The existence of cosmic time functions

1969 ◽  
Vol 308 (1494) ◽  
pp. 433-435 ◽  
Keyword(s):  
Cosmic Time ◽  
Space Time ◽  
Time Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Null Curve ◽  
Null Curves ◽  
Stable Causality ◽  
Necessary And Sufficient

It is shown that stable causality is the necessary and sufficient condition that there should exist a cosmic time function which increases along every future directed timelike or null curve. Stable causality means that there are no closed timelike or null curves in any Lorentz metric that is sufficiently close to the space-time metric.

scholarly journals A Surface Family with a Common Asymptotic Null Curve in Minkowski 3-Space E 1 3

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Nadia Alluhaibi ◽  
Rashad A. Abdel-Baky
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Developable Surfaces ◽  
Null Curve ◽  
Necessary And Sufficient

This approach is on constructing a surface family with a common asymptotic null curve. It has provided the necessary and sufficient condition for the curve to be an asymptotic null curve and extended the study to ruled and developable surfaces. Subsequently, the study has examined the Bertrand offsets of a surface family with a common asymptotic null curve. Lastly, we support the results of this approach by some examples.

Spherically symmetric space-time of class one and electromagnetism

1968 ◽  
Vol 64 (3) ◽  
pp. 757-764 ◽  
Author(s):  
S. N. Pandey ◽  
I. D Kansal
Keyword(s):  
Symmetric Space ◽  
Flat Space ◽  
Space Time ◽  
Transformation Property ◽  
Spherically Symmetric ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Necessary And Sufficient

AbstractIt is well known that a spherically symmetric space-time is, in general, of class two. A necessary and sufficient condition for a spherically symmetric space-time to be of class one has been obtained in terms of the Riemann curvature tensor. By means of a transformation property of s.s. space-time, three distinct cases are shown to exist. The incompatibility of class one spherically symmetric space-times with Rainich algebraic conditions is established in these three cases. It is concluded that spherically symmetric electromagnetic fields cannot be embedded in a flat space of 5-dimensions.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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