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 derived the differential equation governing the evolution of the photon sphere for dynamical black hole spacetimes with or without spherical symmetry. Numerical solution of the same depicting evolution of the photon sphere has been presented for Vaidya, Reissner-Nordström-Vaidya and de Sitter Vaidya spacetimes. It has been pointed out that evolution of the photon sphere depends crucially on the validity of the null energy condition by the infalling matter and may present an observational window to even test it through black hole shadow. We have also presented the evolution of the photon sphere for slowly rotating Kerr-Vaidya spacetime and associated structure of black hole shadow. Finally, the effective graviton metric for Einstein-Gauss-Bonnet gravity has been presented, and the graviton sphere has been contrasted with the photon sphere in this context.

The emergent gravity paradigm interprets gravitational field equations as describing the thermodynamic limit of the underlying statistical mechanics of microscopic degrees of freedom of the spacetime. The connection is established by attributing a heat density $Ts$ to the null surfaces where $T$ is the appropriate Davies-Unruh temperature and $s$ is the entropy density. The field equations can be obtained from a thermodynamic variational principle which extremizes the total heat density of all null surfaces. The explicit form of $s$ determines the nature of the theory. We explore the consequences of this paradigm for an arbitrary null surface and highlight the thermodynamic significance of various geometrical quantities. In particular, we show that (a) a conserved current, associated with the time development vector in a natural fashion, has direct thermodynamic interpretation in all Lanczos-Lovelock models of gravity; (b) one can generalize the notion of gravitational momentum, introduced in T. Padmanabhan, [arXiv:1506.03814] to all Lanczos-Lovelock models of gravity such that the conservation of the total momentum leads to the relevant field equations; (c) the thermodynamic variational principle which leads to the field equations of gravity can also be expressed in terms of the gravitational momentum in all Lanczos-Lovelock models; and (d) three different projections of gravitational momentum related to an arbitrary null surface in the spacetime lead to three different equations, all of which have thermodynamic interpretation. The first one reduces to a Navier-Stokes equation for the transverse drift velocity. The second can be written as a thermodynamic identity $TdS=dE+PdV$. The third describes the time evolution of the null surface in terms of suitably defined surface and bulk degrees of freedom. The implications are discussed.

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.