Black hole shadows in the <i>R</i> h = <i>ct</i> universe

ABSTRACT The Lambda cold dark matter ($\Lambda$CDM) model still enjoys the title of being the standard model in cosmology. Yet an alternative model that has received a lot of attention over the last decade is the $R_{\mathrm{h}}=ct$ universe. This model provides an age for the Universe similar to that of $\Lambda$CDM and like $\Lambda$CDM it is also based on a Friedmann–Robertson–Walker (FRW) cosmology. However, the total energy density $\rho$ and pressure p of the cosmic fluid for the $R_{\mathrm{h}}=ct$ model satisfy the simple equation of state (EOS) $\rho + 3p = 0$, i.e. it has a vanishing total active gravitational mass. Unlike the $\Lambda$CDM, the $R_{\mathrm{h}}=ct$ is a linearly expanding (coasting) model and therefore has a vanishing deceleration parameter, which apparently is not inconsistent with observations. In fact, various observational tests seem to favour the $R_{\mathrm{h}}=ct$ model over $\Lambda$CDM. In this paper, we compute the shadow of a black hole embedded in the $R_{\mathrm{h}}=ct$ universe as observed by a comoving observer at an arbitrary distance from the black hole. To do this we use the method of matched asymptotic expansions introduced by Tsupko &amp; Bisnovatyi-Kogan (IJMPD, 29 2050062 (2020)). We also compare these black hole shadows with those in other cosmological models including the $\Lambda$CDM universe.