Radiation coordinates in general relativity

1966 ◽  
Vol 292 (1428) ◽  
pp. 1-13 ◽  
Keyword(s):  
Gravitational Radiation ◽  
General System ◽  
Space Time ◽  
Timelike Curve ◽  
Null Cone ◽  
Metric Tensor ◽  
Curved Space ◽  
The World ◽  
The Future ◽  
World Function

This paper introduces a system of coordinates (called radiation coordinates ) which may be useful in discussing problems of gravitational radiation. Starting with a general system of coordinates x i in curved space-time, an assigned timelike curve C , and an orthonormal tetrad assigned along C , the radiation coordinates x a of any event P are defined by a formula involving the world function. In radiation coordinates the equation of any null cone, drawn from an event x a' on C into the future, has the Minkowskian form This paper introduces a system of coordinates (called radiation coordinates ) which may be useful in discussing problems of gravitational radiation. Starting with a general system of coordinates x i in curved space-time, an assigned timelike curve C , and an orthonormal tetrad assigned along C , the radiation coordinates x a of any event P are defined by a formula involving the world function. In radiation coordinates the equation of any null cone, drawn from an event x a' on C into the future, has the Minkowskian form ƞ ab (x a - x a' ) (x b - x b’ ) = 0, ƞ ab = diag (1, 1, 1, - 1 ) . The metric tensor satisfies the coordinate conditions g ab (x b - x b' ) = ƞ ab (x b - x b' ), where x b' are regarded as functions of x b viz. the coordinates of the point of intersection of C with the null cone drawn into the past from x b . Continuity on C of the Jacobian matrix of the transformation x → x^ ~ is ensured by demanding the constancy of the components on the tetrad of the unit tangent vector to C . Continuity of the second derivatives of the transformation cannot be obtained except in very special circumstances. If space-time is flat, C a geodesic, and the orthonormal tetrad transported parallelly along C with the fourth vector tangent to C , then radiation coordinates reduce to the usual Minkowskian coordinates having C for time axis.

scholarly journals Connection Between Non-Rotating Local Reference Frames by Means of the World Function

1991 ◽  
Vol 127 ◽  
pp. 262-265
Author(s):  
J.M. Gambi ◽  
P. Romero ◽  
A.San Miguel ◽  
F. Vicente
Keyword(s):  
Reference Frames ◽  
Riemann Tensor ◽  
Space Time ◽  
General Character ◽  
Order Of Approximation ◽  
First Order ◽  
The World ◽  
Local Reference ◽  
General Relativistic ◽  
World Function

AbstractBy means of the world function an approximate transformation showing the Riemann tensor between the Fermi coordinates associated to two non-rotating local reference frames is derived in a General Relativistic space-time. One of the observer’s world lines is resticted to be a time-like geodesic of the space-time, and the other is a time-like curve of a general character. The space-time where the transformation is evaluated is supposed to be of small curvature, and the calculations are carried out in a first order of approximation with respect to the Riemann tensor.

Electrodynamics in curved space-time: Free-space longitudinal wave propagation

2019 ◽  
Vol 32 (3) ◽  
pp. 282-291 ◽  
Author(s):  
Ole Keller ◽  
Lee M. Hively
Keyword(s):  
Scalar Field ◽  
Longitudinal Wave ◽  
Free Space ◽  
Quantum Electrodynamics ◽  
Wave Theory ◽  
Space Time ◽  
Metric Tensor ◽  
Curved Space ◽  
Magnetization Density ◽  
General Relativistic

Jiménez and Maroto [Phys. Rev. D 83, 023514 (2011)] predicted free-space, longitudinal electrodynamic waves in curved space-time, if the Lorenz condition is relaxed. A general-relativistic extension of Woodside’s electrodynamics [Am. J. Phys. 77, 438 (2009)] includes a dynamical, scalar field in both the potential- and electric/magnetic-field formulations without mixing the two. We formulate a longitudinal-wave theory, eliminating curvature polarization, magnetization density, and scalar field in favor of the electric/magnetic fields and the metric tensor. We obtain a wave equation for the longitudinal electric field for a spatially flat, expanding universe with a scale factor. This work is important, because: (i) the scalar- and longitudinal-fields do not cancel, as in classical quantum electrodynamics; and (ii) this new approach provides a first-principles path to an extended quantum theory that includes acceleration and gravity.

scholarly journals On the definition of distance in curved space, and the displacement of the spectral lines of distant sources

1931 ◽  
Vol 133 (821) ◽  
pp. 93-105 ◽  
Keyword(s):  
Dimensional Space ◽  
Null Geodesic ◽  
Space Time ◽  
Spectral Lines ◽  
Relativity Theory ◽  
Spatial Distance ◽  
Curved Space ◽  
The World ◽  
Andromeda Nebula ◽  
World Point

