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Register a new userCorrect light deflection in Weyl conformal gravity
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Added by
Kamal Kanti Nandi Dr
Publication date
2013
fields
Physics
and research's language is
English
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The conformal gravity fit to observed galactic rotation curves requires {gamma}>0. On the other hand, conventional method for light deflection by galaxies gives a negative contribution to Schwarzschild value for {gamma}>0, which is contrary to observation. Thus, it is very important that the contribution to bending should in principle be positive, no matter how small its magnitude is. Here we show that the Rindler-Ishak method gives a positive contribution to Schwarzschild deflection for {gamma}>0, as desired. We also obtain the exact local coupling term derived earlier by Sereno. These results indicate that conformal gravity can potentially test well against all astrophysical observations to date.
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We study here, using the Mannheim-Kazanas solution of Weyl conformal theory, the mass decomposition in the representative subsample of $57$ early-type elliptical lens galaxies of the SLACS on board the HST. We begin by showing that the solution need not be an exclusive solution of conformal gravity but can also be viewed as a solution of a class of $f(R)$ gravity theories coupled to non-linear electrodynamics thereby rendering the ensuing results more universal. Since lensing involves light bending, we shall first show that the solution adds to Schwarzschild light bending caused by the luminous mass ($M_{ast }$) a positive contribution $+gamma R$ contrary to the previous results in the literature, thereby resolving a long standing problem. The cause of the error is critically examined. Applying the expressions for light bending together with an input equating Einstein and Weyl angles, we develop a novel algorithm for separating the luminous component from the total lens mass (luminous+dark) within the Einstein radius. Our results indicate that the luminous mass estimates differ from the observed total lens masses by a linear proportionality factor. In quantitative detail, we observe that the ratios of luminous over total lens mass ($f^{ast }$) within the Einstein radius of individual galaxies take on values near unity, many of which remarkably fall inside or just marginally outside the specified error bars obtained from a simulation based on the Bruzual-Charlot stellar population synthesis model together with the Salpeter IMF favored on the ground of metallicity [Grillo,2009]. We shall also calculate the average dark matter density of individual galaxies within their respective Einstein spheres. The present approach, being truly analytic, seems to be the first of its kind attempting to provide a new decomposition scheme distinct from the simulational ones.
With the assumptions of a quartic scalar field, finite energy of the scalar field in a volume, and vanishing radial component of 4-current at infinity, an exact static and spherically symmetric hairy black hole solution exists in the framework of Horndeski theory with parameter $Q$, which encompasses the Schwarzschild black hole ($Q=0$). We obtain the axially symmetric counterpart of this hairy solution, namely the rotating Horndeski black hole, which contains as a special case the Kerr black hole ($Q=0$). Interestingly, for a set of parameters ($M, a$, and $Q$), there exists an extremal value of the parameter $Q=Q_{e}$, which corresponds to an extremal black hole with degenerate horizons, while for $Q<Q_{e}$, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for $Q>Q_{e}$. We investigate the effect of the $Q$ on the rotating black hole spacetime geometry and analytically deduce corrections to the light deflection angle from the Kerr and nonrotating Horndeski gravity black hole values. For the S2 source star, we calculate the deflection angle for the Sgr A* model of rotating Horndeski gravity black hole for both prograde and retrograde photons and show that it is larger than the Kerr black hole value.
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 $gamma$ 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 $gamma$. 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 $gamma$, i.e. by setting $gamma=0$, 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 $beta$ and $k$ of the Schwarzschild-like metric.
We consider the gravitational radiation in conformal gravity theory. We perturb the metric from flat Mikowski space and obtain the wave equation after introducing the appropriate transformation for perturbation. We derive the effective energy-momentum tensor for the gravitational radiation, which can be used to determine the energy carried by gravitational waves.
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.
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