E. Minguzzi
It is proven that K-causality coincides with stable causality, and that in a K-causal spacetime the relation K^+ coincides with the Seifert's relation. As a consequence the causal relation "the spacetime is strongly causal and the closure of the causal relation is transitive" stays between stable causality and causal continuity.
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By definition a spacetime is stably causal if it is possible to widen the light cones all over the spacetime without spoiling causality. We prove that if the spacetime is at least non-total imprisoning then it is stably causal provided the light cones can be widened outside any compact arbitrarily large set, i.e. in a neighborhood of infinity, without spoiling causality. Furthermore, we prove that the new causality level `compact stable causality' can be obtained as the antisymmetry condition of a new causal relation which we identify, but it cannot be obtained as a causal stability condition …
Hawking's stable causality implies Sorkin and Woolgar's K-causality. The work investigates the possible equivalence between the two causality requirements, an issue which was first considered by H. Seifert and then raised again by R. Low after the introduction of K-causality. First, a new proof is given that a spacetime is stably causal iff the Seifert causal relation is a partial order. It is then shown that given a K-causal spacetime and chosen an event, the light cones can be widened in a neighborhood of the event without spoiling K-causality. The idea is that this widening of the light con…
We show stable causality of the Pomeransky-Senkov black rings.
We prove that the Black Saturns are stably causal on the closure of the domain of outer communications.
The causal relation $K^+$ was introduced by Sorkin and Woolgar to extend the standard causal analysis of $C^2$ spacetimes to those that are only $C^0$. Most of their results also hold true in the case of spacetimes with degeneracies. In this paper we seek to examine $K^+$ explicitly in the case of Lorentzian topology changing Morse spacetimes containing isolated degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that $K^+$ is robust and that it coincides with the Seifert relation when the spacetime is stably c…
We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the validity of most results of the regular Lorentzian causality theory including causal ladder, Fermat's principle, notable singularity theorems in their causal formulation, Avez-Seifert theorem, characterizations of stable causality and global hyperbolicity by means of (smooth) time functions. For instance, we give the first proof for these structures of the equi…
We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Horava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable …
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the problem of fundamental causal stability conditions. Several questions are raised and some of the potential consequences of recent results regarding the causality problem in general relativity are presented. A key question is whether causality violating regions are locally allowed. The new concept of almost stable causality is introduced; meanwhile, related cond…
We present a topologically trivial, non-vacuum solution of the Einstein's field equations in four-dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid $p=ω\…
Causal and stable first-order chiral hydrodynamics
本文推导一阶相对论手征流体动力学满足非线性因果性与线性稳定性的充要不等式，给出首个可证因果稳定的黏性理论，并将结果整理为适合数值模拟的形式。
The causal properties of curved spacetime, which underpin our sense of time in gravitational theories, are defined by the null cones of the spacetime metric. In classical general relativity, it is assumed that these coincide with the light cones determined by the physical propagation of light rays. However, the quantum vacuum acts as a dispersive medium for the propagation of light, since vacuum polarisation in QED induces interactions which effectively violate the strong equivalence principle (SEP). For low frequencies the phenomenon of gravitational birefringence occurs and indeed, for some …
Stable Causality and Microcausality for Drummond-Hathrell Photons
研究 DH 光子在引力背景中超光速传播的因果性，通过两种诊断方法证明其因果无害。
We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R x S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.
In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity, causal simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.
Relativity opens the door to a counter-intuitive fact: a state can be stable to perturbations in one frame of reference, and unstable in another one. For this reason, the job of testing the stability of states that are not Lorentz-invariant can be very cumbersome. We show that two observers can disagree on whether a state is stable or unstable only if the perturbations can exit the light-cone. Furthermore, we show that, if a perturbation exits the light-cone, and its intensity changes with time, due to dissipation, then there are always two observers that disagree on the stability of the state…
Dispersion relations alone cannot guarantee causality
该研究证明单值协变稳定的单个色散关系无法保证亚光速传播的因果性，因果性需通过物理模型所有激发分支的叠加抵消实现，且在局域协变稳定物质理论中自动发生，类比了相对论流体非流体模式与相对论量子反粒子的需求。
The representation of spacetime through time functions
通过时间函数抽象表示时空，将因果性和度量性统一于额外维度空间中的因果性，证明时间完全表征时空。
The causal spacetimes admitting a covariantly constant null vector provide a connection between relativistic and non-relativistic physics. We explore this relationship in several directions. We start proving a formula which relates the Lorentzian distance in the full spacetime with the least action of a mechanical system living in a quotient classical space time. The timelike eikonal equation satisfied by the Lorentzian distance is proved to be equivalent to the Hamilton-Jacobi equation for the least action. We also prove that the Legendre transform on the classical base corresponds to the mus…
Destructuring Physics: A functional derivation of spacetime
本文提出用极简数学结构重构时空概念，将时空抽象为任意集合上的一族函数，以去除冗余数学复杂性并保留核心物理性质。
We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the "hydrody…
Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functio…
It is often argued that superluminal velocities and nontrivial spacetime topologies, allowed by the theory of relativity, may lead to causal paradoxes. By emphasizing that the notion of causality assumes the existence of a time arrow (TA) that points from the past to the future, the apparent paradoxes appear to be an artefact of the wrong tacit assumption that the relativistic coordinate TA coincides with the physical TA. The latter should be identified with the thermodynamic TA, which, by being absolute and irrotational, does not lead to paradoxes.
Causal structure and topology change in (2+1)-dimensional simplicial gravity
研究(2+1)维简形引力中因果结构与拓扑变化，通过分类洛rentzian四面体因果类型，揭示顶点和hinge因果性的独立性及其对离散量子引力的影响。
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causality in Lorentzian geometry. In the present paper, these tools are further developed in several directions such as: (i) causal mappings --and, thus, abstract chronological ones-- do not preserve two levels of the standard hierarchy of causality conditions (however, they preserve t…
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