Tracing a Black Hole: Probing Cosmic Darkness in Anthropocenic Times

In April 2019, the Event Horizon Telescope (EHT) project released an unprecedented image of a supermassive black hole at the centre of galaxy Messier 87. The image, which shows a dark disc outlined by swirling hot gas circling the black hole’s event horizon, exhibits a 55 million-year-old cosmic event in the Virgo galaxy cluster—a void of stellar mass measuring some 6.5 billion times that of our sun. Situated within today’s (Good) Anthropocene scenario, characterized as it is by both the rise of an inhospitable planet but also a range of good vibes and affirmative mantras, this tracing explores this newly “discovered” black hole in terms of the unthinkable questions and speculative trajectories it raises for education and its futures. Through a series of forays into astrophysics, historical examples of cosmic imaging, and further exploration of the image created by EHT, this tracing outlines the black hole and its apparent horizons in order to propose a strange vantage point from which pedagogical problem-posing might be interrupted, mutated, and relaunched. By turning to that which lies outside of the traditional science classroom—beyond the school, beyond curriculum, indeed, beyond the planet itself—this tracing seeks to probe this black hole event in terms of its weird and weirding pedagogical trajectories so as to speculate on unthought possibilities for resituating (science) education in the age of the Anthropocene.

Estimation of temperature of cosmological apparent horizons: a new approach

We consider radiation from cosmological apparent horizon in Friedmann–Lemaitre–Robertson–Walker (FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.

Evolution of cosmological horizons of wormhole cosmology

Recently, we solved Einstein’s field equations to obtain the exact solution of the cosmological model with the Morris–Thorne-type wormhole. We found the apparent horizons and analyzed their geometric natures, including the causal structures. We also derived the Hawking temperature near the apparent cosmological horizon. In this paper, we investigate the dynamic properties of the apparent horizons under the matter-dominated universe and lambda-dominated universe. As a more realistic universe, we also adopt the [Formula: see text]CDM universe which contains both the matter and lambda. The past light cone and the particle horizon are examined for what happens in the case of the model with wormhole. Since the spatial coordinates of the spacetime with the wormhole are limited outside the throat, the past light cone can be operated by removing the smaller-than-wormhole region. The past light cones without wormhole begin to start earlier than the past light cones with wormhole in conformal time-proper distance coordinates. The light cone consists of two parts: the information from our universe and the information from other universe or far distant region through the wormhole. Therefore, the particle horizon distance determined from the observer’s past light cone cannot be defined in a unique way.

Final fate of charged anisotropic fluid collapse in f(R) gravity

In this paper, the spherically symmetric gravitational collapse of anisotropic fluid in the presence of charge in metric [Formula: see text] theory is analyzed. We consider the static and non static spherically symmetric spacetimes for outer and inner regions of collapsing object respectively. For the smooth matching of inner and outer regions, the Senovilla as well as Darmois matching conditions are utilized. The closed form solutions are obtained from field equations. Moreover, we examine the apparent horizons and their physical significance. The effect of cosmological constant and [Formula: see text] term is same and the collapsing rate speeds up as compared to that of anisotropic fluid case when the electromagnetic field is introduced. Electromagnetic charge also affects the time interval of singularities and cosmological horizons.

Bartnik mass via vacuum extensions

We construct asymptotically flat, scalar flat extensions of Bartnik data [Formula: see text], where [Formula: see text] is a metric of positive Gauss curvature on a two-sphere [Formula: see text], and [Formula: see text] is a function that is either positive or identically zero on [Formula: see text], such that the mass of the extension can be made arbitrarily close to the half area radius of [Formula: see text]. In the case of [Formula: see text], the result gives an analog of a theorem of Mantoulidis and Schoen [On the Bartnik mass of apparent horizons, Class. Quantum Grav. 32(20) (2015) 205002, 16 pp.], but with extensions that have vanishing scalar curvature. In the context of initial data sets in general relativity, the result produces asymptotically flat, time-symmetric, vacuum initial data with an apparent horizon [Formula: see text], for any metric [Formula: see text] with positive Gauss curvature, such that the mass of the initial data is arbitrarily close to the optimal value in the Riemannian Penrose inequality. The method we use is the Shi–Tam type metric construction from [Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, J. Differential Geom. 62(1) (2002) 79–125] and a refined Shi–Tam monotonicity, found by the first named author in [On a localized Riemannian Penrose inequality, Commun. Math. Phys. 292(1) (2009) 271–284].

Charged perfect fluid gravitational collapse in f(R, T) gravity

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

Five-dimensional spherical symmetric perfect fluid collapse in f(R, T) gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the framework of f(R, T) modified theory of gravity using five-dimensional background. We consider the five-dimensional spherical symmetric metric as the interior region and a five-dimensional Schwarzschild metric as an exterior region. The Darmois junction conditions between exterior and interior regions are discussed. By taking the particular f(R, T) model, the corresponding field equations are evaluated for both marginally bound L(r) = 1 and non-marginally bound L(r) ≠ 1 cases. We find the gravitational mass of the collapsing system and discuss the apparent horizons and their time formation for different possible cases. Also, the cosmological and black hole horizons have been discussed. It has been concluded that the term involving λ plays a double role: it accelerates the collapse in the region where ρ0 < 4p0 and it slows down the collapsing of matter when ρ0 > 4p0. Further, it is noted that our results reduce to the results found by Sharif and Ahmad (J. Korean Phys. Soc. 52, 980 (2008). doi: 10.3938/jkps.52.980) in general relativity for λ = 0.