We obtain an exact Kerr like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane rc decreases with the Lorentz breaking constant ℓ > 0, and increases with ℓ < 0.

In the framework of the Einstein-Maxwell-aether theory, we present two new classes of exact charged black hole solutions, which are asymptotically flat and possess the universal as well as Killing horizons. We also construct the Smarr formulas, and calculate the temperatures of the horizons, using the Smarr mass-area relation. We find that, in contrast to the neutral case, such obtained temperature is not proportional to its surface gravity at any of the two kinds of the horizons. Einstein-Maxwell-aether black holes with the cosmological constant and their topological cousins are also given.Comment: revtex4, 3 figures. To appear in Phys. Rev. D. arXiv admin note: text overlap with arXiv:1202.4497 by other author

We study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles.We find that the CM energy depends not only on the rotation parameter, a, but also on the NUT charge of the Kerr-Taub-NUT spacetime, n. Especially, for the extremal Kerr-Taub-NUT spacetime, an unlimited CM energy can be approached if the parameter a is in the range [1,√ 2], which is different from that of the Kerr and Kerr-Newman black holes.