Abstract
We present an analysis of the null geodesics of the static, spherically symmetric, vacuum solution to the equations of conformal (Weyl) gravity. We classify the full range of exotic spacetimes arising from the parameter space of the metric. The nature of various notable features of these spacetimes is investigated including light spheres, horizons and physical singularities.
Highlights
For over one hundred years Einstein’s theory of general relativity has dominated the narrative in our understanding of space, time, matter and energy in elds from planetary dynamics to cosmology
We present an analysis of the null geodesics of the static, spherically symmetric, vacuum solution to the equations of conformal (Weyl) gravity
A great many more distant observations seem to validate general relativity: changing orbital periods of binary pulsars [5]; redshift of light leaving the gravitational potential of white dwarfs [6] and gravitational waves released by merging black holes [7]
Summary
For over one hundred years Einstein’s theory of general relativity has dominated the narrative in our understanding of space, time, matter and energy in elds from planetary dynamics to cosmology. General relativity on galactic and cosmological scales requires the invocation of extra matter and energy to explain observations. This extra content in the Universe has so far resisted investigation and has, been referred to as dark. Where αg is a parameter for the strength of the gravitational eld These equations differ from those used in general relativity because both the Bach tensor Wμν and the energy-momentum tensor Tμν are traceless in conformal gravity and the only constant αg is dimensionless. We will conclude by discussing the nature of these features in greater detail (section 4)
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