scholarly journals The Relation between General Relativity’s Metrics and Special Relativity’s Gravitational Scalar Generalized Potentials and Case Studies on the Schwarzschild Metric, Teleparallel Gravity, and Newtonian Potential

Particles ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 536-576
Author(s):  
Spyridon Vossos ◽  
Elias Vossos ◽  
Christos G. Massouros
Keyword(s):  
Teleparallel Gravity ◽  
Riemannian Metric ◽  
Time Dilation ◽  
Red Shift ◽  
Newtonian Potential ◽  
Schwarzschild Metric ◽  
Gravitational Fields ◽  
Generalized Potential ◽  
Gravitational Deflection Of Light

This paper shows that gravitational results of general relativity (GR) can be reached by using special relativity (SR) via a SR Lagrangian that derives from the corresponding GR time dilation and vice versa. It also presents a new SR gravitational central scalar generalized potential V=V(r,r.,ϕ.), where r is the distance from the center of gravity and r.,ϕ. are the radial and angular velocity, respectively. This is associated with the Schwarzschild GR time dilation from where a SR scalar generalized potential is obtained, which is exactly equivalent to the Schwarzschild metric. Thus, the Precession of Mercury’s Perihelion, the Gravitational Deflection of Light, the Shapiro time delay, the Gravitational Red Shift, etc., are explained with the use of SR only. The techniques used in this paper can be applied to any GR spacetime metric, Teleparallel Gravity, etc., in order to obtain the corresponding SR gravitational scalar generalized potential and vice versa. Thus, the case study of Newtonian Gravitational Potential according to SR leads to the corresponding non-Riemannian metric of GR. Finally, it is shown that the mainstream consideration of the Gravitational Red Shift contains two approximations, which are valid in weak gravitational fields only.

scholarly journals Quantum interference in external gravitational fields beyond General Relativity

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Luca Buoninfante ◽  
Gaetano Lambiase ◽  
Luciano Petruzziello
Keyword(s):  
General Relativity ◽  
Quantum Interference ◽  
Relativistic Effects ◽  
Newtonian Potential ◽  
Alternative Theories Of Gravity ◽  
Gravitational Fields ◽  
Decoherence Rate ◽  
Relativistic Regime ◽  
Theories Of Gravity ◽  
To Come

AbstractIn this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.

scholarly journals Is the expansion of universe accelerating or the Photons decelerating?

2015 ◽  
Vol 3 (1) ◽  
pp. 40
Author(s):  
Hasmukh Tank
Keyword(s):  
Big Bang ◽  
Time Dilation ◽  
Red Shift ◽  
Light Curves ◽  
Accelerated Expansion ◽  
Gravitational Acceleration ◽  
Expansion Of The Universe ◽  
Pi Mesons ◽  
The Big Bang ◽  
The Universe

<p>Astronomical observations of the cosmological red-shift are currently interpreted in terms of ‘expansion of universe’ and ‘accelerated-expansion of the universe’, at the rate of <em>H<sub>0</sub> c</em>; here <em>H<sub>0</sub></em> is Hubble’s constant, and c is the speed of light. Whereas a straight-forward derivation presented here suggests that: rather it is the photon which is decelerating, at the rate of <em>H<sub>0</sub> c</em>. Such a deceleration of photons can be caused by virtual electrons, positrons and pi-mesons, contained in the extra galactic quantum vacuum, because: they do have gravitational-acceleration of the same order as <em>H<sub>0</sub> c</em> at their “surfaces”; or by decay of a photon into a lighter photon and a particle of mass <em>h H<sub>0</sub> / c<sup>2</sup></em>. Tired-light interpretations of the cosmological red-shift’ were so far considered as not compatible with the observations of ‘time-dilation of super-novae light-curves’; so in a paper titled: “Wave-theoretical insight into the relativistic ‘length-contraction’ and ‘time-dilation of super-novae light-curves’” (Tank, Hasmukh K. 2013), it has been already shown that any mechanism which can cause ‘cosmological red-shift’ will also cause ‘time-dilation of super-novae light-curves’.  Therefore, we now need not to remain confined to the Big-Bang model of cosmology.</p>

scholarly journals Generalized potential functions in differential geometry and information geometry

2019 ◽  
Vol 16 (supp01) ◽  
pp. 1940002 ◽  
Author(s):  
F. M. Ciaglia ◽  
G. Marmo ◽  
J. M. Pérez-Pardo
Keyword(s):  
Differential Geometry ◽  
Inverse Problem ◽  
Riemannian Manifold ◽  
Information Geometry ◽  
Riemannian Metric ◽  
Negative Answer ◽  
Potential Functions ◽  
Point Of View ◽  
Geometric Structures ◽  
Generalized Potential

Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

General relativity in terms of a background space

1963 ◽  
Vol 276 (1366) ◽  
pp. 413-417 ◽  
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Test Particle ◽  
Space Time ◽  
Red Shift ◽  
Schwarzschild Metric ◽  
Background Space ◽  
Light Rays ◽  
Theory Of Gravitation

R. d’E. Atkinson has shown that the path of a test particle, the light rays and the gravitational red shift predicted by general relativity for the case of the Schwarzschild metric may all be interpreted in terms of Euclidean space. By introducing the concept of a background space it is shown that Atkinson’s interpretation may be extended for the case of any finite static gravitating system. It is pointed out that the interpretation is applicable to any theory of gravitation in which the path of a test particle and the light rays are geodesics of the space-time metric.

scholarly journals Resonance interaction between two entangled gravitational polarizable objects

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Yongshun Hu ◽  
Jiawei Hu ◽  
Hongwei Yu ◽  
Puxun Wu
Keyword(s):  
Quantum Gravity ◽  
Interaction Energy ◽  
Quadrupole Interaction ◽  
Quantum Correction ◽  
Gravitational Interaction ◽  
Ground States ◽  
Resonance Interaction ◽  
Newtonian Potential ◽  
Entangled State ◽  
Gravitational Fields

