Gravitational “Doppler Boosting / De-boosting” Effect within the Framework of General Relativity

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Mark Zilberman ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Special Relativity ◽  
Spectral Index ◽  
Equivalence Principle ◽  
Relativistic Effect ◽  
Gravitational Redshift ◽  
Astronomical Observations ◽  
Complete Set ◽  
Einstein's Equivalence Principle

The “Doppler boosting / de-boosting” relativistic effect increases / decreases the apparent luminosity of approaching / receding sources of radiation. This effect was analyzed in detail within the Special Relativity framework and was confirmed in many astronomical observations. It is however not clear if “Doppler boosting / de-boosting” exists in the framework of General Relativity as well, and if it exists, which equations describe it. The “Einstein’s elevator” and Einstein’s “Equivalence principle” allow to obtain the formula for “Doppler boosting / de-boosting” for a uniform gravitational field within the vicinity of the emitter/receiver. Under these simplified conditions, the ratio ℳ between apparent (L) and intrinsic (Lo) luminosity can be conveniently represented using source’s spectral index α and gravitational redshift z as ℳ(z, α) ≡ L/Lo=(z+1)^(α-3). This is the first step towards the complete set of equations that describe the gravitational "Doppler boosting / de-boosting" effect within the General Relativity framework including radial gravitational field and arbitrary values of distance h between emitter and receiver.

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.

scholarly journals Shouldn’t Doppler 'De-boosting' be accounted for in calculations of intrinsic luminosity of Standard Candles?

2021 ◽  
Author(s):  
Mark Zilberman
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Spectral Index ◽  
Binary Systems ◽  
Relativistic Effect ◽  
Light Sources ◽  
Relativistic Jets ◽  
Radiation Sources ◽  
Standard Candle ◽  
Type Ia

"Doppler boosting / de-boosting" is a well-known relativistic effect that alters the apparent luminosity of approaching/receding radiation sources. "Doppler boosting" alters the apparent luminosity of approaching light sources to appear brighter, while "Doppler de-boosting" alters the apparent luminosity of receding light sources to appear fainter. While "Doppler boosting / de-boosting" has been successfully accounted for and observed in relativistic jets of AGN, double white dwarfs, in search of exoplanets and stars in binary systems it was ignored in the establishment of Standard Candles for cosmological distances. A Standard Candle adjustment appears necessary for "Doppler de-boosting" for high Z, otherwise we would incorrectly assume that Standard Candles appear dimmer, not because of "Doppler de-boosting" but because of the excessive distance, which would affect the entire Standard Candles ladder at cosmological distances. The ratio between apparent (L) and intrinsic (Lo) luminosities as a function of redshift Z and spectral index α is given by the formula ℳ(Z) = L/Lo=(Z+1)^(α-3) and for Type Ia supernova as ℳ(Z) = L/Lo=(Z+1)^(-2). These formulas are obtained within the framework of Special Relativity and may require adjustments within the General Relativity framework.

NEW TESTS OF THE GRAVITATIONAL REDSHIFT EFFECT

1990 ◽  
Vol 05 (23) ◽  
pp. 1809-1813 ◽  
Author(s):  
TIMOTHY P. KRISHER
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equivalence Principle ◽  
Total Mass ◽  
Good Accuracy ◽  
Gravitational Redshift ◽  
Outer Planets ◽  
The Earth ◽  
Detailed Composition ◽  
Future Status

Tests of the gravitational redshift effect provide a way to check the validity of the Einstein Equivalence Principle (EEP) and, more specifically, of general relativity. If the EEP is valid, then the redshift should be the same for different clocks. Also, according to general relativity, the redshift should depend upon only the total mass of a gravitating body without reference to its detailed composition. These predictions have been tested mainly in the gravitational field of the Earth. It is now possible to measure, with space probes, the redshift effect to good accuracy in the vicinity of other bodies in the solar system, in particular at the massive outer planets. The present and future status of these experiments is discussed.

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 Gravitational Redshifts and the Mass-Radius Relation

1989 ◽  
Vol 114 ◽  
pp. 401-407
Author(s):  
Gary Wegner
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Solar System ◽  
White Dwarf ◽  
Sufficient Accuracy ◽  
Gravitational Redshift ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Tests Of General Relativity ◽  
Gravitational Field Equations

The gravitational redshift is one of Einstein’s three original tests of General Relativity and derives from time’s slowing near a massive body. For velocities well below c, this is represented with sufficient accuracy by:As detailed by Will (1981), Schiff’s conjecture argues that the gravitational redshift actually tests the principle of equivalence rather than the gravitational field equations. For low redshifts, solar system tests give highest accuracy. LoPresto & Pierce (1986) have shown that the redshift at the Sun’s limb is good to about ±3%. Rocket experiments produce an accuracy of ±0.02% (Vessot et al. 1980), while for 40 Eri B the best white dwarf, the observed and predicted VRS agree to only about ±_5% (Wegner 1980).

scholarly journals The Uniformly Accelerated Frame as a Test Bed for Analysing the Gravitational Redshift

