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The Janis-Newman-Winicour spacetime corresponds to a static spherically symmetric solution of Einstein equations with the energy momentum tensor of a massless quintessence field. It is understood that the spacetime describes a naked singularity. The solution has two parameters, $b$ and $s$. To our knowledge, the exact physical meaning of the two parameters is still unclear. In this paper, starting from the Janis-Newman-Winicour naked singularity solution, we first obtain a wormhole solution by a complex transformation. Then let the parameter $s$ approaching infinity, we obtain the well-known exponential wormhole solution. After that, we embed both the Janis-Newman-Winicour naked singularity and its wormhole counterpart in the background of de Sitter or anti-de Sitter Universe with the energy momentum tensor of massive quintessence and massive phantom fields, respectively. To our surprise, the resulting quintessence potential is actually the dilaton potential found by one of us. It hints us that, by modulating the parameters in the charged dilaton black hole solutions we can get the Janis-Newman-Winicour solution. Furthermore, a charged wormhole solution is obtained by performing complex transformation on the charged dilaton black hole solutions in the background of de Sitter or anti-de Sitter Universe. We eventually find that $s$ is actually related to the coupling constant of dilaton field to Maxwell field and $b$ is related to a negative mass for the dilaton black holes. A negative black hole mass is physically forbidden. Therefore, we conclude that the Janis-Newman-Winicour naked singularity solution is not physically allowed., Comment: 20 pages,3 figures

In this article, we consider the $4+n$ dimensional spacetimes among which one is the four dimensional physical Universe and the other is an n-dimensional sphere with constant radius in the framework of Lanczos-Lovelock gravity. We find that the curvature of extra dimensional sphere contributes a huge but negative energy density provided that its radius is sufficiently small, such as the scale of Planck length. Therefore, the huge positive vacuum energy, i.e. the large positive cosmological constant is exactly cancelled out by the curvature of extra sphere. In the mean time the higher order of Lanczos-Lovelock term contributes an observations-allowed small cosmological constant if the number of extra dimensions is sufficiently large, such as $n\approx{69}$., Comment: 8 pages

K-essence theories are usually studied in the framework of one scalar field $\phi$. Namely, the Lagrangian of K-essence is the function of scalar field $\phi$ and its covariant derivative. However, in this paper, we explore a two-field pure K-essence, i.e. the corresponding Lagrangian is the function of covariant derivatives of two scalar fields without the dependency of scalar fields themselves. That is why we call it pure K-essence. The novelty of this K-essence is that its Lagrangian contains the quotient term of the kinetic energies from the two scalar fields. This results in the presence of many interesting features, for example, the equation of state can be arbitrarily small and arbitrarily large. As a comparison, the range for equation of state of quintessence is from $-1$ to $+1$. Interestingly, this novel K-essence can play the role of inflation field, dark matter and dark energy. Finally, the absence of the scalar fields themselves in the equations of motion makes the study considerable simple such that even the exact black hole solutions can be found., Comment: 12 pages,18 figures

We propose the metric for general rotating spacetimes. These spacetimes are stationary, axially symmetric and spatially asymptotically flat. They can be the spacetimes outside of rotating black holes or rotating celestial bodies such as the Sun and the Earth. The metric functions are expanded in power series of distance and the angle variable is included in the expansion coefficients., Comment: 11 pages

It is commonly assumed that the Lagrangian of multi-field theories of gravity contains the sum of kinetic terms of scalar fields. However, we propose here the Lagrangian contains not the sum but the quotient of kinetic terms. With this novel change, we find the inflationary universe can be acquired with two scalars without the slow-roll approximation. On the other hand, a constant dark energy density can also be achieved with two scalars while without the need of Einstein cosmological constant., Comment: 10 pages, references added

Hartle and Hawking have shown that, except for the case of only point monopoles as sources, both the Majumdar-Papapetrou and the Perj\'es-Israel-Wilson solutions have naked singularities if the space is asymptotically flat. In this article, by using the method of introducing interior solutions, these naked singularities are erased., Comment: 9 pages