Abstract We investigate the resonance quadrupole-quadrupole interaction between two entangled gravitationally polarizable objects induced by a bath of fluctuating quantum gravitational fields in vacuum in the framework of linearized quantum gravity. Our result shows that, the interaction energy behaves as $$r^{-5}$$r-5 in the near regime, and oscillates with a decreasing amplitude proportional to $$r^{-1}$$r-1 in the far regime, where r is the distance between the two objects. Compared to the case when the two objects are in their ground states, the quantum gravitational interaction is significantly enhanced when the objects are in an entangled state. Remarkably, in the far regime, the resonance quantum gravitational interaction can give the dominating quantum correction to the Newtonian potential, since the extremum is much greater than the monopole-monopole quantum gravitational interaction.

scholarly journals The "Dimming Effect" Produced by the Application of Doppler Effect on the Quantity of Photons Arriving to a Receiver and its Implication to Astronomy (ver. 2)

2020 ◽  
Author(s):  
Mark Zilberman
Keyword(s):  
Dark Energy ◽  
Light Source ◽  
Doppler Effect ◽  
Time Dilation ◽  
Red Shift ◽  
Light Sources ◽  
Wave Component ◽  
Shift Parameter ◽  
Low Speed ◽  
The Doppler Effect

This article describes the "Dimming effect" that is produced by the Doppler effect applied to a quantity of individual photons arriving to a receiver from a moving source of light. The corpuscular-wave dualism of light suggests that the well-known Doppler effect, which is currently applied only to the wave component of light, should also be considered for the corpuscular component of light. Application of the Doppler effect on a quantity of photons leads to the "Dimming Effect" - as the faster light source is moving away from observer - the dimmer its brightness appears. While the described dimming effect is negligible for low-speed light sources, it becomes significant for light sources with a velocity comparable to light speed in a vacuum. The relativistic adjustments for time dilation cause the described dimming effect to be even stronger. For example, the "Dimming Effect" for an object moving away from the observer with the speed 0.1c is 0.904 and for an object moving away from the observer with the speed 0.5c is 0.577. Article also provides the formula for the calculation of "Dimming effect" values using the red-shift parameter Z widely used in astronomy as N/N0=1/(Z+1). If confirmed, the "Dimming effect" must be taken into account in calculations of astronomical "Standard Candles" and in particular in the "Supernova Cosmology Project", which has claimed the acceleration of the Universe's expansion and led to the introduction of dark energy.

Gravitational red shift and time delay of radar echo in f(R)-gravity

2016 ◽  
Vol 13 (04) ◽  
pp. 1650051
Author(s):  
Ying Wang ◽  
Feng He
Keyword(s):  
Time Delay ◽  
Experimental Observation ◽  
Space Time ◽  
Red Shift ◽  
Spectral Lines ◽  
Observation Data ◽  
The Sun ◽  
Schwarzschild Metric ◽  
Radar Echo ◽  
Asymptotic Speed

Sobouti proposes an action-based [Formula: see text] modification of Einstein’s gravity, which admits a similar Schwarzschild metric. A test star moving in such a space–time acquires a constant asymptotic speed at large distances. As we are concerned with two classical tests of Einstein’s theory which are gravitational red shift of spectral lines and time delay of radar echo passing the sun, we shall calculate them in the [Formula: see text]-gravity and show that the results are consistent with the experimental observation data.

Systematic approximations in the calculation of gravitational fields

1962 ◽  
Vol 270 (1342) ◽  
pp. 315-326
Keyword(s):  
Differential Equation ◽  
Mass Distribution ◽  
Empty Space ◽  
Residual Energy ◽  
Newtonian Potential ◽  
Energy Tensor ◽  
Systematic Calculation ◽  
Gravitational Fields ◽  
First Approximation

The determination of Newtonian gravitational fields is of trivial simplicity in comparison with corresponding relativistic problems. To find the Newtonian potential we do not have to solve any differential equation; it is given as an integral taken over the instantaneous mass distribution, and any difficulties there may be arise merely in evaluating the integral. In giving the well-known retarded-potential formula, Einstein (1916) took the first step towards the systematic calculation of relativistic gravitational fields. But it is only a first approximation, leaving in what purports to be empty space a residual energy tensor which is uncomfortably large. Further, the usual derivation of the retarded potential formula does not seem to open the way to higher approximations.

scholarly journals THE LUKASH PLANE-WAVE ATTRACTOR AND RELATIVE ENERGY

2007 ◽  
Vol 22 (21) ◽  
pp. 1601-1609
Author(s):  
MURAT KORUNUR ◽  
MUSTAFA SALTI ◽  
OKTAY AYDOGDU
Keyword(s):  
Plane Wave ◽  
Energy Distribution ◽  
Energy Momentum Tensor ◽  
Teleparallel Gravity ◽  
Relative Energy ◽  
Momentum Tensor ◽  
Gravitational Fields ◽  
Teleparallel Theory ◽  
The Universe ◽  
Special Case

We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VIIδ spacetimes described by the Lukash metric. For this calculation, we consider the teleparallel gravity analogs of the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz. We find that Einstein and Bergmann–Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau–Lifshitz complex does not. Energy density turns out to be nonvanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write ω = 1 and Ξ2 = 1 in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz as obtained for the Lukash spacetime. Furthermore, our results support the hypothesis by Cooperstock that the energy is confined to the region of nonvanishing energy–momentum tensor of matter and all non-gravitational fields, and also sustain the importance of the energy–momentum definitions in the evaluation of the energy distribution associated with a given spacetime.

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