Lovelock theory is a natural extension of the Einstein theory of general relativity to higher dimensions in which the first and second orders correspond, respectively, to general relativity and Einstein-Gauss-Bonnet gravity. We present exact black hole solutions of D ≥ 4-dimensional spacetime for first-, second-, and third-order Lovelock gravities in a string cloud background. Further, we compute the mass, temperature, and entropy of black hole solutions for the higher-dimensional general relativity and Einstein-Gauss-Bonnet theories and also perform thermodynamic stability of black holes. It turns out that the presence of the Gauss-Bonnet term and/or background string cloud completely changes the black hole thermodynamics. Interestingly, the entropy of a black hole is unaffected due to a background string cloud. We rediscover several known spherically symmetric black hole solutions in the appropriate limits.

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study the shadow cast by the five-dimensional Myers-Perry black hole with equal rotation parameters. We demonstrate that the null geodesic equations can be integrated that allows us to investigate the shadow cast by a black hole. The shadow of a black hole is found to be a dark zone covered by deformed circle. Interestingly, the shapes of the black hole shadow are more distorted and size decreases for larger black hole spins. Interestingly, it turns out that, for fixed values of rotation parameter, the shadow is slightly smaller and less deformed than for its four-dimensional Kerr black counterpart. Further, the shadow of the five-dimensional Kerr black hole is concentric deformed circles. The effect of rotation parameter on the shape and size of a naked singularity shadow is also analyzed.Comment: 11 pages, 8 figures, accepted for publication in Physical Review

We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). We studied the null geodesic equations and obtained the shadow of the charged rotating BH to see the effects of PFDM parameter $\gamma$, charge $Q$ and rotation parameter $a$, and it is noticed that the size as well as the shape of BH shadow is affected due to PFDM parameter, charge and rotation parameter. Thus, it is seen that the presence of dark matter around a BH affects its spacetime. We also investigated the influence of all the parameters (PFDM parameter $\gamma$, BHs charge $Q$ and rotational parameter $a$) on effective potential, energy emission by graphical representation, and compare all the results with the non rotating case in usual general relativity. To this end, we have also explored the effect of PFDM on the deflection angle and the size of Einstein rings.

We derive an exact radiating Kerr-Newman like black hole solution, with constant curvature R = R0 imposed, to metric f (R) gravity via complex transformations suggested by Newman-Janis. This generates a geometry which is precisely that of radiating Kerr-Newman-de Sitter / anti-de Sitter with the f (R) gravity contributing an R0 cosmological-like term. The structure of three horizonlike surfaces, viz. timelike limit surface, apparent horizon and event horizon, are determined. We demonstrate the existence of an additional cosmological horizon, in f (R) gravity model, apart from the regular black hole horizons that exist in the analogous general relativity case. In particular, the known stationary Kerr-Newman black hole solutions of f (R) gravity and general relativity are retrieved. We find that the timelike limit surface becomes less prolate with R0 thereby affecting the shape of the corresponding ergosphere.

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