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We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-direct extensions of the Heisenberg group are classified, thus providing new background solutions in conformal gravity. [ABSTRACT FROM AUTHOR]

We show that Einstein's conformal gravity can explain, simply, and on the geometric ground, galactic rotation curves, without the need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained, making a singular rescaling of Schwarzschild's spacetime. The new exact solution, asymptotically anti-de Sitter, manifests an unattainable singularity at infinity that cannot be reached in finite proper time; namely, the spacetime is geodetically complete. It deserves to be noticed that, in this paper, we have a different opinion from the usual one. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular than Schwarzschild's. Finally, it is crucial to point out that Weyl's conformal symmetry is spontaneously broken into the new singular vacuum rather than the asymptotically flat Schwarzschild's one. The metric is unique according to the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistent with the observations and the Tully–Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and show that our velocity profile very well interpolates the galactic rotation curves after a proper choice of the only free parameter in the metric. The mass-to-luminosity ratios of galaxies turn out to be close to 1, consistent with the absence of dark matter. [ABSTRACT FROM AUTHOR]

We present the deep connections among (Anti) de Sitter geometry, and complex conformal gravity-Maxwell theory, stemming directly from a gauge theory of gravity based on the complex Clifford algebra Cl(4, C). This is attained by simply promoting the de (Anti) Sitter algebras so(4, 1), so(3, 2) to the real Clifford algebras Cl(4, 1, R), Cl(3, 2, R), respectively. This interplay between gauge theories of gravity based on Cl(4, 1, R), Cl(3, 2, R) , whose bivector-generators encode the de (Anti) Sitter algebras so(4, 1), so(3, 2), respectively, and 4D conformal gravity based on Cl(3, 1, R) is reminiscent of the A d S D + 1 / C F T D correspondence between D + 1 -dim gravity in the bulk and conformal field theory in the D-dim boundary. Although a plausible cancellation mechanism of the cosmological constant terms appearing in the real-valued curvature components associated with complex conformal gravity is possible, it does not occur simultaneously in the imaginary curvature components. Nevertheless, by including a Lagrange multiplier term in the action, it is still plausible that one might be able to find a restricted set of on-shell field configurations leading to a cancellation of the cosmological constant in curvature-squared actions due to the coupling among the real and imaginary components of the vierbein. We finalize with a brief discussion related to U (4) × U (4) grand-unification models with gravity based on C l (5 , C) = C l (4 , C) ⊕ C l (4 , C) . It is plausible that these grand-unification models could also be traded for models based on G L (4 , C) × G L (4 , C) . [ABSTRACT FROM AUTHOR]

We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations provide a natural non-redundant set of scalar equations. The same vectors suggest the form of a Faraday tensor, that is studied in itself and in (non)-linear electrodynamics. In spherical symmetry, we evaluate the explicit expressions of the Ricci, the Weyl, the Cotton and the Bach tensors. Simple restrictions on the coefficients yield well known and new solutions in Einstein, f(R), Cotton and Conformal gravity, with or without charges, in vacuo or with fluid source. [ABSTRACT FROM AUTHOR]

We assume a modified (conformal) gravity theory, which produces a stronger interaction at large scale, in order to discuss the statistical distribution of the galaxy clusters based on thermodynamics. We develop N-body partition function and exploit it to study the equations of state of the system. The probability distribution function is deduced from the partition function taking the modified gravity theory into account. We compare the theoretical model with the data available through SDSS (III) via its 12th data release. [ABSTRACT FROM AUTHOR]

In the present paper, strong deflection gravitational lensing is studied in a conformal gravity black hole. With the help of geometric optics limits, we have formulated the light cone conditions for the photons coupled to the Weyl tensor in a conformal gravity black hole. It is explicitly found that strong deflection gravitational lensing depends on the coupling with the Weyl tensor, the polarization directions, and the black hole configuration parameters. We have applied the results of the strong deflection gravitational lensing to the supermassive black holes S g r A * and M 87 * and studied the possibility of encountering quantum improvement. It is not practicable to recognize similar black holes through the strong deflection gravitational lensing observables in the near future, except for the possible size of the black hole's shadow. We also notice that by directly adopting the constraint of the measured shadow of M 87 * , the quantum effect demands immense care. [ABSTRACT FROM AUTHOR]

