We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F (X) , X ≡ φ ,α φ ,α . A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F (X) is required to have a finite derivative dF/dX . Two exact solutions are obtained for special cases of k-essence: one for F (X) = F 0 X 1/3 , another for F (X) = F 0 |X| 1/2 − 2Λ , where F 0 and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained no-go theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.

The k-essence theory with a power-law function of (∂φ) 2 and Rastall's non-conservative theory of gravity with a scalar field are shown to have the same solutions for the metric under the assumption that both the metric and the scalar fields depend on a single coordinate. This equivalence (called k-R duality) holds for static configurations with various symmetries (spherical, plane, cylindrical, etc.) and all homogeneous cosmologies. In the presence of matter, Rastall's theory requires additional assumptions on how the stressenergy tensor non-conservation is distributed between different contributions. Two versions of such nonconservation are considered in the case of isotropic spatially flat cosmological models with a perfect fluid: one (R1) in which there is no coupling between the scalar field and the fluid, and another (R2) in which the fluid separately obeys the usual conservation law. In version R1 it is shown that k-R duality holds not only for the cosmological models themselves but also for their adiabatic perturbations. In version R2, among other results, a particular model is singled out that reproduces the same cosmological expansion history as the standard Λ CDM model but predicts different behaviors of small fluctuations in the k-essence and Rastall frameworks. 1

We study the stability properties of static, spherically symmetric configurations in k-essence theories with the Lagrangians of the form F (X), X ≡ φ ,α φ ,α . The instability under spherically symmetric perturbations is proved for two recently obtained exact solutions for F (X) = F 0 X 1/3 and for F (X) = F 0 X 1/2 −2Λ , where F 0 and Λ are constants. The first solution describes a black hole in an asymptotically singular space-time, the second one contains two horizons of infinite area connected by a wormhole. It is argued that spherically symmetric k-essence configurations with n < 1/2 are generically unstable because the perturbation equation is not of hyperbolic type.

In this paper we investigate three theories characterised by non-vanishing divergence of the stress-energy tensor, namely f (R, LM ), f (R, T ), and Rastall theory. We show that it is not possible to obtain the third from the first two, unless in some very specific case. Nonetheless, we show that in the framework of cosmology in the f (R, T ) theory, a result similar to that found in the Rastall one is reproduced, namely that the dynamics of the ΛCDM model of standard cosmology can be exactly mimicked, even though the dark energy component is able to cluster.

We review some properties of black hole structures appearing in gravity with a massless scalar field, with both minimal and nonminimal coupling. The main properties of the resulting cold black holes are described. The study of black holes in scalar-gravity systems is extended to k-essence theories, and some examples are explicitly worked out. In these cases, even while the existence of horizons is possible, the metric regularity requirement on the horizon implies either a cold black type structure or a singular behavior of the scalar field. * kb20@yandex.ru †

We classified and studied the charged black hole and wormhole solutions in the Einstein–Maxwell system in the presence of a massless, real scalar field. The possible existence of charged black holes in general scalar–tensor theories was studied in Bronnikov et al, 1999; black holes and wormholes exist for a negative kinetic term for the scalar field. Using a conformal transformation, the static, spherically symmetric possible structures in the minimal coupled system are described. Besides wormholes and naked singularities, only a restricted class of black hole exists, exhibiting a horizon with an infinite surface and a timelike central singularity. The black holes and wormholes defined in the Einstein frame have some specificities with respect to the non-minimal coupling original frame, which are discussed in the text.

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Quantum gravity is effective in domains where both quantum effects and gravity are important, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity hidden inside the event horizon. Describing the system with a Hamiltonian formalism, we apply the covariant integral method to find the Wheeler-DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum, and the time coefficient g 00 provides the dynamics for this model in a non-trivial way. In a semi-classical analysis, different configurations for the phase space of a Schwarzschild black hole is obtained. I. IntroductionBetween the detection of gravitational waves produced by the merge of two black holes and the release of a shadow-image by the Event Horizon Telescope team, it seems safe to say that the near future of black-hole physics is exciting. New observational techniques and technology provide promising tools for us to learn more about those objects, and the theory tells us there is still plenty to unveil about them. Perhaps the most curious feature of those objects is the singularity hidden by the event horizon-a hole of infinity density in the fabric of space-time. Strange as it is, it is still a proper prediction of general relativity (GR) [1]. It is, however, located in a region forever outside of our reach. The interior of a black hole is inaccessible to external observers. Nevertheless, there is still a chance to test theories about that region via measurable phenomena, like gravitational waves and Hawking radiation.The investigation of black holes using quantum theory is not new. In fact, the thermodynamical theory, proposed in the early 1970s [2], requires the consideration of quantum effects near the event horizon. The imbalance of particle/anti-particle production in this region leads to a low but constant rate of produced particles being emitted to infinity-the Hawking radiation. In the extreme environment of the neighborhood around the singularity, however, gravity virtually annuls any *