scholarly journals Expansion of Rindler Coordinate Theory and Light’s Doppler Effect

2021 ◽  
Author(s):  
Sangwha Yi

In the general theory of relativity the Rindler coordinate theory has been extended to the Rindler coordinate theory of accelerated observer that has already some initial velocity. In this paper, we present this extended theory that uses the tetrad as the new method, and discover the new inverse-coordinate transformation. Specially, if, a0 < 0 , this theory treats the observer with the initial velocity that does slowdown by the constant negative acceleration in the Rindler’s time-space. We consider the light’s Doppler Effect in the accelerated system as well as the decelerated system.

2015 ◽  
Vol 24 (06) ◽  
pp. 1550039 ◽  
Author(s):  
Slava G. Turyshev ◽  
Viktor T. Toth

We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical N-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using an arbitrary energy–momentum tensor and assumed to possess any number of internal multipole moments. The solution of the gravitational field equations in any reference frame is presented as a sum of three terms: (i) The inertial flat spacetime in that frame, (ii) unperturbed solutions for each body in the system that is covariantly transformed to the coordinates of this frame and (iii) the gravitational interaction term. We use the harmonic gauge conditions that allow reconstruction of a significant part of the structure of the post-Galilean coordinate transformation functions relating global coordinates of the inertial reference frame to the local coordinates of the noninertial frame associated with a particular body. The remaining parts of these functions are determined from dynamical conditions, obtained by constructing the relativistic proper reference frame associated with a particular body. In this frame, the effect of external forces acting on the body is balanced by the fictitious frame-reaction force that is needed to keep the body at rest with respect to the frame, conserving its relativistic three-momentum. We find that this is sufficient to determine explicitly all the terms of the coordinate transformation. The same method is then used to develop the inverse transformations. The resulting post-Galilean coordinate transformations have an approximate group structure that extends the Poincaré group of global transformations to the case of accelerating observers in a gravitational field of N-body system. We present and discuss the structure of the metric tensors corresponding to the reference frames involved, the rules for transforming relativistic gravitational potentials, the coordinate transformations between frames and the resulting relativistic equations of motion.


1988 ◽  
Vol 155 (7) ◽  
pp. 517-527 ◽  
Author(s):  
Ya.B. Zel'dovich ◽  
Leonid P. Grishchuk

2019 ◽  
Author(s):  
Vitaly Kuyukov

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.


Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Lorenzo Iorio

Recently, the secular pericentre precession was analytically computed to the second post-Newtonian (2PN) order by the present author with the Gauss equations in terms of the osculating Keplerian orbital elements in order to obtain closer contact with the observations in astronomical and astrophysical scenarios of potential interest. A discrepancy in previous results from other authors was found. Moreover, some of such findings by the same authors were deemed as mutually inconsistent. In this paper, it is demonstrated that, in fact, some calculation errors plagued the most recent calculations by the present author. They are explicitly disclosed and corrected. As a result, all of the examined approaches mutually agree, yielding the same analytical expression for the total 2PN pericentre precession once the appropriate conversions from the adopted parameterisations are made. It is also shown that, in the future, it may become measurable, at least in principle, for some of the recently discovered short-period S-stars in Sgr A*, such as S62 and S4714.


1973 ◽  
Vol 17 (1) ◽  
pp. 122-128 ◽  
Author(s):  
V. A. Wynne ◽  
G. H. Derrick

2021 ◽  
Vol 58 (4) ◽  
pp. 175-195
Author(s):  
Vladimir P. Vizgin ◽  

The article is based on the concepts of epistemic virtues and epistemic vices and explores A. Einstein’s contribution to the creation of fundamental physical theories, namely the special theory of relativity and general theory of relativity, as well as to the development of a unified field theory on the basis of the geometric field program, which never led to success. Among the main epistemic virtues that led Einstein to success in the construction of the special theory of relativity are the following: a unique physical intuition based on the method of thought experiment and the need for an experimental justification of space-time concepts; striving for simplicity and elegance of theory; scientific courage, rebelliousness, signifying the readiness to engage in confrontation with scientific conventional dogmas and authorities. In the creation of general theory of relativity, another intellectual virtue was added to these virtues: the belief in the heuristic power of the mathematical aspect of physics. At the same time, he had to overcome his initial underestimation of the H. Minkowski’s four-dimensional concept of space and time, which has manifested in a distinctive flexibility of thinking typical for Einstein in his early years. The creative role of Einstein’s mistakes on the way to general relativity was emphasized. These mistakes were mostly related to the difficulties of harmonizing the mathematical and physical aspects of theory, less so to epistemic vices. The ambivalence of the concept of epistemic virtues, which can be transformed into epistemic vices, is noted. This transformation happened in the second half of Einstein’s life, when he for more than thirty years unsuccessfully tried to build a unified geometric field theory and to find an alternative to quantum mechanics with their probabilistic and Copenhagen interpretation In this case, we can talk about the following epistemic vices: the revaluation of mathematical aspect and underestimation of experimentally – empirical aspect of the theory; adopting the concepts general relativity is based on (continualism, classical causality, geometric nature of fundamental interactions) as fundamental; unprecedented persistence in defending the GFP (geometrical field program), despite its failures, and a certain loss of the flexibility of thinking. A cosmological history that is associated both with the application of GTR (general theory of relativity) to the structure of the Universe, and with the missed possibility of discovering the theory of the expanding Universe is intermediate in relation to Einstein’s epistemic virtues and vices. This opportunity was realized by A.A. Friedmann, who defeated Einstein in the dispute about if the Universe was stationary or nonstationary. In this dispute some of Einstein’s vices were revealed, which Friedman did not have. The connection between epistemic virtues and the methodological principles of physics and also with the “fallibilist” concept of scientific knowledge development has been noted.


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