In this paper, we use the holographic method to compute the entanglement entropy for different regions in the fourth-order scale-invariant theory of gravity. In four dimensions, the action of scale-invariant gravity contains a parameter where the moduli space has some distinguished points, precisely, the space of solutions contains the Log-gravity and for this specific solution, we compute the entanglement entropy. We also use the numerical method to investigate mutual information and tripartite information. Moreover, we make a comment on the sign of these quantities. [ABSTRACT FROM AUTHOR]

We investigate the null and timelike circular geodesics in Mannheim-Kazanas spacetime. The effective potential, circular orbits and their stability are discussed, in terms of Lyapunov exponent. The critical null and timelike geodesics are compared to the ones obtained in Schwarzschild's case. Finally, we focus on the black hole's thermodynamic properties. [ABSTRACT FROM AUTHOR]

We revisit the structure of conformal gravity in the presence of a c-number, conformally coupled, long range, macroscopic scalar field. And in the static, spherically symmetric case discuss two classes of exact exterior solutions. In one solution the scalar field has a constant value and in the other solution, which is due to Brihaye and Verbin, it has a dependence on the radial coordinate, with the two exterior solutions being relatable by a conformal transformation. In light of these two solutions Horne and then Hobson and Lasenby raised the concern that the fitting of conformal gravity to galactic rotation curves had been misapplied and thus called the successful fitting of the conformal theory into question. In this paper we show that the analysis of Brihaye and Verbin needs to reappraised, with their reported result not being as general as they had indicated, but nonetheless being valid in the particular case that they studied. For the analyses of Horne and of Hobson and Lasenby we show that this macroscopic scalar field is not related to the mass generation that is required in a conformal theory. Rather, not just in conformal gravity, but also in standard Einstein gravity, the presence of such a long range scalar field would lead to test particles whose masses would be of the same order as the masses of the galaxies around which they orbit. Since particle masses are not at all of this form, such macroscopic fields cannot be responsible for mass generation; and the existence of any such mass-generating scalar fields can be excluded, consistent with there actually being no known massless scalar particles in nature. Instead, mass generation has to be due to c-number vacuum expectation values of q-number fields. Such expectation values are microscopic not macroscopic and only vary within particle interiors, giving particles an extended, baglike structure, as needed for localization in a conformal theory. And being purely internal they have no effect on galactic orbits, to thus leave the good conformal gravity fitting to galactic rotation curves intact. [ABSTRACT FROM AUTHOR]

A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an example of a general gauge theory. We also present some early attempts at quantization of conformal gravity and use the generalized framework of covariant quantization due to Faddeev and Popov. Some salient issues such as the need for conformal gauge-fixing, an issue with conformal third ghosts, and discontinuities in conformal gravity are studied as well. Finally, we provide some explanations of the original ad hoc methods of computation valid at the first quantum loop level in conformal gravity. [ABSTRACT FROM AUTHOR]

The postulate of universal conformal (local Weyl scaling) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) generates an effective cosmological constant that fits the observed accelerating Hubble expansion for redshifts z ≤ 1 (7.33 Gyr) accurately with only one free parameter. Growth of a galaxy is modeled by the central accumulation of matter from an enclosing empty spherical halo whose radius expands with depletion. Details of this process account for the nonclassical, radial centripetal acceleration observed at excessive orbital velocities in galactic haloes. There is no need for dark matter. [ABSTRACT FROM AUTHOR]

In this paper, we study the sparsity of Hawking radiation from nonrotating singularity-free black holes in conformal gravity. We give a rigorous bound on the greybody factor for massless scalar field and calculate the sparsity of Hawking radiation from the black hole. Besides, we investigate the dependence of the bound of the greybody factor and the sparsity of Hawking radiation on the conformal parameters, respectively. Our study shows that when the conformal parameters are large, the increase of conformal parameters will lead to a more sparse Hawking radiation, while to a less sparse Hawking radiation if the conformal parameters are small. [ABSTRACT FROM AUTHOR]

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory. [ABSTRACT FROM AUTHOR]

