Correct light deflection in Weyl conformal gravity

Cattani, Carlo; Scalia, Massimo; Laserra, Ettore; Bochicchio, Ivana; Nandi, K. K.

doi:10.1103/physrevd.87.047503

Cited by 58 publications

(74 citation statements)

References 9 publications

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“…Hence, we can neglect contributions of the gravitational potential and the kinetic energy to the energy-momentum tensor T µν in Eq. (53). In general these approximations do not hold true for binaries consisting of compact objects like neutron stars.…”

Section: Gravitational Waves From a Binary Systemmentioning

confidence: 99%

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Astrophysical gravitational waves in conformal gravity

2018

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We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum gravity. Here we show that gravitational radiation emitted by compact binaries allows us to strongly constrain both models.We work in Weyl gauge, which fixes the rescaling invariance of the models, and derive the linearized fourth-order equation of motion for the metric, which describes massless and massive modes of propagation. In the limit of a large graviton mass, MCG reduces to general relativity (GR), whereas CG does not. Coordinates are fixed by Teyssandier gauge to show that for a conserved energymomentum tensor the gravitational radiation is due to the time-dependent quadrupole moment of a non-relativistic source and we derive the gravitational energy-momentum tensor for both models. We apply our findings to the case of close binaries on circular orbits, which have been used to indirectly infer the existence of gravitational radiation prior to the direct observation of gravitational waves.As an example, we analyze the binary system PSR J1012+5307, chosen for its small eccentricity. When fixing the graviton mass in CG such that observed galaxy rotation curves could be explained without dark matter, the gravitational radiation of a binary system is much smaller than in GR. The same holds for MCG for small masses of the graviton. Thus gravitational radiation cannot explain the orbital decay of binary systems and replace dark matter simultaneously. We also analyse MCG for large graviton masses and conclude that MCG can describe the orbital periods of compact binaries in agreement with data, as it reduces to GR in that limit.

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Section: Gravitational Waves From a Binary Systemmentioning

confidence: 99%

“…Now, we transform (57) back to real space, insert it into (53), expand in k ω |x · n| 1 and keep terms up to the quadrupole contribution. This yieldŝ…”

Section: B Gravitational Waves From Binary Systemsmentioning

confidence: 99%

Astrophysical gravitational waves in conformal gravity

2018

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“…The most relevant issue of previous work is the severe disagreement between different studies. The disagreement concerns (1) the sign of γ [16,53]; (2) the association of the mass of the lens to different combinations of the parameters in the metric (1.3) [54,55]; (3) the choice of the geometric definition of the deflection angle [56].…”

Section: Consequences On Light Deflection In Cgmentioning

confidence: 99%

Conformal gravity: light deflection revisited and the galactic rotation curve failure

Campigotto

Diaferio

Fatibene

2019

Class. Quantum Grav.

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We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter γ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on γ. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on γ, i.e. by setting γ = 0, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters β and k of the Schwarzschild-like metric.

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“…Recently, the Weyl-gravity solution has been studied to explain rotation curves of galaxy samples without introducing a dark matter component [13] and the model may provide also a possible size of individual galaxies [14]. Moreover, the gravitational lensing by this black hole model has been discussed by several groups [15,16].…”

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confidence: 99%

“…The k parameter may play the same role as the cosmological constant in the Kottler spacetime. It is more convenient to rearrange this original form of the metric into another one [16] as…”

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confidence: 99%

Application of Sturm's theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

Ono¹,

Suzuki²,

Fushimi³

et al. 2015

EPL

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-In terms of Sturm's theorem, we reexamine a marginal stable circular orbit (MSCO) such as the innermost stable circular orbit (ISCO) of a timelike geodesic in any spherically symmetric and static spacetime. MSCOs for some of exact solutions to the Einstein's equation are discussed. Strum's theorem is explicitly applied to the Kottler (often called Schwarzschild-de Sitter) spacetime. Moreover, we analyze MSCOs for a spherically symmetric, static and vacuum solution in Weyl conformal gravity.

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Correct light deflection in Weyl conformal gravity

Cited by 58 publications

References 9 publications

Astrophysical gravitational waves in conformal gravity

Astrophysical gravitational waves in conformal gravity

Conformal gravity: light deflection revisited and the galactic rotation curve failure

Application of Sturm's theorem to marginal stable circular orbits of a test body in spherically symmetric and static spacetimes

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