Abstract
We have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic degenerate higher-order scalar–tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quickly rotation and the more negative deformation parameter. Especially, for the near-extreme black hole with negative deformation parameter, there exist a “pedicel”-like structure appeared in the shadow, which increases with the absolute value of deformation parameter. The eyebrow-like shadow and the self-similar fractal structures also appear in the shadow for the disformal Kerr black hole in DHOST theory. These features in the black hole shadow originating from the scalar field could help us to understand the non-stealth disformal Kerr black hole and quadratic DHOST theory.
Highlights
It is well known that scalar–tensor theories are a kind of alternative theories of gravity, where there exists a scalar degree of freedom besides the gravitational metric
The presence of α means that the disformal Kerr metric (4) is a non-stealth solution in quadratic degenerate higher-order scalar–tensor (DHOST) theory because the scalar field modifies the metric of spacetime, which is difference from that in the stealth solution case
Many other smaller eyebrow-like structures can be detected in the shadow of the disformal Kerr black hole (4). This means that the shadow of a disformal Kerr black hole in DHOST theory possesses a self-similar fractal structure caused by chaotic scattering of photon, which is qualitatively different from that in usual Kerr black hole spacetime
Summary
It is well known that scalar–tensor theories are a kind of alternative theories of gravity, where there exists a scalar degree of freedom besides the gravitational metric. 2, we introduce briefly the rotating non-stealth black hole solution in quadratic DHOST theories [22,23], and study equation of motion for the photons in this spacetime. Let us to introduce briefly the disformal Kerr black hole with an extra deformation parameter, which is a non-stealth rotating solution in quadratic DHOST theory. The disformal Kerr metric (4) in quadratic DHOST theory owns three parameters: the mass parameter M and spin parameter a together with a new deformation parameter α encoded precisely the deviations from general relativity. The presence of α means that the disformal Kerr metric (4) is a non-stealth solution in quadratic DHOST theory because the scalar field modifies the metric of spacetime, which is difference from that in the stealth solution case. It is expected that the shadow of a disformal Kerr black hole should possess some new properties which do not belong to Kerr one
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