The displacement of lines in the spectrum of a distant star, on the assumption that space-time is of constant curvature (the “de Sitter world”) has been extensively studied. The question, however, is not yet settled, different investigators reaching conclusions which are not apparently concordant. The origin of some of the discordances may be traced to the ambiguities which are involved in the use of the terms “ time,” “spatial distance” and “velocity,” when applied by an observer to an object which is remote from him in curved space-time. The “interval” which is defined by ds 2 = ∑ p, q g pq dx p dx q involves space and time blended together; and although any particular observer at any instant perceives in his immediate neighbourhood an “instantaneous three-dimensional space,” consisting of world-points which he regards as simultaneous, and within which the formulæ of the “restricted relativity theory” are valid, yet this space cannot be defined beyond his immediate neighbourhood; for with a general Riemannian metric, it is not possible to define simultaneity (with respect to a particular observer) over any finite extent of space-time. The concept of “spatial distance between two material particles” is, however, not really dependent on the concept of “simultaneity.” When the astronomer asserts that “the distance of the Andromeda nebula is a million light-years,” he is stating a relation between the world-point occupied by ourselves at the present instant and the world-point occupied by the Andromeda nebula at the instant when the light left it which arrives here now; that is, he is asserting a relation between two world-points such that a light-pulse, emitted by one, arrives at the other; or in geometrical language, between two world-points which lie on the same null geodesic. The spatial distance of two material particles in a general Riemannian space-time may, then, be thought of as a relation between two world-points which are on the same null geodesic . It is obviously right that “spatial distance” should exist only between two world-points which are on the same null geodesic; for it is only then that the particles at these points are in direct physical relation with each other. This statement brings out into sharp relief the contrast between “spatial distance” and the “interval” defined by ds 2 = ∑ p, q g pq dx p dx q ; for between two points on the same null geodesic the “interval” is always zero. Thus “ spatial distance ” exists when, and only when, the “interval” is zero.

scholarly journals New Paradigms of Understanding a Child, Quality of Childhood and Childhood Institutionalization

2018 ◽  
Vol 64 (1) ◽  
pp. 11-18
Author(s):  
Anka Jurčević Lozančić
Keyword(s):  
Space Time ◽  
Decisive Factor ◽  
Active Participant ◽  
Child Quality ◽  
Ethical Identity ◽  
The World ◽  
The Future ◽  
The Status ◽  
Preparatory Stage

According to the contemporary understanding, a child is an integral being, an active participant in his/her own education, a curious and competent being with diverse interests, capabilities, knowledge and understanding, and a person who, driven by an innate curiosity, explores the world surrounding him/her, and actively acquires knowledge. These new paradigms have influenced the revision of understanding a child and his/her childhood, which is not only a preparatory stage for the future, but the period of life that has its own values and culture. Childhood is a process that is contextualized, always in relation to a specific space, time and culture, and varies according to different conditions and cultures in which it occurs. And it is the status of a child, conceived by adults, that is reflected in the overall education of the child, thus becoming a decisive factor in determining his/her social and ethical identity. This paper discusses the basic attitudes relating to a child and his/her childhood, upbringing, development and education within family and institutional surroundings.

scholarly journals Non-Hermitian Dirac Hamiltonian in Three-Dimensional Gravity and Pseudosupersymmetry

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Özlem Yeşiltaş
Keyword(s):  
Dirac Equation ◽  
Three Dimensional ◽  
Space Time ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
De Sitter ◽  
Metric Tensor ◽  
Curved Space ◽  
Dimensional Gravity ◽  
Dirac Hamiltonian

The Dirac Hamiltonian in the(2+1)-dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is two spheres. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudosupersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is generated. Usingη-pseudo-Hermiticity, the intertwining operator connecting the non-Hermitian Hamiltonians to the Hermitian counterparts is found. We have obtained a new metric tensor related to the new Hamiltonian.

8. Temporality, transcendence, and freedom

2019 ◽  
pp. 85-95
Author(s):  
Michael Inwood
Keyword(s):  
Space Time ◽  
Hostile Environment ◽  
Time And Space ◽  
The Past ◽  
The World ◽  
The Future ◽  
Sense Of Time

‘Temporality, transcendence, and freedom’ considers Dasein’s place within time and space. Time is a result of Dasein striving to impose order and significance on an apparently hostile environment. The past informs the opportunities to be found in the present and the future. As such, time makes living in the world possible. Dasein’s sense of time allows it to transcend the world and transcend temporality by actualizing its own purposes and constructing its own encounters. This ability to view the entities as possibilities rather than sheer actualities relies on the freedom that Dasein has. Thus, Dasein asks for the grounds of things because ‘to exist is already to philosophize’.

scholarly journals Points of intersection of space-time planes of the “foreign world” in epistolary prose of the English romanticists

Litera ◽  
2021 ◽  
pp. 64-79
Author(s):  
Natal'ya Viktorovna Dominenko ◽  
Yuliya Yur'evna Kravinskaya
Keyword(s):  
Literary Criticism ◽  
Traffic Accident ◽  
Space Time ◽  
Future Research ◽  
The Road ◽  
Access Code ◽  
The World ◽  
The Future ◽  
General Scientific ◽  
The Subject

