We consider the rotating black hole, the Kerr solution, and the rotating black hole with charge, the Kerr–Newman solution. We describe their symmetries and causal structure, including the new features of the ring singularity and the ergosphere, with frame-dragging (observers are forced to rotate with the black hole) and calculate the Penrose diagram. Finally, we describe the Penrose process of extracting energy and angular momentum from the rotating black hole.

Transvaginal ultrasound scan is the mainstay of diagnosis of miscarriage. Evidence based criteria should be fulfilled in all cases, with interval scans as needed to avoid inadvertent interventions when the pregnancy may be viable. Incomplete, inevitable and complete miscarriages have specific ultrasound findings. Several ultrasound factors, including slow embryonic heart rate, small embryo or gestation sac size and an enlarged yolk sac, alone or in combination, help predict impending pregnancy loss. Uterine factors such as fibroids, adenomyosis and adhesions after previous caesarean birth may make ultrasound assessment for early pregnancy more challenging.

The History of Mary Prince is a geographically layered narrative: The text transcribes Prince’s experiences of enslavement in the Caribbean from her birth in 1788 in Brackish Pond, Bermuda, to her harrowing labor on the salt industries on Grand Turk to her efforts to purchase her freedom in Antigua in the 1820s to her journey to London in 1828, where she continued her campaign for emancipation. Yet this chapter turns to The History to meditate on the methods we use for recovering Black geographies that may remain oblique in colonial archives. It argues that contemporary Black poets offer insights into Prince’s movements that may only exist as palimpsests within The History by speculating on her knowledge of Caribbean resistance movements, such as the Haitian Revolution and the Sunday Market Revolt in Antigua. By assembling this diachronic reading method, the chapter resists the impulse to achieve conclusive answers about Prince’s geographical relations but instead unfolds alternative possibilities for locating her in Black spaces.

In Renaissance Europe, war and the use of force were regular phenomena and likewise subject of common rules. The theory of ‘just war’, dating back to ancient times, was further developed by legal scholars, and all belligerents claimed to have a just cause, often explained in printed pamphlets. International law consisted of theory and practice, and thus, they should be considered in a mutual context. The focus was still on the question of who had a right to wage war, i.e. on the jus ad bellum, and barely on regulations of warfare or on a containment of war. International law in Renaissance Europe rooted in its very society, in its rules and values. Legal debates and war justifications consolidated the Christian European community, which even in war times did not break apart, even if it was contradictory to the principle of sovereignty and the idea that a sovereign owes no justification to anyone. Moreover, scholars and belligerents argued with natural law and insisted in the universality of international law, although it was in fact basically European. Thus, in Renaissance Europe well-established traditions existed for how to handle war, but they were more and more challenged by the idea of sovereignty, as well as by the European expansion and by global interaction.

This chapter is an introduction to the Enlightenment mock arts, set out in three historical hypotheses. First, early-modern writers became increasingly interested in the cognitive (rather than simply material) value in the work of skilled technicians. The mock-arts were models for the intuitions involved in skilled manufacture, related to certain ineffable components of literary production. Second, the literary framing for those investigations was invariably satirical (or oblique and critical in other ways). As specialists in literary wit, authors of mock arts put themselves forward as experts in curiosity, invention and communication. Third, writers became more subtle in their assumptions about the print trade and the suitability of books as tools that might contribute to the communication of personal knowledge. Since convention defined that sort of knowledge by the impossibility of pinning it down in books, this opened another field for irony and indirection.