Direct Control of Nonlinearities in the Einstein Equations

Oil-rich countries have oftentimes been confronted with the challenge of diversifying their economies away from oil dependence given the exhaustible nature of these fossil fuels. Investing in sovereign wealth funds has been one of the most ubiquitous ways of preparing for the post-oil period. Investing in sovereign wealth funds rather than directly injecting the oil revenues in the economy not only precludes the outbreak of the Dutch Disease (which is known for giving rise to an exchange rate appreciation, crowding out non-oil industries and keeping the economy reliant on oil), but it also saves for future generations. Yet, in the case of Azerbaijan, the Sovereign Wealth Fund of Azerbaijan (SOFAZ), founded in 1999, has only increased this reliance on oil. Using the rentier states theoretical framework, this paper will argue that the direct control over SOFAZ exercised by the president and the lack of consultation with the NGOs have made corruption easier, making the task of economic diversification more difficult. This has been possible because through corruption the president has often resorted to oil money to buy peace rather than invest it in economic diversification. As a result, since the foundation of SOFAZ, the country is more reliant, not less, on oil. Full text available at: https://doi.org/10.22215/rera.v8i1.223

Download Full-text

The Kerr solution

10.1093/oso/9780198786399.003.0048 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Kerr Black Hole ◽

Geodesic Equation ◽

Einstein Equations ◽

Kerr Metric ◽

Kerr Solution ◽

Axially Symmetric ◽

Observable Universe ◽

Einstein Vacuum Equations ◽

Einstein Vacuum ◽

The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

Download Full-text

The Qizilbāsh and their Shah: The Preservation of Royal Prerogative during the Early Reign of Shah Ṭahmāsp

Journal of the Royal Asiatic Society ◽

10.1017/s1356186321000250 ◽

2021 ◽

pp. 1-16

Author(s):

GREGORY ALDOUS

Keyword(s):

The Other ◽

Close Reading ◽

Direct Control ◽

Historical Literature

Abstract Modern historians of Persia's Safavid period (1501–1722) have long assumed that there was an interregnum between the death of Shah Ismāʿīl I in 1524 and the date when his son Ṭahmāsp came of age and established direct control in the 1530s. This idea of an interregnum takes two forms in the historiography. According to one narrative, during this time the Qizilbāsh amirs were disloyal to the young Ṭahmāsp and tried to seize control of Persia for themselves. According to the other, there was a war of succession in which Qizilbāsh factions supported different sons of Ismāʿīl I. Both of these narratives co-exist in the contemporary historical literature even though they disagree. Based on a close reading of the early Safavid chronicles, this article demonstrates that both narratives are incorrect and there was no interregnum. The Qizilbāsh continued throughout Ṭahmāsp's minority to respect him and treat him as their leader. Unsurprisingly, given his youth and inexperience, he deferred matters of state to his amirs. Nevertheless, his amirs derived their legitimacy to rule from him, and when leadership passed from one amir to another, it did so only with Ṭahmāsp's approval. Moreover, there was no dispute over the succession during Ṭahmāsp's minority.

Download Full-text

RECENT INVESTIGATIONS AT TULA CHICO, TULA, HIDALGO

Ancient Mesoamerica ◽

10.1017/s0956536120000139 ◽

2021 ◽

Vol 32 (1) ◽

pp. 41-55

Author(s):

Robert H. Cobean ◽

Dan M. Healan ◽

María Elena Suárez

Keyword(s):

Classic Period ◽

Cultural Continuity ◽

Direct Control ◽

Early Postclassic ◽

Initial Settlement ◽

Show Evidence ◽

History Of

AbstractRecent excavations at Tula Chico, the monumental center for Tula's earliest settlement, revealed a long and complex history of occupation, beginning with its initial settlement in the Middle Classic period by Coyotlatelco peoples, when much of the region was under Teotihuacan's direct control. During the Epiclassic period, a program of monumental construction began that developed the monumental complex seen today over a period of about 200 years. Although Tula Chico was superseded by Tula Grande, the monumental center for the Early Postclassic city, it continued to be occupied and maintained until its destruction by fire. Tula Chico and Tula Grande show evidence of clear cultural continuity in ceramics, architecture, and sculpture, including “Toltec style” sculpture characteristic of Tula Grande that is present in temporally early contexts at Tula Chico.

Download Full-text