On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.Comment: Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for publication in Classical and Quantum Gravit

Space-time defects :Domain walls and torsion

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature $\delta$-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenb\"{o}ck planar walls are caracterized by torsion $\delta$-singularities and zero curvature. It is shown that Weitzenb\"{o}ck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenb\"{o}ck nonstatic torsion walls is investigated.Comment: J.Math.Phys.39,(1998),Jan. issu

Comments on the tethered galaxy problem

In a recent paper Davis et al. make the counter intuitive assertion that a galaxy held `tethered' at a fixed distance from our own could emit blueshifted light. Moreover, this effect may be derived from the simplest Friedmann-Robertson-Walker spacetimes and the (0.3,0.7) case which is believed to be a good late time model of our own universe. In this paper we recover the previous authors' results in a more transparent form. We show how their results rely on a choice of cosmological distance scale and revise the calculations in terms of observable quantities which are coordinate independent. By this method we see that, although such a tethering would reduce the redshift of a receding object, it would not do so sufficiently to cause the proposed blueshift. The effect is also demonstrated to be much smaller than conjectured below the largest intergalactic scales. We also discuss some important issues, raised by this scenario, relating to the interpretation of redshift and distance in relativistic cosmology.Comment: 6 pages, 3 figures, submitted to Am.J.Phy

Five-Dimensional Unification of the Cosmological Constant and the Photon Mass

Using a non-Riemannian geometry that is adapted to the 4+1 decomposition of space-time in Kaluza-Klein theory, the translational part of the connection form is related to the electromagnetic vector potential and a Stueckelberg scalar. The consideration of a five-dimensional gravitational action functional that shares the symmetries of the chosen geometry leads to a unification of the four-dimensional cosmological term and a mass term for the vector potential.Comment: 8 pages, LaTe

Corporate Directors\u27 and Officers\u27 Cybersecurity Standard of Care: The Yahoo Data Breach

On September 22, 2016, Yahoo! Inc. ( Yahoo ) announced that a data breach and theft of information from over 500 million user accounts had taken place during 2014, marking the largest data breach ever at the time. The information stolen likely included names, birthdays, telephone numbers, email addresses, hashed passwords, and, in some cases, encrypted or unencrypted security questions and answers. Yahoo further disclosed its belief that the stolen data did not include unprotected passwords, payment card data, or bank account information. Just two months before Yahoo disclosed its 2014 data breach, it announced a proposed sale of the company\u27s core business to Verizon Communications. Then, during mid-December 2016, Yahoo announced that another 1 billion customer accounts had been compromised during 2013, a new record for largest data breach. Social media and electronic commerce websites face significant risk factors, and an acquirer may inherit cyber liability and vulnerabilities. The fact pattern in this announced acquisition raises a number of important corporate governance issues: whether Yahoo\u27s conduct leading up to the data breaches and its subsequent conduct constituted a breach of the duty to shareholders to provide security, the duty to monitor, the duty to disclose, or some combination thereof the impact on Verizon shareholders of the acquisition price renegotiation and Verizon\u27s assumption of post-closing cyber liabilities; and whether more drastic compensation clawbacks for key Yahoo executives would be appropriate. Cybersecurity remains a threat to all enterprises, and this Article contributes to the corporate governance literature, particularly as it applies to mergers and acquisitions and the management of cyber liability risk

Newtonian Counterparts of Spin 2 Massless Discontinuities

Massive spin 2 theories in flat or cosmological ($\Lambda \ne 0$) backgrounds are subject to discontinuities as the masses tend to zero. We show and explain physically why their Newtonian limits do not inherit this behaviour. On the other hand, conventional ``Newtonian cosmology'', where $\Lambda$ is a constant source of the potential, displays discontinuities: e.g. for any finite range, $\Lambda$ can be totally removed.Comment: 6 pages, amplifies the ``Newtonian cosmology'' analysis. To appear as a Class. Quantum Grav. Lette

