The kinematics of general relativity is described. General relativity is given by intrinsically curved spacetimes, for non-Euclidean geometry, based on two assumptions, leading to two physical principles for the kinematics (plus one equation for the dynamics). The kinematics is based on the same parallel transport as for gauge theories. The motion of free particles is on geodesics in the curved spacetime.

We consider the black hole with charge, the Reissner–Nordstrom black hole. We describe the solution, and the BPS bound and its saturation, for extremal black holes, of mass = charge. We describe properties of the event horizon. Finally, we calculate the Penrose diagram of the Reissner–Nordstrom black hole, in the non-extremal and extremal cases.

Previous chapters have examined forms of action that the standard belief-desire model ignores. This chapter starts to dig deeper into the standard model itself. It is about how decisions get made (especially decisions that are commonly described as conscious ones), and about how those decisions subsequently give rise to actions. It draws on the scientific literature on prospection and on what is often called “neuroeconomics” to argue that valence (pleasure and displeasure) is the common currency of all decision-making. It also argues that the goals and intentions that result from decision-making are real, and distinct from beliefs and affective forms of desire. The chapter begins by showing that the ordinary notion of desire conflates two very different kinds of mental state, however, and it concludes by discussing how intentions and affective desires interact when they conflict.

The Mexican Constitution has been amended an extremely high number of times, challenging all theoretical expectations including the one in this book. Closer analysis indicates three reasons for this discrepancy: first, the length and inconsistency of the Mexican Constitution second, the institutional requirements for amendments (the stringent rules of Article 135 requiring two-thirds of both chambers and a majority of states combines with the loose requirements of Article 63 specifying that the presence of only half of the members is required), and third, the political consensus prevailing in the Mexican political scene (crucial instances, such as the onset of multipartyism with concertacesión and pivotal reforms to Articles 27 and 73, offer deeper context) all make amendments feasible. A comprehensive analysis of the sixty-eight constitutional amendments from 2000 to 2013 corroborates these expectations concerning institutional thresholds, coalition dynamics, and amendment significance.

In Chapter 9 we consider a recurrent Markov chain possessing an invariant measure which is either probabilistic in the case of positive recurrence or σ-finite in the case of null recurrence. Our main aim here is to describe the asymptotic behaviour of the invariant distribution tail for a class of Markov chains with asymptotically zero drift going to zero more slowly than 1/x. We start with a result which states that a typical stationary Markov chain with asymptotically zero drift always generates a heavy-tailed invariant distribution which is very different from the case of Markov chains with asymptotically negative drift bounded away from zero. Then we develop techniques needed for deriving precise tail asymptotics of Weibullian type.

This chapter argues that the implications of territorial disputes for individuals are seldom considered in the Court’s legal reasoning and proposes ways to do so. It first observes that the Court traditionally resolves territorial disputes with reference to a firm hierarchy of titles, few of which allow for the consideration of individuals. It then considers how the title of effectivités could potentially allow for the consideration of individuals and acknowledges that their rights and needs have been mentioned by the Court as an afterthought in certain judgments. It analyses the reasons for the Court’s approach and argues that the principle of equity could play a stronger role in allowing for the consideration of individuals in territorial disputes.

This chapter argues that while great strides have been made to humanise the law of diplomatic protection, its practice in the courtroom is not in alignment with this as the protected individual does not participate in proceedings. It first dismantles the famous Mavrommatis fiction and argues that other conditions for diplomatic protection (such as nationality and the exhaustion of local remedies) and its features (such as state discretion and state responsibility) have been increasingly humanised to place emphasis on the individual. Second, it analyses the case law to show how the individual does not participate in proceedings at the Peace Palace. Finally, it provides suggestions to advocate for stronger procedural participation for the injured individual in cases of diplomatic protection at the ICJ.