We construct the conserved charge of generic gravity theories built on arbitrary contractions of the Riemann tensor (but not on its derivatives) for asymptotically (anti)-de Sitter spacetimes. Our construction is a generalization of the Abbott-Deser-Tekin charges of linear and quadratic gravity theories in cosmological backgrounds. As an explicit example we find the energy and angular momentum of the Banados-Teitelboim-Zanelli black hole in the (2 þ 1)-dimensional Born-Infeld gravity.

We present a new stationary solution to the field equations of Hořava-Lifshitz gravity with the detailed balance condition and for any value of the coupling constant > 1=3. This is the generalization of the corresponding spherically symmetric solution earlier found by Lü, Mei, and Pope to include a small amount of angular momentum. For the relativistic value ¼ 1, the solution describes slowly rotating AdS type black holes. With a soft violation of the detailed balance condition and for ¼ 1, we also find such a generalization for the Schwarzschild type black hole solution of the theory. Finally, using the canonical Hamiltonian approach, we calculate the mass and the angular momentum of these solutions.

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the “aether”. In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory (NAT)—a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordström-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT: We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions—AdS-plane waves and pp-waves—in this theory in any dimension . Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a “mass” determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.

We study some physical properties of black holes in Null Aether Theory (NAT)a vector-tensor theory of gravity. We first review the black hole solutions in NAT and then derive the first law of black hole thermodynamics. The temperature of the black holes depends on both the mass and the NAT "charge" of the black holes. The extreme cases where the temperature vanishes resemble the extreme Reissner-Nordström black holes. We also discuss the contribution of the NAT charge to the geodesics of massive and massless particles around the NAT black holes. *

The collision of pure electromagnetic plane waves with collinear polarization in N-dimensional (N = 2 + n) Einstein-Maxwell theory is considered. A class of exact solutions for the higher dimensional Bell-Szekeres metric is obtained and its singularity structure is examined. © 2003 The American Physical Society