The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.
We present optical, UV and X-ray monitoring of the short orbital period black hole X-ray binary candidate Swift J1753.5-0127, focusing on the final stages of its 12−year long outburst that started in 2005. From September 2016 onward, the source started to fade and within three months, the optical flux almost reached the quiescent level. Soon after that, using a new proposed rebrightening classification method we recorded a mini-outburst and a reflare in the optical light curves, peaking in February (V∼17.0) and May (V∼17.9) 2017, respectively. Remarkably, the mini-outburst has a peak flux consistent with the extrapolation of the slow decay before the fading phase preceding it. The following reflare was fainter and shorter. We found from optical colors that the temperature of the outer disk was ∼ 11,000 K when the source started to fade rapidly. According to the disk instability model, this is close to the critical temperature when a cooling wave is expected to form in the disk, shutting down the outburst. The optical color could be a useful tool to predict decay rates in some X-ray transients. We notice that all X-ray binaries that show mini-outbursts following a main outburst are short orbital period systems (< 7 h). In analogy with another class of short period binaries showing similar mini-outbursts, the cataclysmic variables of the RZ LMi type, we suggest mini-outbursts could occur if there is a hot inner disk at the end of the outburst decay.
Designing and implementing online or digital learning material is a demanding task for teachers. This is even more the case when this material is used for more engaged forms of learning, such as inquiry learning. In this article, we give an informed account of Go-Lab, an ecosystem that supports teachers in creating Inquiry Learning Spaces (ILSs). These ILSs are built around STEM–related online laboratories. Within the Go-Lab ecosystem, teachers can combine these online laboratories with multimedia material and learning apps, which are small applications that support learners in their inquiry learning process. The Go-Lab ecosystem offers teachers ready–made structures, such as a standard inquiry cycle, alternative scenarios or complete ILSs that can be used as they are, but it also allows teachers to configure these structures to create personalized ILSs. For this article, we analyzed data on the design process and structure of 2414 ILSs that were (co)created by teachers and that our usage data suggest have been used in classrooms. Our data show that teachers prefer to start their design from empty templates instead of more domain–related elements, that the makeup of the design team (a single teacher, a group of collaborating teachers, or a mix of teachers and project members) influences key design process characteristics such as time spent designing the ILS and number of actions involved, that the characteristics of the resulting ILSs also depend on the type of design team and that ILSs that are openly shared (i.e., published in a public repository) have different characteristics than those that are kept private.
Within the efforts to bring frontline interactive astrophysics and astronomy to the classroom, the Hands on Universe (HOU) developed a set of exercises and platform using real data obtained by some of the most advanced ground and space observatories. The backbone of this endeavour is a new free software Web tool -Such a Lovely Software for Astronomy based on ImageJ (SalsaJ). It is student-friendly and developed specifically for the HOU project and targets middle and high schools. It allows students to display, analyze, and explore professionally obtained astronomical images, while learning concepts on gravitational dynamics, kinematics, nuclear fusion, electromagnetism. The continuous evolving set of exercises and tutorials is being completed with real (professionally obtained) data to download and detailed tutorials. The flexibility of the SalsaJ platform tool enables students and teachers to extend the exercises with their own observations through the use of robotic telescopes. The software developed for the HOU program has been designed to be a multiplatform, multi-lingual experience for image manipulation and analysis in the classroom. Its design enables easy implementation of new facilities (extensions and plugins), minimal in-situ maintenance and flexibility for exercise plugin. Here, we describe some of the most advanced exercises about astrophysics in the classroom, addressing particular examples on gravitational dynamics, concepts currently introduced in most sciences curricula in middle and high schools.
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