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 in-falling 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. * akash.mishra@iitgn.ac.in

Deterministic nature of general relativity is ensured by the strong cosmic censorship conjecture, which asserts that spacetime cannot be extended beyond Cauchy horizon with square integrable connection. Although this conjecture holds true for asymptotically flat black hole spacetimes in general relativity, a potential violation of this conjecture occurs in charged asymptotically de Sitter spacetimes. Since it is expected that Einstein-Hilbert action will involve higher curvature corrections, in this article we have studied whether one can restore faith in the strong cosmic censorship when higher curvature corrections to general relativity are considered. Contrary to our expectations, we have explicitly demonstrated that not only a violation to the conjecture occurs near extremality, but the violation appears to become stronger as the strength of the higher curvature term increases. * akash.mishra@iitgn.ac.in

Physical process version of the first law of black hole mechanics relates the change in entropy of a perturbed Killing horizon, between two asymptotic cross sections, to the matter flow into the horizon. Here, we study the mathematical structure of the physical process first law for a general diffeomorphism invariant theory of gravity. We analyze the effect of ambiguities in the Wald's definition of entropy on the physical process first law. We show that for linearized perturbations, the integrated version of the physical process law, which determines the change of entropy between two asymptotic cross-sections, is independent of these ambiguities. In case of entropy change between two intermediate cross sections of the horizon, we show that it inherits additional contributions, which coincide with the membrane energy associated with the horizon fluid. Using this interpretation, we write down a physical process first law for entropy change between two arbitrary non-stationary cross sections of the horizon for both general relativity and Lanczos-Lovelock gravity. * akash.mishra@iitgn.ac.in † sumantac.physics@gmail.com ‡ avirup.ghosh@iitgn.ac.in § sudiptas@iitgn.ac.in 1 The requirement that a regular bifurcation surface be present can however be avoided in some quasi-local definitions of horizons viz. Isolated horizons [11,12].

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We study the generalization of the gadenken experiment of overcharging an extremal black hole proposed by Wald in the context of a multi black hole solution. In particular, we attempt to overcharge a system of two extremal black holes via test particle absorption to produce a system involving a black hole and a naked singularity. If such a process is possible, then this would be a potential violation of the cosmic censorship hypothesis. However, we find that, analogous to Wald's result for a single charged black hole, such a test particle which can expose the singularity, would not be able to enter the horizon. This provides an interesting and non-trivial example that supports the validity of the cosmic censorship hypothesisin four dimensional general relativity. * akash.mishra@iitgn.ac.in † sudiptas@iitgn.ac.in

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass M and the angular momentum J, known as the ‘tidal charge’ parameter, $$\beta $$ β . In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through – (a) negative values of $$\beta $$ β , and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of $$\beta $$ β correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given $$\beta $$ β ) of the frequency and damping time of the least-damped $$\ell =2,m=2$$ ℓ = 2 , m = 2 quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, $$\beta \lesssim -0.05$$ β ≲ - 0.05 , providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.

Dark Energy is the dominant component of the energy density of the universe. In a previous paper, we have shown that the collapse of dark energy fields leads to the formation of Super Massive Black Holes with masses comparable to the masses of Black Holes at the centers of galaxies. Thus it becomes a pressing issue to investigate the other physical consequences of the collapse of Dark Energy fields. Given that the primary interactions of Dark Energy fields with the rest of the Universe are gravitational, it is particularly interesting to investigate the gravitational wave signals emitted during the process of the collapse of Dark Energy fields. This is the focus of the current work described in this paper. We describe and use the 3+1 BSSN formalism to follow the evolution of the dark energy fields coupled with gravity and to extract the gravitational wave signals. Finally, we describe the results of our numerical computations and the gravitational wave signals produced as a result of the collapse of the dark energy fields.

General relativity may be an effective theory with higher curvature correction terms in the action. Inclusion of these terms leads to exciting new possibilities, e.g., gravitational and electromagnetic perturbations following different geodesics; leading to a time delay. Such a time delay was observed between the gravitational wave event GW170817 and its electromagnetic counterpart GRB 170817A. We describe how this effect can be used to constrain the coupling of the higher curvature term. Our method is sufficiently general and applicable to any higher curvature theory.