Linear perturbations of spatially locally homogeneous spacetimes

Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III (Thurston's H^2 x R) type, while the other is the Bianchi II (Thurston's Nil) type. With a brief summary of previous results on the Bianchi III perturbations, asymptotic solutions for the gauge-invariant variables for the Bianchi III are shown, with which (in)stability of the background solution is also examined. The issue of linear stability for a Bianchi II solution is still an open problem. To approach it, appropriate eigenfunctions are presented for an explicitly compactified Bianchi II manifold and based on that, some field equations on the Bianchi II background spacetime are studied. Differences between perturbation analyses for Bianchi class B (to which Bianchi III belongs) and class A (to which Bianchi II belongs) are stressed for an intention to be helpful for applications to other models.Comment: Eq.(2.2) and Eq.(3.1) swapped. Errata to the (yet-to-be) published version attached. 16 pages, to appear in Contemporary Mathematics, AM

Criticality and Averaging in Cosmology

We propose comparing cosmological solutions in terms of their total spatial volumes $V(\tau)$ as functions of proper time $\tau$, assuming synchronous gauge, and with this intention evaluate the variations of $V(\tau)$ about the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions for dust. This can be done successfully in a simple manner without solving perturbation equations. In particular, we find that first variations vanish with respect to all directions which do not possess homogeneity and isotropy preserving components; in other words, every FLRW solution is a {\it critical point} for $V(\tau)$ in the properly restricted subspace of the space of solutions. This property may support a validity of the interpretation of the FLRW solutions as constituting an averaged model. We also briefly investigate the second variations of $V(\tau)$.Comment: 12 pages, PTPTeX, some minor corrections, final version for publication in Prog. Theor. Phy

"Housework and the Consumption History in pre-war Japan"

This paper aims to explor e the practice of housework in modern Japan from the point of view of consumption history. Gary Becker's seminal argument provides us with the basic framework in considering the relationship between consuming "goods" and "housework" in a household, which combines time and market goods to produce more basic commodities that directly enter their utility functions. Based on this framework, this paper tries to explore how housework related to consuming activities in modern Japan, by observing the practice of housework in farming households as well as investigating the role of domestic servants in non-farming households in the inter war period. We raise two points as the concluding remarks of this paper. The first is the complementary nature of the housework to the consumption of goods in Japan's households. The positive correlation between household expens es and housework hours, explored by a quantitative analysis using the data from economic survey of farming households, suggests this, and this finding might propose the inconsistent image of housework to that of Jan de Vries, which formulated the changing pattern of consumption in Europe, as he assumes the goods-intensive nature of the consumption at the expense of housework (substitutive nature of housework to the consumption of goods) during the industrializing period in the West. This discrepancy might suggest a possible hypothesis that Japan's pattern can be formulated as labour -intensive way of growing consumption, though it requires further comparative studies on the role of housework for material lives. Secondly, we noticed the supply side of housework by measuring the contribution of family members and domestic servants. The plurality of the family members engaged in housework implies that the nature of the Japan's households is far different from that of the breadwinner hous ehold model. It also suggests the link between housework and family system, or more interestingly, the relationship between family system and consumption pattern.

"Capital Accumulation and the Local Economy: Brewers and Local Notables"; forthcoming in Tanimoto, Masayuki ed, The Role of Tradition in Japan's Industrialization, Oxford University Press.

This essay focuses on the holders of accumulated capital in the brewing industry to examine the characteristics of the capital accumulation process and the connection between accumulated capital and the start of Japan's industrialisation in Meiji period. The characteristic feature of brewing as a so-called "traditional industry" was that individual entrepreneurs accumulated a relatively large amount of capital and labour. The multi-layered structure of the brewing industry, with large-sized brewers selling to urban markets and small and medium-sized producers supplying areas outside the cities, resulted in this feature and formed a necessary condition for the investment activities of brewers. According to the examination of historical materials on particular brewery businesses [the Hamaguchi family and the Sekiguchi family], the brewers dared to invest their capital locally - in areas where they maintained close relationships. Capital accumulation in "traditional" industries was thus linked to the emergence of modern enterprises, and this linkage was supported by a regional community in which "traditional capitalists"' acted as "local notables" as much as entrepreneurs. The investment activities rooted in the regional community were the hidden driving force in initiating Japan's industrial revolution and full-scale industrialisation.

"Capital Accumulation and the Local Economy: Brewers and Local Notables"

This essay focuses on the holders of accumulated capital in the brewing industry to examine the characteristics of the capital accumulation process and the connection between accumulated capital and the start of Japan's industrialisation in Meiji period. The characteristic feature of brewing as a so-called "traditional industry" was that individual entrepreneurs accumulated a relatively large amount of capital and labour. The multi-layered structure of the brewing industry, with large-sized brewers selling to urban markets and small and medium-sized producers supplying areas outside the cities, resulted in this feature and formed a necessary condition for the investment activities of brewers. According to the examination of historical materials on particular brewery businesses [the Hamaguchi family and the Sekiguchi family], the brewers dared to invest their capital locally - in areas where they maintained close relationships. Capital accumulation in "traditional" industries was thus linked to the emergence of modern enterprises, and this linkage was supported by a regional community in which "traditional capitalists"' acted as "local notables" as much as entrepreneurs. The investment activities rooted in the regional community were the hidden driving force in initiating Japan's industrial revolution and full-scale industrialisation.

"The Role of Tradition in Japan's Industrialization: A Perspective of "Indigenous Development""

This paper explores Japan's industrialization from the perspective of "indigenous development", focusing on what may be identified as "traditional" or "indigenous" factors. First, we describe the typical indigenous development process by looking at a case study of one rural weaving industry. After that, we investigate the functions of various institutions supporting "indigenous development" in modern Japan. Through these, we conclude that the peculiar logic functioning on the supply side of the developmental trajectory was the key to understand the existence of "indigenous development" in Japan's industrialization process. The existence of the household economy practicing a "rational" labour allocation strategy among household members within the framework of the traditional institution of the ie regulated behavior on the labour side. The measures and institutions run by the central and local governments supported the organization and market adaptation on the management side. Regional society also functioned to stabilize the relation between labour and management. All these factors worked to construct the system. Since each of the factors, including the intensity of labour inputs with relative low wages within peasant and small business households, and the benefits from a division of labour generated by this style of organization, contributed to competitiveness in the market, this system could have functioned as the basis of indigenous development.