By using the Taylor series method and the solution-generating method, we construct exact black hole solutions with minimally coupled scalar field. We find that the black hole solutions can have many hairs except for the physical mass. These hairs come from the scalar potential. Unlike the mass, there is no symmetry corresponding to these hairs, thus they are not conserved and one cannot understand them as Noether charges. They arise as coupling constants. Although there are many hairs, the black hole has only one horizon. The scalar potential becomes negative for sufficient large $\phi$ (or in the vicinity of black hole singularity). Therefore, the no-scalar-hair theorem does not apply to our solutions since the latter does not obey the dominant energy condition. Although the scalar potential becomes negative for sufficient large $\phi$, the black holes are stable to both odd parity perturbations and scalar perturbations. As for even parity perturbations, we find there remains parameter space for the stability of the black holes. Finally, the black hole thermodynamics are developed., Comment: 12 pages, 4 figures

The Bekenstein's theorem allows us to generate a Einstein-conformal scalar solution from a single Einstein-ordinary scalar solution. In this article, we extend this theorem to Einstein-Maxwell-scalar (EMS) theory with a non-minimal coupling between the scalar and Maxwell field. As applications of this extended theorem, the well-known static dilaton solution and rotating solution with a specific coupling between dilaton and Maxwell field are considered, and new conformal dilaton black hole solutions are found. The Noether charges such as the mass, electric charge, angular momentum are compared between the old and new black hole solutions connected by conformal transformations, and they are found conformally invariant. We speculate that the theorem may be helpful in the computations of metric perturbations and spontaneous scalarization of black holes in the Einstein-Maxwell-conformal-scalar theory since they can be mapped to the corresponding EMS theories, which have been investigated in detail.

In this article, we construct exact black hole solutions with many horizons (more than number two) in the Einstein-nonlinear electrodynamic theories. In particular, we acquire the explicit expression of nonlinear electrodynamic Lagrangian for the 3-horizon black holes. Then we make the investigations of 3-horizon black holes on the horizons, the null and timelike geodesics, the Love numbers and the thermodynamics., Comment: 15 pages,5 figures,some references added. To appear in PRD

It is found that, when the coupling constants $\alpha_p$ in the theory of regularized Lovelock gravity are properly chosen and the number of Lovelock tensors $p\rightarrow \infty$, there exist a fairly large number of nonsingular (singularity free) black holes and nonsingular universes. Some nonsingular black holes have numerous horizons and numerous energy levels (a bit like atom) inside the outer event horizon. On the other hand, some nonsingular universes start and end in two de Sitter phases. The ratio of energy densities for the two phases are $120$ orders. It is thus helpful to understand the cosmological constant problem., Comment: 22 pages, 12 figures, 8 tables

The recently proposed regularized Lovelock tensors are kinetically coupled to the scalar field. The resulting equation of motion is second order. In particular, it is found that when the $p=3$ regularized Lovelock tensor is kinetically coupled to the scalar field, the scalar field is the potential candidate of cosmic dark energy., Comment: 7 pages, 2 figures

We construct higher dimensional and exact black holes in Einstein-Maxwell-scalar-theory. The strategy we adopted is to extend the known, static and spherically symmetric black holes in the Einstein-Maxwell-dilaton gravity and Einstein-Maxwell-scalar theory. Then we investigate the black hole thermodynamics. Concretely, the generalized Smarr formula and the first law of thermodynamics are derived., Comment: 12 pages 2 figures

Exact black hole solutions in the Einstein-Maxwell-scalar theory are constructed. They are the extensions of dilaton black holes in de Sitter or anti de Sitter universe. As a result, except for a scalar potential, a coupling function between the scalar field and the Maxwell invariant is present. Then the corresponding Smarr formula and the first law of thermodynamics are investigated., Comment: 25 pages,8 figures

We find an exact black hole solution with a minimally coupled scalar field. The corresponding spacetime has two horizons and one of the them is the black hole event horizon and the other is the cosmic horizon. In this sense, the solution is analogous to the Schwarzschild-de Sitter (or anti-de Sitter) spacetime. We investigate the thermodynamics and construct the first law of thermodynamics. At the same time, we make a study on the shadow and quasinormal modes of this black hole solution., Comment: 9 pages, 4 figures

We propose gravity, matters and dark energy may be confined on different four dimensional \emph{minimal surfaces} for the observer in five dimensional spacetime. Following this idea, we construct the equations of motion when gravity, matters and dark energy are confined on different minimal surfaces. Then in the background of Friedman-Robertson-Walker universe, we investigate the cosmic evolution when gravity and quintessence are confined on the minimal surfaces., Comment: 10pages,6figures