It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein 4-metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian setting. Following an approach pioneered by Fefferman and Graham for the Einstein equation, we find formal power series for conformally compactifiable, asymptotically hyperbolic Bach-flat 4-metrics expanded about conformal infinity. We also consider Bach-flat metrics in the special case of constant scalar curvature and in the special case of constant Q-curvature. This allows us to determine the free data at conformal infinity and to select those choices that lead to Einstein metrics. The asymptotically hyperbolic mass is part of that free data, in contrast to the pure Einstein case. Higher-dimensional generalizations of the Bach tensor lack some of the geometrical meaning of the 4-dimensional case, but for a generalized Bach equation suited to the Fefferman–Graham technique, we are able to obtain a relatively complete result illustrating an interesting splitting of the free data into low-order "Dirichlet" and high-order "Neumann" pairs. [ABSTRACT FROM AUTHOR]

The postulate of universal conformal (local Weyl scaling) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) generates an effective cosmological constant that fits the observed accelerating Hubble expansion for redshifts z≤1 (7.33 Gyr) accurately with only one free parameter. Growth of a galaxy is modeled by the central accumulation of matter from an enclosing empty spherical halo whose radius expands with depletion. Details of this process account for the nonclassical, radial centripetal acceleration observed at excessive orbital velocities in galactic haloes. There is no need for dark matter.

Abstract We show that if the $$\alpha $$ α -attractor model is realized by the spontaneous breaking of the scale symmetry, then the stability and the dynamics of the vector field that gauges the scale symmetry can severely constrain the $$\alpha $$ α -parameter as $$5/6< \alpha < 1$$ 5 / 6 < α < 1 restricting the inflationary predictions in a very tiny region in the $$n_s - r$$ n s - r plane that are in great agreement with the latest Planck data. Although the different values of $$\alpha $$ α do not make a tangible difference for $$n_s$$ n s and r, they provide radically different scenarios for the post-inflationary dynamics which determines the standard BBN processes and the large scale isotropy of the universe.

We discuss arguments both in favor of and against dark matter. With the repeated failure of experiment to date to detect dark matter we discuss what could be done instead, and to this end look for clues in the data themselves. We identify various regularities in galactic rotation curve data that correlate the total gravitational potential with luminous matter rather than dark matter. We identify a contribution to galactic rotation curves coming from the rest of the visible universe, and suggest that dark matter is just an attempt to describe this global effect in terms of standard local Newtonian gravity within galaxies. Thus the missing mass is not missing at all — it has been hiding in plain sight all along as the rest of the visible mass in the universe. [ABSTRACT FROM AUTHOR]

We study the matching conditions on singular hypersurfaces in Weyl + Einstein gravity. Unlike General Relativity, the so-called quadratic gravity allows the existence of a double layer, i.e. the derivative of δ -function. This double layer is a purely geometrical phenomenon and it may be treated as the purely gravitational shock wave. The mathematical formalism was elaborated by Senovilla for generic quadratic gravity. We derived the matching conditions for the spherically symmetric singular hypersurface in the Weyl + Einstein gravity. It was found that in the presence of the double layer, the matching conditions contain an arbitrary function. One of the consequences of such freedom is that a trace of the extrinsic curvature tensor of a singular hypersurface is necessarily equal to zero. We suggested that the S 0 n and S n n components of the surface matter energy–momentum tensor of the shell describe energy flow S 0 n and momentum transfer S n n of particles produced by the double layer itself. Moreover, the requirement of the zero trace of the extrinsic curvature tensor (mentioned above) implies that S n n = 0 , and this fact also supports our suggestion, because it means that for the observer sitting on the shell, particles will be seen created by pairs, and the sum of their momentum transfers must be zero. We found also that the spherically symmetric null double layer in the Weyl + Einstein gravity does not exist at all. [ABSTRACT FROM AUTHOR]

During the 2016 International Workshop on Astronomy and Relativistic Astrophysics (IWARA), the question was raised as to whether conformal gravity (CG) could explain the timely result which showed a universal nature found in the centripetal accelerations of spiral galaxies. At the time of the conference, the McGaugh result was only published for 2 weeks. Since then, the result has become known as the radial acceleration relation (RAR) and has been considered tantamount to a natural law. In this paper, we summarize how CG can explain the RAR in a manner consistent with the findings of the original authors without the need for dark matter. [ABSTRACT FROM AUTHOR]