Universe ◽  
2020 ◽  
Vol 7 (1) ◽  
pp. 4
Author(s):  
Don Koks
Keyword(s):  
Gravitational Field ◽  
Special Relativity ◽  
Proper Time ◽  
Gravitational Redshift ◽  
Test Bed ◽  
Curved Spacetime ◽  
Coordinate Time ◽  
Flat Spacetime ◽  
Spacetime Curvature ◽  
Shed Light

Ever since Eddington’s analysis of the gravitational redshift a century ago, and the arguments in the relativity community that it produced, fine details of the roles of proper time and coordinate time in the redshift remain somewhat obscure. We shed light on these roles by appealing to the physics of the uniformly accelerated frame, in which coordinate time and proper time are well defined and easy to understand; and because that frame exists in flat spacetime, special relativity is sufficient to analyse it. We conclude that Eddington’s analysis was indeed correct—as was the 1980 analysis of his detractors, Earman and Glymour, who (it turns out) were following a different route. We also use the uniformly accelerated frame to pronounce invalid Schild’s old argument for spacetime curvature, which has been reproduced by many authors as a pedagogical introduction to curved spacetime. More generally, because the uniformly accelerated frame simulates a gravitational field, it can play a strong role in discussions of proper and coordinate times in advanced relativity.

scholarly journals RADIATION FROM A UNIFORMLY ACCELERATED CHARGE IN THE OUTSKIRTS OF A WORMHOLE THROAT

2000 ◽  
Vol 15 (36) ◽  
pp. 2219-2228 ◽  
Author(s):  
LUIS A. ANCHORDOQUI ◽  
S. CAPOZZIELLO ◽  
G. LAMBIASE ◽  
DIEGO F. TORRES
Keyword(s):  
General Relativity ◽  
Refractive Index ◽  
Gravitational Field ◽  
Equivalence Principle ◽  
Ricci Tensor ◽  
Energy Condition ◽  
Theoretical Background ◽  
Traversable Wormholes ◽  
Spatial Part ◽  
Accelerated Charge

Using traversable wormholes as theoretical background, we revisit a deep question of general relativity: Does a uniformly accelerated charged particle radiate? We particularize to the recently proposed gravitational Čerenkov radiation, that happens when the spatial part of the Ricci tensor is negative. If (3+1)Rii<0 the matter threading the gravitational field violates the weak energy condition. In this case, the effective refractive index for light is larger than 1, i.e. particles propagate faster than photons in that medium. This leads to a violation of the equivalence principle.

scholarly journals A fundamental special-relativistic theory valid for all real-valued speeds

1984 ◽  
Vol 7 (3) ◽  
pp. 565-589
Author(s):  
Vedprakash Sewjathan
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relativistic Theory ◽  
Equivalence Principle ◽  
Rest Mass ◽  
Space Time ◽  
Twin Paradox ◽  
Relativistic Factor ◽  
Time Frames ◽  
Time Transformations

This paper constitutes a fundamental rederivation of special relativity based on thec-invariance postulate but independent of the assumptionds′2=±ds2(Einstein [1], Kittel et al [2], Recami [3]), the equivalence principle, homogeneity of space-time, isotropy of space, group properties and linearity of space-time transformations or the coincidence of the origins of inertial space-time frames. The mathematical formalism is simpler than Einstein's [4] and Recami's [3]. Whilst Einstein's subluminal and Recami's superluminal theories are rederived in this paper by further assuming the equivalence principle and “mathematical inverses” [4,3], this paper derives (independent of these assumptions) with physico-mathematical motivation an alternate singularity-free special-relativistic theory which replaces Einstein's factor[1/(1−V2/c2)]12and Recami's extended-relativistic factor[1/(V2/c2−1)]12by[(1−(V2/c2)n)/(1−V2/c2)]12, wherenequals the value of(m(V)/m0)2as|V|→c. In this theory both Newton's and Einstein's subluminal theories are experimentally valid on account of negligible terms. This theory implies that non-zero rest mass luxons will not be detected as ordinary non-zero rest mass bradyons because of spatial collapse, and non-zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.

scholarly journals TORSION GRAVITY: A REAPPRAISAL

2004 ◽  
Vol 13 (10) ◽  
pp. 2193-2240 ◽  
Author(s):  
H. I. ARCOS ◽  
J. G. PEREIRA
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equivalence Principle ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Point Of View ◽  
Affine Groups ◽  
Conceptual Question ◽  
Curvature And Torsion ◽  
Strong Equivalence Principle

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein–Cartan and gauge theories for the Poincaré and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution ultimately favors the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.

THE CONFRONTATION BETWEEN GENERAL RELATIVITY AND EXPERIMENT: A 1992 UPDATE

1992 ◽  
Vol 01 (01) ◽  
pp. 13-68 ◽  
Author(s):  
CLIFFORD M. WILL
Keyword(s):  
General Relativity ◽  
Equivalence Principle ◽  
Experimental Tests ◽  
Advanced Technology ◽  
Theoretical Frameworks ◽  
Binary Pulsar ◽  
Tests Of General Relativity ◽  
Lunar Motion ◽  
The Status ◽  
Einstein's Equivalence Principle

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein’s equivalence principle is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Tests of general relativity have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected to half a percent using the binary pulsar, and new binary pulsar systems promise further improvements. The status of the “fifth force” is discussed, along with the frontiers of experimental relativity, including proposals for testing relativistic gravity with advanced technology and spacecraft.

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