Abstract
A new method is applied for deriving simultaneously the redshift and shadow of a Schwarzschild black hole moving freely in the de Sitter expanding universe as recorded by a remote co-moving observer. This method is mainly algebraic, focusing on the transformation of the conserved quantities under the de Sitter isometry relating the black hole co-moving frame to observer’s one. Hereby one extracts the general expressions of the redshifts and shadows of the black holes having peculiar velocities but their expressions are too extended to be written down here. Therefore, only some particular cases and intuitive expansions are presented while the complete results are given in an algebraic code (Cotăescu in Maple code BH01, https://physics.uvt.ro/~cota/CCFT/codes, 2020).
Highlights
The light emitted by cosmic objects is one of the principal sources of empirical data in astrophysics
The light emitted by a black hole comes from an apparent source situated on a sphere, surrounding the black hole, which is observed as the black hole shadow
We start with precise initial conditions determining the suitable isometry relating the black hole and observer proper frames. This will give the conserved quantities measured in the observer’s frame we need for extracting physical results without resorting to geodesics or other geometric objects. For this reason we say that our method is algebraic, observing that there are some advantages among them the principal one is of a coherent framework offered by the de Sitter relativity which prevent us of using supplemental hypotheses
Summary
The light emitted by cosmic objects is one of the principal sources of empirical data in astrophysics. The light emitted by a black hole comes from an apparent source situated on a sphere, surrounding the black hole, which is observed as the black hole shadow When this is not negligible, as in the case of the object M87 [12,13], and the black hole may have a peculiar velocity, the Doppler effect is no longer longitudinal such that the transverse contributions due to the black hole shadow must be evaluated. As in this paper we would like to study the relation between the redshifts and shadows of the Schwarzschild black holes having peculiar velocities in de Sitter expanding universe we must abandon the geometric method adopting the algebraic approach of Ref. As the actual observations show with reasonable accuracy that this universe is spatially
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