The subject of this research is the points of intersection of space-time relations of the “foreign world” in such form of authorial self-expression as correspondence of the English romanticists. The goal is to examine the key elements of the chronotope of “foreign world”, and determine the peculiarities of their functionality in the romantic epistolary prose. The object of this research is the 50 letters of W. Wordsworth, 224 letters of G. G. Byron, 67 letters of P. B. Shelley, 51 letters of J. Keats, and 200 letters of R. Southey. The article employs a set of general scientific and special literary criticism methods, such as descriptive, biographical, historical-genetic, historical-functional, structural-semantic, and comparative-typological. It is established that the “foreign world” in the correspondence of English romanticists is represented by the following points of intersection of space-time planes: chronotope of the road / road meetup / traffic accident; contact / meetup / date; cities / countries / villages, with the dominant motifs of the road and contact. Leaning on the analysis of space-time plane of the “foreign world” in the correspondence of English romanticists, the conclusion is made that the chronotope of “foreign world” is a certain access code to the world pattern of English romanticists, the key category that resembles the worldview of a particular epoch, namely romanticism. The scientific novelty lies in the fact that this work is first to analyze space-time relations of “foreign world” in the correspondence of English romanticists. The future research should focus on the types and peculiarities of functionality of the chronotope of “native world” in the correspondence of English romanticists, as well as the interaction of space and time in the correspondence of English realist writers, determining and comparing the integral and variable traits characteristic to epistolary prose as a whole.

Visual space is not cognitively impenetrable

1999 ◽  
Vol 22 (3) ◽  
pp. 366-367
Author(s):  
Yiannis Aloimonos ◽  
Cornelia Fermüller
Keyword(s):  
Visual Perception ◽  
Vision System ◽  
Visual Space ◽  
Space Time ◽  
Computational Vision ◽  
Objective Reality ◽  
Curved Space ◽  
The World

Cognitive impenetrability (CI) of a large part of visual perception is taken for granted by those of us in the field of computational vision who attempt to recover descriptions of space using geometry and statistics as tools. These tools clearly point out, however, that CI cannot extend to the level of structured descriptions of object surfaces, as Pylyshyn suggests. The reason is that visual space – the description of the world inside our heads – is a nonEuclidean curved space. As a consequence, the only alternative for a vision system is to develop several descriptions of space–time; these are representations of reduced intricacy and capture partial aspects of objective reality. As such, they make sense in the context of a class of tasks/actions/plans/purposes, and thus cannot be cognitively impenetrable.

Spinorielle Feldtheorien und Noether-Theorem in der gekrümmten Raum-Zeit

1964 ◽  
Vol 19 (9) ◽  
pp. 1027-1031 ◽  
Author(s):  
Ernst Schmutzer
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Space Time ◽  
Point Of View ◽  
Coordinate Transformations ◽  
Noether Theorem ◽  
Metric Tensor ◽  
Curved Space ◽  
Spinor Fields ◽  
Tensor Expression

On the basis of a curved space-time with RIEMANNEAN geometry the conception of spinors is analyzed. It is shown that a consequent treatment of spinors as invariants with respect to coordinate transformations (SOMMERFELD’S first point of view) gives the well known energy-momentum-tensor and the correct spin integral. For this purpose it is necessary to develop NOETHER’S theorem in such a way that not the metric tensor gmn but the metric spintensor is the fundamental metrical quantity. This fact is the cause that the BELINFANTE tensor expression cannot be applied. A new tensor expression for spinor fields is derived. In this connection DIRAC’S theory and HEISENBERG’S theory are investigated.

Becoming Politicized

2017 ◽  
Vol 225 (4) ◽  
pp. 324-335 ◽  
Author(s):  
Dimitrios Barkas ◽  
Xenia Chryssochoou
Keyword(s):  
Collective Identity ◽  
Political Socialization ◽  
Greek Society ◽  
Economic Vulnerability ◽  
The World ◽  
The Future ◽  
Identity Model ◽  
Beliefs About The Future ◽  
Of Greece ◽  
The Way

Abstract. This research took place just after the end of the protests following the killing of a 16-year-old boy by a policeman in Greece in December 2008. Participants (N = 224) were 16-year-olds in different schools in Attiki. Informed by the Politicized Collective Identity Model ( Simon & Klandermans, 2001 ), a questionnaire measuring grievances, adversarial attributions, emotions, vulnerability, identifications with students and activists, and questions about justice and Greek society in the future, as well as about youngsters’ participation in different actions, was completed. Four profiles of the participants emerged from a cluster analysis using representations of the conflict, emotions, and identifications with activists and students. These profiles differed on beliefs about the future of Greece, participants’ economic vulnerability, and forms of participation. Importantly, the clusters corresponded to students from schools of different socioeconomic areas. The results indicate that the way young people interpret the events and the context, their levels of identification, and the way they represent society are important factors of their political socialization that impacts on their forms of participation. Political socialization seems to be related to youngsters’ position in society which probably constitutes an important anchoring point of their interpretation of the world.

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