Abstract
We study the shadows of the fully non-linear, asymptotically flat Einstein–dilaton–Gauss–Bonnet (EdGB) black holes (BHs), for both static and rotating solutions. We find that, in all cases, these shadows are smaller than for comparable Kerr BHs, i.e. with the same total mass and angular momentum under similar observation conditions. In order to compare both cases we provide quantitative shadow parameters, observing in particular that the differences in the shadows mean radii are never larger than the percent level. Therefore, generically, EdGB BHs cannot be excluded by (near future) shadow observations alone. On the theoretical side, we find no clear signature of some exotic features of EdGB BHs on the corresponding shadows, such as the regions of negative (Komar, say) energy density outside the horizon. We speculate that this is due to the fact that the Komar energy interior to the light rings (or more precisely, the surfaces of constant radial coordinate that intersect the light rings in the equatorial plane) is always smaller than the ADM mass, and consequently the corresponding shadows are smaller than those of comparable Kerr BHs. The analysis herein provides a clear example that it is the light ring impact parameter, rather than its “size”, that determines a BH shadow.
Highlights
Ultraviolet theoretical inconsistencies of Einstein’s General Relativity, such as its nonrenormalizability [1, 2, 3] and the existence of singularities, have since long motivated the suggestion that higher curvature corrections should be taken into account, in an improved theory of gravity
The shadow of a EdGB black holes (BHs) is always smaller than the comparable Kerr one
At the same time any near-horizon odd effects are concealed from a remote observer by the shadow. It may come as another surprise, that the light ring size12 of EdGB BHs can, for instance, change by as much as ≃ 4%, when considering the static case with γ = 0.5, and this effect will increase with further decreasing γ
Summary
Ultraviolet theoretical inconsistencies of Einstein’s General Relativity, such as its nonrenormalizability [1, 2, 3] and the existence of singularities, have since long motivated the suggestion that higher curvature corrections should be taken into account, in an improved theory of gravity (see e.g. [4]). A possible interpretation of this qualitative behaviour is the following: the total mass (and angular momentum) of the hairy BHs is partly stored in the scalar field outside the horizon; in particular the existence of some energy outside the region of unstable spherical photon orbits, referred to as photon region (see section 3.1) [35], implies that less energy exists inside this region and the light rings should be smaller (within an appropriate measure) as compared to their vacuum counterparts and so should be the shadows. The above interpretation raises an interesting question in relation to the BHs in EdGB theory Since these have negative energy densities outside the horizon, how do these regions of effective exotic matter impact on their shadows?
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