Comment on "Astrophysical gravitational waves in conformal gravity"
F. F. Faria
TL;DR
This paper critically examines recent claims about gravitational radiation in conformal gravity, clarifying that the theories differ significantly depending on parameter signs, impacting their physical interpretations.
Contribution
It clarifies the distinction between conformal gravity and massive conformal gravity, challenging previous assumptions about their equivalence based on parameter signs.
Findings
The sign of the parameter critically affects the theory's correspondence.
Massive conformal gravity is not equivalent to conformal gravity for positive parameters.
The previous claim of equivalence is invalid for certain parameter choices.
Abstract
Recently, in Phys. Rev. D 98, 084002 (2018), an investigation was carried out on the gravitational radiation from binary systems in conformal gravity and massive conformal gravity. According to the authors of the paper, these two theories differ only by the sign of a parameter in the matter action of a general conformal theory. For a negative parameter the general conformal theory indeed corresponds to conformal gravity. However, here, we argue that for a positive parameter the general conformal theory does not correspond to massive conformal gravity.
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Comment on “Astrophysical gravitational waves in conformal gravity”
F. F. Faria
Centro de Ciências da Natureza, Universidade Estadual do Piauí, 64.002-150 Teresina, PI, Brazil
Abstract
Recently, in Phys. Rev. D 98, 084002 (2018), an investigation was carried out on the gravitational radiation from binary systems in conformal gravity and massive conformal gravity. According to the authors of the paper, these two theories differ only by the sign of a parameter in the matter action of a general conformal theory. For a negative parameter the general conformal theory indeed corresponds to conformal gravity. However, here, we argue that for a positive parameter the general conformal theory does not correspond to massive conformal gravity.
As addressed in Ref. [70] of Ref. Caprini , the massive conformal gravity has one scalar field (dilaton field) coupled to the gravitational part of the theory Faria1 and a second scalar field (Higgs field) coupled to the fermionic matter part of the theory Faria2 . It is then stated in Ref. [70] of Ref. Caprini that, after the imposition of a Weyl gauge, the massive conformal gravity corresponds to the general conformal theory with a positive parameter considered in Ref. Caprini . This is indeed true if the Weyl gauge is imposed on the massive conformal gravity action. However, this procedure is not suit for the gauge analysis of the theory. By imposing the Weyl gauge on the massive conformal gravity field equations, we find . Since this condition does not hold in the general conformal theory with a positive parameter Foot , then the two theories do not correspond to each other.
Acknowledgments
The author would like to thank the authors of Ref. Caprini , in particular P. Hölscher, for useful discussions.
The reference list from the paper itself. Each links out to its DOI / PubMed record.
- 1(1) C. Caprini, P. Hölscher and D. J. Schwarz, Phys. Rev. D 98 , 084002 (2018).
- 2(2) F. F. Faria, Adv. High Energy Phys. 2014 , 520259 (2014).
- 3(3) F. F. Faria, arxiv:1410.5104.
- 4(4) The authors of Ref. Caprini have suggested calling this theory “conformal Einstein-Weyl-Higgs gravity” for future reference, with which I agree.