Real Property -- 1954 Tennessee Survey

Champertous Deeds and Adverse Possession: There were two cases, Robinson v. Harris, and State v. McNabb, which used the questionable champertous deed concept to reach what seem to be just results. The sixteenth century doctrine, enacted by statute in Tennessee, is that a deed of conveyance executed and delivered by a title owner while the land is held in the adverse possession of another is void. As pointed out in the 1953 Survey article, however, recent Tennessee cases have tended to ignore a line of nationally recognized Tennessee equity cases holding that the deed is not void; that the transfer is good as between the grantor and the grantee and all persons in privity with them; that the grantee is entitled to sue in the name of the grantor; and that if the grantor recovers possession from the adverse possessor, it inures to the benefit of the grantee

Gender Role Identity and Attitudes Toward Feminism

In this study we examined relationships among gender role identity, support for feminism, nontraditional gender roles, and willingness to consider oneself a feminist in a sample of college students (N D 301). For female participants, we found positive relationships among higher masculinity on the PAQ (Personal Attributes Questionnaire), nontraditional attitudes toward gender roles, and the combined SRAI (Sex Role Attitudinal Inventory). A negative correlation was also found between lower scores on the PAQ masculinity–femininity index and the combined SRAI in women. For male participants, we found positive relationships among high femininity on the SIS (Sexual Identity Scale), willingness to consider oneself a feminist, positive attitudes toward the women’s movement, and the combined SRAI. We also found a negative relationship between high masculinity on the PAQ and willingness to consider oneself a feminist in men. The implications of these findings for the feminist movement are discussed

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

Research Progress Report: Fox-Pheasant Relationships in South Dakota, 1965

A 5-year cooperative study designed to obtain information regarding effects of foxes on pheasant populations in eastern South Dakota was initiated in 1964. Specific objectives were to determine (1) population fluctuations of foxes and pheasants, (2) fox food habits and reproductive characteristics and (3) effectiveness and cost of fox reduction to increase pheasant abundance. Studies were conducted on four pairs of 100-square-mile areas. Fox populations were reduced on one member of each pair beginning in January 1965, and individual foxes were removed on a complaint basis on the other. Each pair of areas is referred to as a unit. When summer pheasant data on the fox-reduction and check areas are considered, significant differences are noted in adult pheasants per mile, broods per mile, and brood size from 1964 to 1965. Changes in adult pheasants per mile in Unit 2 showed the decline in the fox-reduction area was significantly (0. 01) less than in the check area. However, in Units 1 and 4 the declines in the check areas were significantly (0. 01) less than those in the fox-reduction areas. The difference in decline in broods per mile in the fox-reduction compared to the check area from 1964 to 1965 was negligible in Unit 1. In Unit 2 the fox-reduction area showed a slight increase compared to a decrease in the check area. This difference is significant (0. 01). In Unit 4 a smaller decline occurred in the fox-reduction area than in the check area. The difference in Unit 4 is significant (0. 05). The proportion of hens with broods showed an increase from 1964 to 1965 in the fox-reduction areas of Units 1, 2, and 4 and a lesser increase or a decrease in the corresponding check areas. A significant (0. 01) increase in brood size occurred from 1964 to 1965 in the fox-reduction compared to the check area of Unit 1. A non-significant increase occurred in the check area compared to the fox-reduction area in Unit 2. The adult pheasant-per-mile averages during the spring of 1965 showed more birds in the fox-reduction area than in the check area of Unit 1, and the reverse in Unit 2. Neither difference is significant. Units 3 and 4 showed significantly (0. 01) more adults per mile in the fox reduction than in the check areas during this same period. Fox data revealed that counting tracks in snow along transects is the best of three methods for determining fox activity in an area. Such counts in reduction and check areas within each unit showed that fox activity was sufficiently comparable in each pair of areas prior to fox reduction. Methods used to reduce fox populations also reduced to some extent other predators, including nest robbers. Grasses, mice, pheasants, rabbits, and insects, in descending order, respectively, were the most frequently occurring items found in stomachs of foxes taken in the study areas from January to June 1965. Grasses were found in stomachs that also contained mice and insects. Pheasants were the item composing the greatest volume, followed by rabbits and mice. Prairie deer mice made up the majority of small mammal remains. (See more in Text