Potential

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Gravitational Potential ◽  
Gravitational Redshift ◽  
Gravitational Acceleration ◽  
Distant Observer ◽  
Spacetime Metric ◽  
Theory Of Gravity

At any given event gravity accelerates all particles equally—yet gravity is very strong in some places and very weak in others. In this chapter, we learn a powerful thinking tool to help us deal with these variations: the gravitational potential. The potential takes the concept of “acceleration times height” that, we previously found, determines the march of time and generalizes it to cases where the gravitational acceleration varies with position. The potential encodes global relationships, such as the gravitational redshift of light emitted from one point and received by a distant observer, as well as the local acceleration at each point.We also showhow the spacetime metric is affected by the potential. Incorporating the potential into themetric neatly unites gravity with relativity and eliminates any need for a theory of gravity involving forces.

The Equivalence Principle

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Time Dilation ◽  
Gravitational Redshift ◽  
Coordinate Systems ◽  
Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

An improved approach for testing gravitational redshift via spacecraft based three frequency links combination

2021 ◽  
Author(s):  
Ziyu Shen ◽  
Wen-Bin Shen ◽  
Lin He ◽  
Tengxu Zhang ◽  
Zhan Cai
Keyword(s):  
International Space Station ◽  
Gravitational Potential ◽  
Natural Science ◽  
Space Station ◽  
Gravitational Redshift ◽  
New Approach ◽  
International Space ◽  
Hardware Requirement ◽  
Ground Station ◽  
Gravity Probe

<p>We propose a new approach for testing the gravitational redshift based on frequency signals transmission between a spacecraft and a ground station. By a combination of one uplink signal and two downlink signals, the gravitational redshift can be tested at about 6.5×10<sup>-6</sup> level for a GNSS satellite (the signals’ frequencies are about 1.2~1.6 GHz), and about 2.2×10<sup>-6</sup> level for the International Space Station (the signals’ frequencies are up to 14.7 GHz), under the assumption that the clock accuracy is about 10<sup>-17</sup> level. For better desinged cases the accuracy of gravitational redshift test can be improved to several parts in 10<sup>-8</sup> level (the signals’ frequencies are about 8~12 GHz). Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in1976, the new approach does not require any onboard signal transponders, and the frequency values of the three links can be quite arbitrarily given. As the hardware requirement is reduced, a number of spacecrafts could be chosen as candidates for a gravitational redshift experiment. This approach could also be used in gravitational potential determination, which has prospective applications in geodesy. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 42030105, 41721003, 41631072, 41874023, 41804012), Space Station Project (2020)228, and Natural Science Foundation of Hubei Province(grant No. 2019CFB611).</p>

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

scholarly journals Constraints on scalar–tensor theory of gravity by solar system tests

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
P. A. González ◽  
Marco Olivares ◽  
Eleftherios Papantonopoulos ◽  
Yerko Vásquez
Keyword(s):  
Time Delay ◽  
Scalar Field ◽  
Solar System ◽  
Gravitational Redshift ◽  
Scalar Tensor Theory ◽  
Einstein Tensor ◽  
Perihelion Precession ◽  
Deflection Of Light ◽  
Tensor Theory ◽  
Theory Of Gravity

AbstractWe study the motion of particles in the background of a scalar–tensor theory of gravity in which the scalar field is kinetically coupled to the Einstein tensor. We constrain the value of the derivative parameter z through solar system tests. By considering the perihelion precession we obtain the constraint $$\sqrt{z}/m_{\mathrm{p}} > 2.6\times 10^{12}$$ z / m p > 2.6 × 10 12  m, the gravitational redshift $$\frac{\sqrt{z}}{m_{\mathrm{p}}}>2.7\times 10^{\,10}$$ z m p > 2.7 × 10 10  m, the deflection of light $$\sqrt{z}/m_{\mathrm{p}} > 1.6 \times 10^{11}$$ z / m p > 1.6 × 10 11  m, and the gravitational time delay $$\sqrt{z}/m_{\mathrm{p}} > 7.9 \times 10^{12}$$ z / m p > 7.9 × 10 12  m; thereby, our results show that it is possible to constrain the value of the z parameter in agreement with the observational tests that have been considered.

scholarly journals New traversable wormhole solutions in f(T) gravity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950065 ◽  
Author(s):  
R. C. Tefo ◽  
P. H. Logbo ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Time Dependence ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Traversable Wormhole ◽  
Torsion Scalar ◽  
Teleparallel Theory ◽  
Text Model ◽  
Spacetime Metric ◽  
Theory Of Gravity ◽  
Modified Formula

In this paper, we search for dynamical traversable wormhole solutions in the modified [Formula: see text] theory of gravity, [Formula: see text] being the torsion scalar. For such a wormhole, the time dependence is inserted in the static traversable wormhole metric of Morris and Thorne. Two set of tetrads are adopted: the diagonal and the nondiagonal tetrads. The diagonal set of tetrads constrains and reduces [Formula: see text] model to teleparallel theory where usual solutions have been found. With diagonal set of tetrads, free from the teleparallel theory constraint, our results show that the existence of traversable wormhole is possible only for nondynamical spacetime metric, i.e. static traversable wormhole solutions. Moreover we take into account energy condition analysis and the results show that the violation of null energy condition is not determinant for existence of static traversable wormhole solutions.

scholarly journals Vacuum persistence amplitude and gravitational potential in f(R) gravity

2018 ◽  
Vol 33 (21) ◽  
pp. 1850117
Author(s):  
A. Jahan ◽  
S. Heydarnezhad
Keyword(s):  
Gravitational Potential ◽  
Transition Amplitude ◽  
Einstein Theory ◽  
Source Theory ◽  
Theory Of Gravity ◽  
Static Point

The source theory provides a straightforward way to obtain the Newton’s potential upon establishing the vacuum-to-vacuum transition amplitude in quantized Einstein theory of gravity. Here, we use the same method to derive the gravitational potential of two static point masses in f(R) = R + aR2 gravity.