We study the wave equation governing massless fields of all spins (s = 0, 12, 1, 32 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes. [ABSTRACT FROM AUTHOR]

The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Diracs delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl-Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in detail the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless ( massless) shell, it is shown that their dynamics cannot be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl-Einstein gravity, the trajectory of the same type of shell is completely restored even without knowledge of the outside solution. [ABSTRACT FROM AUTHOR]

Magnetized particle motion around black holes in conformal gravity immersed in asymptotically uniform magnetic field has been studied. We have also analyzed the behavior of magnetic fields near the horizon of the black hole in conformal gravity and shown that with the increase of conformal parameters L and N the value of angular component of magnetic field at the stellar surface decreases. The maximum value of the effective potential corresponding to circular motion of the magnetized particle increases with the increase of conformal parameters. It is shown that in all cases of neutral, charged and magnetized particle collisions in the black hole environment the center-of-mass energy decreases with the increase of conformal parameters L and N. In the case of the magnetized and negatively charged particle collisions, the innermost collision point with the maximum center-of-mass energy comes closer to the central object due to the effects of the parameters of the conformal gravity. We have applied the results to the real astrophysical scenario when a pulsar treated as a magnetized particle is orbiting the super massive black hole (SMBH) Sgr A* in the center of our galaxy in order to obtain the estimation of magnetized compact object’s orbital parameter. The possible detection of pulsar in Sgr A* close environment can provide constraints on black hole parameters. Here we have shown that there is degeneracy between spin of SMBH and ambient magnetic field and consequently the interaction of magnetic field ∼ 10 2 Gauss with magnetic moment of magnetized neutron star can in principle mimic spin of Kerr black holes up to 0.6 .

In this work we analyze kinematical conformal cosmology (KCC), an alternative cosmological model based on conformal Weyl gravity (CG), and test it against current type Ia supernova (SNIa) luminosity data and other astrophysical observations. Expanding upon previous work on the subject, we revise the analysis of SNIa data, confirming that KCC can explain the evidence for an accelerating expansion of the Universe without using dark energy or other exotic components. We obtain an independent evaluation of the Hubble constant, H0 = 67:53 kms-1 Mpc-1, very close to the current best estimates. The main KCC and CG parameters are re-evaluated and their revised values are found to be close to previous estimates. We also show that available data for the Hubble parameter as a function of redshift can be fitted using KCC and that this model does not suffer from any apparent age problem. Overall,

We examine the critical behavior, i.e. P- V criticality of conformal gravity (CG) in an extended phase space in which the cosmological constant should be interpreted as a thermodynamic pressure and the corresponding conjugate quantity as a thermodynamic volume. The main potential point of interest in CG is that there exists a nontrivial Rindler parameter in the spacetime geometry. This geometric parameter has an important role to construct a model for gravity at large distances where the parameter '' actually originates. We also investigate the effect of the said parameter on the black hole (BH) thermodynamic equation of state, critical constants, Reverse Isoperimetric Inequality, first law of thermodynamics, Hawking-Page phase transition and Gibbs free energy for this BH. We speculate that due to the presence of the said parameter, there has been a deformation in the shape of the isotherms in the P- V diagram in comparison with the charged-anti de Sitter (AdS) BH and the chargeless-AdS BH. Interestingly, we find that the critical ratio for this BH is , which is greater than the charged AdS BH and Schwarzschild-AdS BH, i.e. . The symbols are defined in the main work. Moreover, we observe that the critical ratio has a constant value and it is independent of the nontrivial Rindler parameter . Finally, we derive the reduced equation of state in terms of the reduced temperature, the reduced volume and the reduced pressure, respectively. [ABSTRACT FROM AUTHOR]

We calculate the characteristics of the 'black hole shadow' for a rotating, neutral black hole in fourth-order conformal Weyl gravity. It is shown that the morphology is not significantly affected by the underlying framework, except for very large masses. Conformal gravity black hole shadows would also significantly differ from their general relativistic counterparts if the values of the main conformal gravity parameters, γ and κ, were increased by several orders of magnitude. Such increased values for γ and κ are currently ruled out by gravitational phenomenology. Therefore, it is unlikely that these differences in black hole shadows will be detected in future observations, carried out by the Event Horizon Telescope or other such experiments. [ABSTRACT FROM AUTHOR]

