The recent observation of the shadow of the supermassive black hole M87*, located at the center of the M87 galaxy, by the Event Horizon Telescope Collaboration has opened up a new window to probe the strong gravity regime. In this paper, we explicitly demonstrate the consequences of this observation on brane world black holes, characterized by existence of a negative tidal charge. Our results based on three observables associated with the shadow, namely, angular diameter, deviation from circularity, and axis ratio reveal that the existence of a negative tidal charge is more favored, possibly marking a deviation from general relativity.

We have explicitly demonstrated that scalar coupled Gauss-Bonnet gravity in four dimensions can have nontrivial effects on the early inflationary stage of our Universe. In particular, we have shown that the scalar coupled Gauss-Bonnet term alone is capable of driving the inflationary stages of the Universe without incorporating slow roll approximation, while remaining compatible with the current observations. Subsequently, to avoid the instability of the tensor perturbation modes we have introduced a self-interacting potential for the inflaton field and have shown that, in this context as well, it is possible to have an inflationary scenario. Moreover, it turns out that presence of the Gauss-Bonnet term is incompatible with the slow roll approximation and hence one must work with the field equations in the most general context. Finally, we have shown that the scalar coupled Gauss-Bonnet term attains smaller and smaller values as the Universe exits from inflation. Thus, at the end of the inflation, the Universe makes a smooth transition to Einstein gravity.

Introducing \(f(\mathcal {R})\) term in the five-dimensional bulk action we derive effective Einstein’s equation on the brane using Gauss–Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with \(f(\mathcal {R})\) gravity in the bulk.

Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for asymptotically flat spacetimes, a potential failure of the strong cosmic censorship conjecture might arise for spacetimes inheriting Cauchy horizon along with a positive cosmological constant. We have explicitly demonstrated that violation of the censorship conjecture holds true in the presence of a Maxwell field even when higher spacetime dimensions are invoked. In particular, for a higher dimensional Reissner-Nordström-de Sitter black hole the violation of cosmic censorship conjecture is at a larger scale compared to the four dimensional one, for certain choices of the cosmological constant. On the other hand, for a brane world black hole, the effect of extra dimension is to make the violation of cosmic censorship conjecture weaker. For rotating black holes, intriguingly, the cosmic censorship conjecture is always respected even in presence of higher dimensions. A similar scenario is also observed for a rotating black hole on the brane.