The recent observation of the shadow of the supermassive compact object M87* by the Event Horizon Telescope (EHT) collaboration has opened up a new window to probe the strong gravity regime. In this paper, we study shadows cast by two viable alternatives to the Kerr black hole, and compare them with the shadow of M87*. The first alternative is a horizonless compact object (HCO) having radius r0 and exterior Kerr geometry. The second one is a rotating generalization of the recently obtained one parameter (r0) static metric by Simpson and Visser. This latter metric, constructed by using the Newman-Janis algorithm, is a special case of a parametrised rotating non-Kerr geometry obtained by Johannsen. Here, we constrain the parameter r0 of these alternatives using the results from M87* observation. We find that, for the mass, inclination angle and the angular diameter of the shadow of M87* reported by the EHT collaboration, the maximum value of the parameter r0 must be in the range 2.54r+ ≤ r0, max ≤ 3.51r+ for the dimensionless spin range 0.5 ≤ a* ≤ 0.94, with r+ being the outer horizon radius of the Kerr black hole at the corresponding spin value. We conclude that these black hole alternatives having r0 below this maximum range (i.e. r0 ≤ r0, max) is consistent with the size and deviation from circularity of the observed shadow of M87*.
Collapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term $$\alpha R^2$$ α R 2 , and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.
We establish the parameter space geometry of a fluid system characterized by two constants, whose equation of state mimics that of the RN-AdS black hole. We call this the RN-AdS fluid. We study the scalar curvature on the parameter space of this system, and show its equivalence with the RN-AdS black hole, in the limit of vanishing specific heat at constant volume. Further, an analytical construction of the Widom line is established. We also numerically study the behavior of geodesics on the parameter space of the fluid, and find a geometric scaling relation near its second order critical point. *
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