the destination’s social, environmental, and cultural impact. To this end, a tourist traceability system requires a knowledge base for processing elements, such as functions, objects, events, and logical connectors among them. A knowledge base provides us with information on the preparation, planning, and implementation or operation stages. In this regard, unifying tourism terminology in a traceability system is a challenge because we need a central repository that promotes standards for tourists and suppliers in forming a formal body of knowledge representation. Some studies are related to the construction of ontologies in tourism, but none focus on tourist traceability systems. For the above, we propose OntoTouTra, an ontology that uses formal specifications to represent knowledge of tourist traceability systems. This paper outlines the development of the OntoTouTra ontology and how we gathered and processed data from ubiquitous computing using Big Data analysis techniques.

Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.

Operational causality in spacetime

The no-signaling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation---the ''dynamical no-signaling principle''---which forbids superluminal signaling via measurements on simple physical objects (e.g., particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal; it can be applied to any theory (classical, quantum, or postquantum) with well-defined rules for calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schr\"odinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or postquantum dynamics.

On null and causal pseudoconvex space-times

The condition of pseudoconvexity has important implications for geodesic structures of space-time. Low showed that this condition guarantees the existence of a smooth structure of the space of geodesics. Recently, the place of this property within the causality ladder is in the attention. There is a conjecture which states that every strongly causal space-time is causally simple if and only if it is null pseudoconvex. In this paper, we study the difference of causal and null pseudoconvexity in space-times and introduce the limit geodesic segment as an equivalence condition to the pseudoconvexity. Then, we show that in the case of open subspaces of n-Minkowski space-time, this is causal geodesic connectedness. Finally, we prove a refined form of the conjecture that says every strongly causal space-time is causally simple if and only if it is maximal null pseudoconvex.

The space of null geodesics and naked singularities

The space of null geodesics, , of a spacetime, is considered, with particular reference to the natural topology and manifold structure introduced by Low, where is a strongly causal spacetime. The topology and geometry of the space of a spacetime are used to study the causal structure of . In particular, the question of whether the topology of is Hausdorff carries information on the global structure of . Low has shown that, if be non-Hausdorff, then must be nakedly singular. The converse fails to hold. In this paper, we first introduce two types of naked singularities called ‘nakedly singular future boundary’ and ‘nakedly singular past boundary’. Then investigate the relationships between the presence of each of these naked singularities in , and failure of the Hausdorff property for .

Can the universe be described by a wave function?

Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkhoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the “mostly empty” universe we observe around us cannot be described by an exact wave function [Formula: see text]. Rather, the weakly coupled particles we see are approximate quasiparticles arising as excitations of a “fuzz”. The “fuzz” does have an exact wave function [Formula: see text], but this exact wave function does not directly describe local particles. The argument proceeds by relating the cosmological setting to the black hole information paradox, and then using the small corrections theorem to show the impossibility of an exact wave function describing the visible universe.

A novel notion of null infinity for c-boundaries and generalized black holes

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.

Setting Time as Purely Imaginary in Regime of Space-Time before Causal Barrier and Planckian Space-Time

We start where we use an inflaton value due to use of a scale factor . In doing so, using the approximations brought up in the case of an early universe generation of a magnetic field, we come up with the stunning datum of a Pre Planckian space-time with purely imaginary time. The consequences of such are brought up in our document. We use what is brought up in a prior article as to Pre Planckian to Planckian generation of Magnetic fields to make our point. Here, we assume, in the Pre Planckian space-time, a singular injection of space-time, which we argue, if there is no spatial variation of the Inflaton field, so used, and we just have ONE Pre Planckian time instant that this will be imaginary valued time, hence leading to pure Tunneling behavior. Whatever we are assuming, using a Penrose cosmology to initiate CCC universe recycling, in terms of energy, is transferred to Planckian space-time.

Einstein-Hilbert type action on spacetimes

The mixed gravitational field equations have been recently introduced for codimension one foliated manifolds, e.g. stably causal and globally hyperbolic spacetimes. These Euler-Lagrange equations for the total mixed scalar curvature (as analog of Einstein-Hilbert action) involve a new kind of Ricci curvature (called the mixed Ricci curvature). In the work, we derive Euler-Lagrange equations of the action for any spacetime, in fact, for a pseudo-Riemannian manifold endowed with a non-degenerate distribution. The obtained equations are presented in the classical form of Einstein field equation with the new Ricci type curvature instead of Ricci curvature

Polish spaces of causal curves

We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves “in accordance” with a chosen time function. Thus obtained topological spaces of causal curves are separable and completely metrizable, i.e. Polish. The latter property renders them particularly useful in the optimal transport theory. To illustrate this fact, we explore the notion of a causal time-evolution of measures in globally hyperbolic spacetimes and discuss its physical interpretation.

On Differentiability of Volume Time Functions

We show differentiability of a class of Geroch's volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally anti-Lipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably causal spacetimes Hawking's time function can be uniformly approximated by smooth time functions with timelike gradient.

Domain Theory in General Relativity

It is proved that k- causal spacetimes, with inner continuous Int(K±(.)), are jointly bicontinuous posets whose interval topology is the manifold topology. In particular, using the relation K +, causally continuous space-times can be reconstructed

A closed form expression for the causal set d’Alembertian

Recently a definition for a Lorentz invariant operator approximating the d’Alembertian in d-dimensional causal set spacetimes has been proposed. This operator contains several dimension-dependent constants which have been determined for d = 2, …, 7. In this note we derive closed form expressions for these constants, which are valid in all dimensions. Using these we prove that the causal set action in any dimension can be defined through this discrete d’Alembertian, with a dimension independent prefactor.