Tesseroids: Forward-modeling gravitational fields in spherical coordinates

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. F41-F48 ◽  
Author(s):  
Leonardo Uieda ◽  
Valéria C. F. Barbosa ◽  
Carla Braitenberg
Keyword(s):  
Gravitational Potential ◽  
Computation Time ◽  
Forward Modeling ◽  
Gravity Gradient ◽  
Maximum Relative Error ◽  
Gravitational Acceleration ◽  
Spherical Coordinates ◽  
Gravity Gradients ◽  
Gravitational Fields ◽  
Adaptive Discretization

We have developed the open-source software Tesseroids, a set of command-line programs to perform forward modeling of gravitational fields in spherical coordinates. The software is implemented in the C programming language and uses tesseroids (spherical prisms) for the discretization of the subsurface mass distribution. The gravitational fields of tesseroids are calculated numerically using the Gauss-Legendre quadrature (GLQ). We have improved upon an adaptive discretization algorithm to guarantee the accuracy of the GLQ integration. Our implementation of adaptive discretization uses a “stack-based” algorithm instead of recursion to achieve more control over execution errors and corner cases. The algorithm is controlled by a scalar value called the distance-size ratio ([Formula: see text]) that determines the accuracy of the integration as well as the computation time. We have determined optimal values of [Formula: see text] for the gravitational potential, gravitational acceleration, and gravity gradient tensor by comparing the computed tesseroids effects with those of a homogenous spherical shell. The values required for a maximum relative error of 0.1% of the shell effects are [Formula: see text] for the gravitational potential, [Formula: see text] for the gravitational acceleration, and [Formula: see text] for the gravity gradients. Contrary to previous assumptions, our results show that the potential and its first and second derivatives require different values of [Formula: see text] to achieve the same accuracy. These values were incorporated as defaults in the software.

THE CLOCK MISSION OPTIS

2007 ◽  
Vol 16 (12b) ◽  
pp. 2499-2510 ◽  
Author(s):  
HANSJÖRG DITTUS ◽  
CLAUS LÄMMERZAHL
Keyword(s):  
Gravitational Potential ◽  
Doppler Effect ◽  
Light Propagation ◽  
Gravitational Redshift ◽  
Speed Of Light ◽  
Fundamental Physics ◽  
Fundamental Structure ◽  
Perihelion Advance ◽  
The Doppler Effect ◽  
Matter Sector

Clocks are an almost universal tool for exploring the fundamental structure of theories related to relativity. For future clock experiments, it is important for them to be performed in space. One mission which has the capability to perform and improve all relativity tests based on clocks by several orders of magnitude is OPTIS. These tests consist of (i) tests of the isotropy of light propagation (from which information about the matter sector which the optical resonators are made of can also be drawn), (ii) tests of the constancy of the speed of light, (iii) tests of the universality of the gravitational redshift by comparing clocks based on light propagation, like light clocks and various atomic clocks, (iv) time dilation based on the Doppler effect, (v) measuring the absolute gravitational redshift, (vi) measuring the perihelion advance of the satellite's orbit by using very precise tracking techniques, (vii) measuring the Lense–Thirring effect, and (viii) testing Newton's gravitational potential law on the scale of Earth-bound satellites. The corresponding tests are not only important for fundamental physics but also indispensable for practical purposes like navigation, Earth sciences, metrology, etc.

scholarly journals Observational constraints in metric-affine gravity

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Sebastian Bahamonde ◽  
Jorge Gigante Valcarcel
Keyword(s):  
Gauge Theory ◽  
White Dwarf ◽  
Vacuum Solution ◽  
Gravitational Redshift ◽  
Observational Constraints ◽  
Perihelion Precession ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Affine Gravity

AbstractWe derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.

scholarly journals Forecasting cosmological bias due to local gravitational redshift

2019 ◽  
Vol 28 (12) ◽  
pp. 1950150
Author(s):  
Haoting Xu ◽  
Zhiqi Huang ◽  
Na Zhang ◽  
Yundong Jiang
Keyword(s):  
Cosmic Microwave Background ◽  
Survey Data ◽  
Gravitational Potential ◽  
Cosmological Parameters ◽  
Gravitational Redshift ◽  
Microwave Background ◽  
Cosmological Distance ◽  
Distant Galaxies ◽  
Redshift Survey ◽  
Pass Through

When photons from distant galaxies and stars pass through our neighboring environment, the wavelengths of the photons would be shifted by our local gravitational potential. This local gravitational redshift effect can potentially have an impact on the measurement of cosmological distance–redshift relation. Using available supernovae data, Wojtak, Davis and Wiis [J. Cosmol. Astropart. Phys. 2015 (2015) 025] found seemingly large biases of cosmological parameters for some extended models (nonflat [Formula: see text]CDM, [Formula: see text]CDM, etc.). Huang [Phys. Rev. D 91 (2015) 121301] pointed out that, however, the biases can be reduced to a negligible level if cosmic microwave background (CMB) data are added to break the strong degeneracy between parameters in the extended models. In this paper, we forecast the cosmological bias due to local gravitational redshifts for a future WFIRST-like supernovae survey. We find that the local gravitational redshift effect remains negligible, provided that CMB data or some future redshift survey data are added to break the degeneracy between parameters.

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