Causal concept for the general black hole shadow is investigated, instead of the photon sphere. We define several `wandering null geodesics' as complete null geodesics accompanied by repetitive conjugate points, which would correspond to null geodesics on the photon sphere in Schwarzschild spacetime. We also define a `wandering set', that is, a set of totally wandering null geodesics as a counterpart of the photon sphere, and moreover, a truncated wandering null geodesic to symbolically discuss its formation. Then we examine the existence of a wandering null geodesic in general black hole spacetimes mainly in terms of Weyl focusing. We will see the essence of the black hole shadow is not the stationary cycling of the photon orbits which is the concept only available in a stationary spacetime, but their accumulation. A wandering null geodesic implies that this accumulation will be occur somewhere in an asymptotically flat spacetime.
In this work, starting from a spherically symmetric scale--dependent black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we get and discuss the shape of its shadow.
In this work, starting from a spherically symmetric polytropic black hole, a rotating solution is obtained by following the Newman--Janis algorithm without complexification. Besides studying the horizon, the static conditions and causality issues of the rotating solution, we obtain and discuss the shape of its shadow. Some other physical features as the Hawking temperature and emission rate of the rotating polytropic black hole solution are also discussed.
In this paper, we investigate the light trajectories and shadow properties in the rotating version of null naked singularity (NNS) spacetime which is derived using the Newman- Janis algorithm without complexification method. We discuss some of the geometrical properties and causal structure of Rotating Naked Singularity (RNS) spacetime. The gravitational lensing in a rotating naked singularity is analyzed, and the results are compared to those of a Kerr black hole. In the case of a Kerr black hole, the photon sphere exists for both prograde and retrograde photon orbits, whereas for RNS, the ph…
Shadow signatures and energy accumulation in Lorentzian-Euclidean black holes
Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；RIKEN iTHEMS（理化学所 iTHEMS）
The role of the wandering null geodesic is studied in a black hole spacetime. Based on the continuity of the solution of the geodesic equation, the wandering null geodesics commonly exist and explain the typical phenomena of the optical observation of event horizons. Moreover, a new concept of `black room' is investigated to relate the wandering null geodesic to the black hole shadow more closely.
Viscosity effects on the shadow of a non-rotating black hole
Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Chanakya University（查纳克雅大学）；Departamento de Matemática da Universidade de Aveiro and Center for Research and Development in Mathematics and Applications (CIDMA)（阿威罗大学数学系及数学与应用研发中心）；Instituto de Astronomía, Universidad Nacional Autónoma de México（墨西哥国立自治大学天文学研究所）；Departamento de Astronomía y Astrofísica, Universitat de València（瓦伦西亚大学天文与天体物理学系）；Observatori Astronòmic, Universitat de València（瓦伦西亚大学天文台）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德空间科学实验室）
Utilizing concepts from dynamical systems theory, we demonstrate how the existence of light rings, or fixed points, in a spacetime will give rise to families of periodic orbits and invariant manifolds in phase space. It is shown that these structures define the shape of the black hole shadow as well as a number of salient features of the spacetime lensing. We illustrate this through the analysis of lensing by a hairy black hole.
In this article, we provide a review of the current state of the research of the black hole shadow, focusing on analytical (as opposed to numerical and observational) studies. We start with particular attention to the definition of the shadow and its relation to the often used concepts of escape cone, critical impact parameter and particle cross-section. For methodological purposes, we present the derivation of the angular size of the shadow for an arbitrary spherically symmetric and static space-time, which allows one to calculate the shadow for an observer at arbitrary distance from the cent…
Regular black holes with Minkowskian cores: causal structure and observational degeneracy
Universidad de La Frontera（拉弗龙特拉大学）；Universidad Católica del Norte（北天主教大学）；University of Queensland（昆士兰大学）；Fukushima University（福岛大学）；Pontificia Universidad Católica de Valparaíso（瓦尔帕莱索天主教 Pontificia 大学）
A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a natural meaning to the concepts of cosmic time, spacelike hypersurfaces and timelike or lightlike flows without assuming the notion of a background metric. The concepts of causal propagators and the speed of causality are discussed. In this approach the concepts of spacetime and dynamics are linked in an essential and inseparable whole, with no meaning to either…
We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.
The causal set approach to quantum gravity embodies the concepts of causality and discreteness. This article explores some foundational and conceptual issues within causal set theory.
We give a brief review on the formation and the calculation of black hole shadow. Firstly, we introduce the conception of black hole shadow and the current works on a variety of black hole shadows. Secondly, we present main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affect the boundary of black hole shadow. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the pattern…
Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining probabilistic predictions and dynamical space-time. Combining the probabilistic nature of quantum theory and dynamical treatment space-time from general relativity is an approach to the problem of quantum gravity. The causaloid framework lays the mathematical groundwork to be able to treat indefinite causal structure. In this paper, we build on the causaloid mathema…
Causal Structure of Spacetime Singularities and Their Observable Signatures
Charotar University of Science and Technology (CHARUSAT)（查拉塔科学与技术大学）；Sardar Vallabhbhai National Institute of Technology, Surat（萨达尔·瓦拉巴伊国立技术学院苏拉特分校）；Universidade de São Paulo（圣保罗大学）
