We study the shadows cast by the different types of rotating regular black holes viz. Ay\'on-Beato-Garc\'ia {(ABG)}, Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$), respectively. Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically and the distortion parameter increases when the value of these parameters increase. A comparison with the standard Kerr case is also investigated. We have also studied the influence of the plasma environment around regular black holes to discuss its shadow. The presence of the plasma affects the apparent size of the regular black hole's shadow to be increased due to two effects (i) gravitational redshift of the photons and (ii) radial dependence of plasma density.Comment: 11 pages, 11 figures, accepted for publication in Physical Review

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.

The spacetime singularities in classical general relativity are inevitable, as predicated by the celebrated singularity theorems. However, it is a general belief that singularities do not exist in Nature and that they are the limitations of the general relativity. In the absence of a welldefined quantum gravity, models of regular black holes have been studied. We employ a probability distribution inspired mass function m(r ) to replace the Kerr black hole mass M to represent a nonsingular rotating black hole that is identified asymptotically (r k, k > 0 constant) exactly as the KerrNewman black hole, and as the Kerr black hole when k = 0. The radiating counterpart renders a nonsingular generalization of Carmeli's spacetime as well as Vaidya's spacetime, in the appropriate limits. The exponential correction factor changing the geometry of the classical black hole to remove the curvature singularity can also be motivated by quantum arguments. The regular rotating spacetime can also be understood as a black hole of general relativity coupled to nonlinear electrodynamics.The celebrated theorems of Penrose and Hawking [1] state that under some circumstances singularities are inevitable in general relativity. For the Kerr solution these singularities have the shape of a ring, this case is timelike. The Kerr metric [2] is undoubtedly the most remarkable exact solution in the Einstein theory of general relativity, which represents the prototypical black hole that can arise from gravitational collapse, which contains an event horizon [3]. Thanks to the no-hair theorem, the vacuum region outside a stationary black hole has a Kerr geometry. It is believed that spacetime singularities do not exist in Nature; they are a creation of general relativity. It turns out that we need to ask to what extent a singularity in general relativity could be adequately explained by some other theory, say, quantum gravity. However, we are yet afar from a specific theory of quantum gravity. So a suitable course of action is to understand the inside of a black hole and resolve its singularity by carrying out research of a