Abstract
We construct the light escape cones of isotropic spot sources of radiation residing in special classes of reference frames in the Kerr–de Sitter (KdS) black hole spacetimes, namely in the fundamental class of ‘non-geodesic’ locally non-rotating reference frames (LNRFs), and two classes of ‘geodesic’ frames, the radial geodesic frames (RGFs), both falling and escaping, and the frames related to the circular geodesic orbits (CGFs). We compare the cones constructed in a given position for the LNRFs, RGFs, and CGFs. We have shown that the photons locally counter-rotating relative to LNRFs with positive impact parameter and negative covariant energy are confined to the ergosphere region. Finally, we demonstrate that the light escaping cones govern the shadows of black holes located in front of a radiating screen, as seen by the observers in the considered frames. For shadows related to distant static observers the LNRFs are relevant.
Highlights
Cosmological observations indicate that recent accelerated expansion of the Universe is governed by a dark energy that can be represented by a very small relict vacuum energy, or by a quintessential field [1,2,6,14,23,25,48,51,57,92]
Locally nonrotating frames (LNRFs) are considered that give the simplest view of physical phenomena in Kerr-de Sitter (KdS) spacetimes, as they properly balance the effect of spacetime dragging [9]
The value v+ = 1 corresponds to the corotating circular photon orbit located at r = r ph+, while v− = −1 holds for the counter-rotating photon orbit located at r = r ph−, where the orientation is determined relative to locally non-rotating reference frames (LNRFs)
Summary
Cosmological observations indicate that recent accelerated expansion of the Universe is governed by a dark energy that can be represented by a very small relict vacuum energy (repulsive cosmological constant > 0), or by a quintessential field [1,2,6,14,23,25,48,51,57,92]. The spherically symmetric black hole spacetimes with the term are described by the vacuum Schwarzschild–de Sitter (SdS) geometry [37,74] Their relevance has been discussed in [3,4,5,24,26,67]. In the KdS black hole spacetimes the free static observers are expected near the so called static radius [66,85] representing the outermost region of gravitationally bound systems in Universe with accelerated expansion [24,69,77], while behind the static radius the radially escaping geodesic observer is a more appropriate choice
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