In this paper, we study the existence of universal horizons in a given static spacetime, and find that the test khronon field can be solved explicitly when its velocity becomes infinitely large, at which point the universal horizon coincides with the sound horizon of the khronon. Choosing the timelike coordinate aligned with the khronon, the static metric takes a simple form, from which it can be seen clearly that the metric is free of singularity at the Killing horizon, but becomes singular at the universal horizon. Applying such developed formulas to three well-known black hole solutions, the Schwarzschild, Schwarzschild anti-de Sitter, and Reissner-Nordstr\"om, we find that in all these solutions universal horizons exist and are always inside the Killing horizons. In particular, in the Eddington-Finkelstein and Painleve-Gullstrand coordinates, in which the metrics are not singular when crossing both of the Killing and universal horizons, the peeling-off behavior of the khronon is found only at the universal horizons, whereby we show that the values of surface gravity of the universal horizons calculated from the peeling-off behavior of the khronon match with those obtained from the covariant definition given recently by Cropp, Liberati, Mohd and Visser.Comment: revtex4, 17 figures. Version appeared in Phys. Rev. D91, 024047 (2015

In this paper, we have studied nonstationary radiative spherically symmetric spacetime, in general covariant theory (U (1) extension) of Hořava-Lifshitz gravity without the projectability condition and in the infrared limit. The Newtonian prepotential ϕ was assumed null. We have shown that there is not the analogue of the Vaidya's solution in the Hořava-Lifshitz Theory (HLT), as we know in the General Relativity Theory (GRT). Therefore, we conclude that the gauge field A should interact with the null radiation field of the Vaidya's spacetime in the HLT.

In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory (U (1) extension) of the Hořava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the post-newtonian approximation (PPN) in the infrared limit. The Newtonian prepotential ϕ was assumed null. The aim of this work is to know if we can have the same spacetime, as we know in the General Relativity Theory (GRT), in Hořava-Lifshitz Theory (HLT) in this limit. We have shown that there is not an analogy of the dust solution in HLT with the minimally coupling, as in GRT. Using non-minimum coupling with matter, we have shown that the solution admits a process of gravitational collapse, leaving a singularity at the end. This solution has, qualitatively, the same temporal behaviour as the dust collapse in GRT. However, we have also found a second possible solution, representing a bounce behavior that is not found in GRT.

The Einstein's equations can be solved in order to find which energy-momentum tensor corresponds to a given geometry of space-time. However, these solutions sometimes have not any physical meaning. To choose which solutions have physical meaning, we use the energy conditions. This work presents the explicit expressions of the energy conditions for the electromagnetic field in the vacuum and in the presence of the cosmological constant. The Analysis of these two cases produces some bounds for the value of cosmological constant, showing a relation between it and the electromagnetic field present in the space-time. In particular, it is shown that the cosmological constant need to have a value bigger than that one considered in cosmological models in order to characterize a dark energy fluid in the presence of electromagnetic fields.