We construct exact black hole solutions to Einstein gravity with nonlinear electrodynamic field. In these solutions, there are in general four parameters. They are physical mass, electric charge, cosmological constant and the coupling constant. Due to the presence of coupling constant, these solutions differ significantly from the Reissner-Nordstrom-de Sitter solution in Einstein-Maxwell gravity with a cosmological constant. In the first place, some of them are endowed with a topological defect on angle $\theta$. Secondly, for the extreme charged black holes, the electric charge can be much larger or much smaller than the mass by varying the coupling constant. Thirdly, for very large coupling constant, the radius of event horizon for some black holes approaches $2M$ regardless of the electric charge. Lastly, some black holes are asymptotically neither flat nor de Sitter (or anti-de Sitter)., Comment: 8 pages, 7figures

We investigate the quasinormal modes of a class of static and spherically symmetric black holes with the derivative coupling. The derivative coupling has rarely been paid attention to the study of black hole quasinormal modes. Specifically, we study the effect of derivative coupling on the quasinormal modes for four kinds of black holes. They are Reissner-Nordstrom black holes, Bardeen black holes, noncommunicative geometry inspired black holes and dilaton black holes. These black holes are not the solutions of vacuum Einstein equations which guarantees the effect of derivative coupling is not trivial. We find the influence of derivative coupling on the quasinormal modes roughly mimics the overtone numbers. In other words, there is a qualitative similarity in the trend of quasinormal modes frequencies due to increasing either the coupling constant and the overtone number., Comment: 13 pages,7 figures. GRG accepted

The Horndeski theories are extended into the Lovelock gravity theory. When the canonical scalar field is uniquely kinetically coupled to the Lovelock tensors, it is named after Lovelock scalar field. The Lovelock scalar field model is a subclass of the new Horndeski theories. A most attractive feature of the Lovelock scalar field is its equation of motion is second order. So it is free of ghosts. We study the cosmology of Lovelock scalar field in the background of $7$ dimensional spacetime and present a class of cosmic solutions. These solutions reveal the physics of the scalar field is rather rich and merit further study., Comment: 9 pages,8 figures. errors corrected, references added

We investigate the problem of static and spherically symmetric solutions in the Starobinsky gravity model. By extending the Lichnerowicz and Israel theorems, William Nelson have demonstrated that the Schwarzschild solution is the unique static, spherically symmetric, and asymptotically flat black hole solution in the Starobinsky model. However, Hong L{\"u} et al find that there are sign errors in the proof of Nelson. This raises the problem whether Nelson's proof is correct or not. In order to answer this question, we explore the corresponding solutions by using the Taylor series expansion method. We find that Nelson's conclusion is indeed correct despite the flaw in the proof., Comment: 7 pages, RAA accepted

A stationary and spherically symmetric black hole (For example, Reissner-Nordstrom black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves., Comment: 14 pages, 7 figures. The Penrose diagrams are corrected. PRD accepted

The Hawking-Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner-Nordstr\"om situation. For a distant observer the {horizon} crossing occurs in an infinite time and the pulsations of the black hole quantum "beating heart" are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any., Comment: 24 pages, 2 figures. GRG accepted

We find a new method for looking for the static and spherically symmetric solutions in $F(R)$ theory of gravity. With this method, a number of new solutions in terms of the analytic functions are obtained. We hope this investigation may be of some help in the searching for some other solutions in $F(R)$ theory of gravity., Comment: 8 pages, 2 figures,accepted by GRG

We find a method to rewrite the equations of motion of scalar fields, generalized DBI field and quintessence, in the autonomous form for\emph{arbitrary} scalar potentials. With the aid of this method, we explore the cosmic evolution of generalized DBI field and quintessence with the potential of multiple vacua. Then we find that the scalars are always frozen in the false or true vacuum in the end. Compared to the evolution of quintessence, the generalized DBI field has more times of oscillations around the vacuum of the potential. The reason for this point is that, with the increasing of speed $\dot{\phi}$, the friction term of generalized DBI field is greatly decreased. Thus the generalized DBI field acquires more times of oscillations., Comment: 8 pages, 9 figures, accepted by IJTP. A number of typos corrected

Motivated by the mathematic theory of split-complex numbers (or hyperbolic numbers, also perplex numbers) and the split-quaternion numbers (or coquaternion numbers), we define the notion of split-complex scalar field and the split-quaternion scalar field. Then we explore the cosmic evolution of these scalar fields in the background of spatially flat Friedmann-Robertson-Walker Universe. We find that both the quintessence field and the phantom field could naturally emerge in these scalar fields. Introducing the metric of field space, these theories fall into a subclass of the multi-field theories which have been extensively studied in inflationary cosmology., Comment: 14 pages, 14 figures