Monochromatic plane-fronted waves in conformal gravity are pure gauge

Journal Article · Sun May 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.104046· OSTI ID:21502617

Fabbri, Luca ^[1]; Paranjape, M B ^[1]

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1. Groupe de physique des particules, Departement de physique, Universite de Montreal, CP 6128, Succursale Centre-ville, Montreal, Quebec, H3C 3J7 (Canada)

We consider plane-fronted, monochromatic gravitational waves on a Minkowski background, in a conformally invariant theory of general relativity. By this we mean waves of the form: g{sup {mu}{nu}}={eta}{sup {mu}{nu}}+{epsilon}{sup {mu}{nu}}F(k{center_dot}x), where {epsilon}{sup {mu}{nu}} is a constant polarization tensor, and k{sub {mu}} is a lightlike vector. We also assume the coordinate gauge condition |g|{sup -1/4}{partial_derivative}{sub {tau}}(|g|{sup 1/4}g{sup {sigma}{tau}})=0 which is the conformal analog of the harmonic gauge condition g{sup {mu}{nu}}{Gamma}{sub {mu}{nu}}{sup {sigma}}=-|g|{sup -1/2}{partial_derivative}{sub {tau}}(|g|{sup 1/2}g{sup {sigma}{tau}})=0, where det{open_square}[g{sub {mu}{nu}}]{identical_to}g. Requiring additionally the conformal gauge condition g=-1 surprisingly implies that the waves are both transverse and traceless. Although the ansatz for the metric is eminently reasonable when considering perturbative gravitational waves, we show that the metric is reducible to the metric of Minkowski space-time via a sequence of coordinate transformations which respect the gauge conditions, without any perturbative approximation that {epsilon}{sup {mu}{nu}} be small. This implies that we have, in fact, exact plane-wave solutions; however, they are simply coordinate/conformal artifacts. As a consequence, they carry no energy. Our result does not imply that conformal gravity does not have gravitational wave phenomena. A different, more generalized ansatz for the deviation, taking into account the fourth-order nature of the field equation, which has the form g{sup {mu}{nu}}={eta}{sup {mu}{nu}}+B{sup {mu}{nu}}(n{center_dot}x)G(k{center_dot}x), indeed yields waves which carry energy and momentum [P. D. Mannheim, Gen. Relativ. Gravit. 43, 703 (2010)]. It is just surprising that transverse, traceless, plane-fronted gravitational waves, those that would be used in any standard, perturbative, quantum analysis of the theory, simply do not exist.

• OSTI ID: 21502617
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 10; Other Information: DOI: 10.1103/PhysRevD.83.104046; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
APPROXIMATIONS
FIELD EQUATIONS
GENERAL RELATIVITY THEORY
GRAVITATION
GRAVITATIONAL WAVES
MATHEMATICAL SOLUTIONS
METRICS
MINKOWSKI SPACE
MONOCHROMATIC RADIATION
PERTURBATION THEORY
POLARIZATION
QUANTUM FIELD THEORY
TRANSFORMATIONS
WAVE PROPAGATION
CALCULATION METHODS
ELECTROMAGNETIC RADIATION
EQUATIONS
FIELD THEORIES
MATHEMATICAL SPACE
RADIATIONS
RELATIVITY THEORY
SPACE