The extended phase-space thermodynamics and heat engines for static spherically symmetric black hole solutions of four-dimensional conformal gravity are studied in detail. It is argued that the equation of states (EOS) for such black holes is always branched, any continuous thermodynamical process cannot drive the system from one branch of the EOS into another branch. Meanwhile, the thermodynamical volume is bounded from above, making the black holes always super-entropic in one branch and may also be super-entropic in another branch in certain range of the temperature. The Carnot and Stirling heat engines associated to such black holes are shown to be distinct from each other. For rectangular heat engines, the efficiency always approaches zero when the rectangle becomes extremely narrow, and given the highest and lowest working temperatures fixed, there is always a maximum for the efficiency of such engines. [ABSTRACT FROM AUTHOR]

The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the Friedmann-Robertson-Walker (FRW) line element. The energy of the Universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the matter field in the FRW model. [ABSTRACT FROM AUTHOR]

In 2013 the Nobel Prize in Physics was awarded to Francois Englert and Peter Higgs for their work in 1964 along with the late Robert Brout on the mass generation mechanism (the Higgs mechanism) in local gauge theories. This mechanism requires the existence of a massive scalar particle, the Higgs boson, and in 2012 the Higgs boson was finally discovered at the Large Hadron Collider after being sought for almost half a century. In this article we review the work that led to the discovery of the Higgs boson and discuss its implications. We approach the topic from the perspective of a dynamically generated Higgs boson that is a fermion–antifermion bound state rather than an elementary field that appears in an input Lagrangian. In particular, we emphasize the connection with the Bardeen–Cooper–Schrieffer theory of superconductivity. We identify the double-well Higgs potential not as a fundamental potential but as a mean-field effective Lagrangian with a dynamical Higgs boson being generated through a residual interaction that accompanies the mean-field Lagrangian. We discuss what we believe to be the key challenge raised by the discovery of the Higgs boson, namely determining whether it is elementary or composite, and through study of a conformal invariant field theory model as realized with critical scaling and anomalous dimensions, suggest that the width of the Higgs boson might serve as a suitable diagnostic for discriminating between an elementary Higgs boson and a composite one. We discuss the implications of Higgs boson mass generation for the cosmological constant problem, as the cosmological constant receives contributions from the very mechanism that generates the Higgs boson mass in the first place. We show that the contribution to the cosmological constant due to a composite Higgs boson is more tractable and under control than the contribution due to an elementary Higgs boson, and is potentially completely under control if there is an underlying conformal symmetry not just in a critical scaling matter sector (which there would have to be if all mass scales are to be dynamical), but equally in the gravity sector to which the matter sector couples. [ABSTRACT FROM AUTHOR]

Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented.

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy–momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided. [ABSTRACT FROM AUTHOR]

The C-metric solution of conformal gravity with a conformally coupled scalar field is presented. The solution belongs to the class of Petrov type D spacetimes and is conformal to the standard AdS C-metric appeared in vacuum Einstein gravity. For all parameter ranges, we identify some of the physically interesting static regions and the corresponding coordinate ranges. The solution may contain a black hole event horizon, an acceleration horizon, either of which may be cut by the conformal infinity or be hidden behind the conformal infinity. Since the model is conformally invariant, we also discussed the possible effects of the conformal gauge choices on the structure of the spacetime. [ABSTRACT FROM AUTHOR]

We shall review conformal gravity as a gauge natural theory and discuss the consequences of Weyl covariance on the definition of physical states. [ABSTRACT FROM AUTHOR]

We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remains the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic matter might still be needed at the junction between our solutions and flat spacetime, but we demonstrate that the averaged null energy condition (as evaluated along radial null geodesics) is satisfied for a particular set of wormhole geometries. Therefore, if fourth-order conformal Weyl gravity is a correct extension of general relativity, traversable wormholes might become a realistic solution for interstellar travel. [ABSTRACT FROM AUTHOR]