We consider relativistic stars and find the equations of gravitational collapse. In particular, we write the Tolman–Oppenheimer–Volkov (TOV) equation. We define general stellar models. We find the Chandrasekhar limit for white dwarfs to break electron degeneracy pressure and collapse to a neutron start, and the TOV limit for neutron stars to break neutron degeneracy pressure and collapse to a black hole. Finally, we describe a simple model (Oppenheimer–Snyder) for collapse to a black hole, and the resulting Penrose diagram.

The standard philosophical model of intentional action-explanation appeals to states of belief and desire to do the explaining. This chapter evaluates what philosophers have had to say about the nature of desire. Chapter 5 showed that the ordinary notion of desire encompasses two very different kinds of mental state: goals and intentions, on the one hand, and affective or emotion-like forms of desire, on the other. The focus here is on the latter. The chapter shows that desires of this sort always incorporate anticipatory pleasure, and that pleasure itself is an analog-magnitude representation of value. The chapter begins with what the science can tell us about the respective natures of pleasure and desire, before comparing the results with claims made by armchair-philosophers. Many of the latter are false, albeit sometimes containing partial insights.

The chapter gives an overview of dispute settlement during the Old Regime. Contrary to older assessments of the historiography, dispute settlement retained its importance in this era, both in qualitative and in quantitative terms. This was true for the field of theoretical literatures, which, from the last decades of the seventeenth century, dealt intensively with the subject. Normally, a clear distinction was made between an elected arbiter, who definitively decided a dispute, and a mediator, who only made peace proposals. Diplomatic practice, which made intensive use of the instruments of dispute settlement until the last decades of the eighteenth century, was much more flexible. The transitions between arbitration and mediation were fluid; the boundaries of confession and rank were also frequently crossed. In Old Regime Europe, mediation was also used for the first time in peace negotiations between Christian and Islamic powers. New forms of mediation emerged as well. One was the armed mediation, in which a power intervened in a conflict uninvited and set a peace ultimatum; this could easily lead to war. This indicates that dispute settlement did not automatically contribute to an increase in peace; the relationship of dispute settlement to war and peace remained rather ambivalent in Old Regime Europe.

This chapter charts the profound transformations undergone by diplomacy, both secular and papal, in an age of dramatic intellectual, political and military upheaval. Considering both scholarship and practice, the chapter assesses the rise of ‘resident diplomacy’ and highlights the new structures that were put in place in order to manage longer missions. The investigation of the right to send ambassadors reveals persistent traits of pluralism in early modern Europe, while the plurality of diplomatic envoys and roles is taken into account to make the complexity of the notion of diplomatic status more apparent: this status, in fact, cannot be reduced to that of a fully fledged ambassador exclusively committed to the object of their official mission. Information-gathering, negotiation and mediation are singled out as the most significant diplomatic functions. Changes in the conception of diplomatic inviolability and immunity are also considered, and include the emergence of the idea of extraterritoriality concerning both the person of the ambassador and diplomatic premises.

The Ottomans had a variety of ways of dealing with non-Muslim foreigners. In theory, Islamic law assumed a constant state of war between Muslim and non-Muslim rulers, but in practice, long-term peace arrangements were possible and even common. In terms of diplomacy, the Ottomans’ instruments and peacemaking procedures were similar to those of the West, the Turks likewise building on established customs and practices from the Byzantine period and beyond. The ahdnames were particularly important for international relations; originally unilateral documents, they evolved into more reciprocal instruments, only to become more unilateral again in the second half of the seventeenth century. In theory, peace with unbelievers should be temporary, but in practice, the duration of treaties concluded by the Ottomans reflected their assessment of the likelihood of hostilities resuming; in the case of countries that did not pose any military threat to the sultan’s domains, peace could even be concluded indefinitely. As long as both sides maintained the friendship between the two parties, there was no need to fear the Turks. The interconnected phenomena of slavery and privateering regularly put a strain on this friendship, as men, women and children on both sides were dragged off and sold as chattel. This loss of life and property sometimes led to international incidents, in which the Ottoman authorities made it clear that the basic Islamic parameters of peace could not be ignored with impunity.

The question of whether or not the sea can be owned or controlled has occupied the minds of many over the centuries. The discovery of America by Columbus made the questions of ownership of the sea and how regimes to govern the sea could be created and managed gain importance on a global scale. This chapter discusses the history of the law of the sea from the perspective of ‘Renaissance Europe’, focusing on the ‘battle of the books’ dominated by the publication of Mare Liberum (1609) by Hugo de Groot (Grotius) and John Selden’s Mare clausum (1635). It shows that the concept of the free sea was perfectly compatible with the adjacent or territorial sea both in legal practice and in principle. The idea of the free sea, defended and made explicit by Grotius, was not new but originated in Roman law and its medieval interpretations. Rather than the free sea, mare clausum was the new contribution of early modern thinking on the law of the sea. The concept of mare clausum had been shaped by the division of the world’s oceans between Spain and Portugal based on the papal bull Inter Caetera (1493) and the treaties of Tordesillas (1494) and Zaragoza (1529).

We consider some general properties of black holes and event horizons, of causality and topology. We define trapped surfaces, congruence, convergence, and show an example of a marginally trapped surface different than the event horizons. We prove the existence of an horizon for de Sitter spacetime, via its Penrose diagram. We then define Rindler spacetime, as the accelerated Minkowski spacetime, that gains an event horizon and mimics what happens for a black hole.