For various reasons a number of authors have mooted an "exponential form" for the spacetime metric: ds 2 = −e −2m/r dt 2 + e +2m/r {dr 2 + r 2 (dθ 2 + sin 2 θ dφ 2 )}.While the weak-field behaviour matches nicely with weak-field general relativity, and so also automatically matches nicely with the Newtonian gravity limit, the strong-field behaviour is markedly different. Proponents of these exponential metrics have very much focussed on the absence of horizons -it is certainly clear that this geometry does not represent a black hole. However, the proponents of these exponential metrics have failed to note that instead one is dealing with a traversable wormhole -with all of the interesting and potentially problematic features that such an observation raises. If one wishes to replace all the black hole candidates astronomers have identified with traversable wormholes, then certainly a careful phenomenological analysis of this quite radical proposal should be carried out.

So-called "dirty" black holes are those surrounded by non-zero stress-energy, rather than vacuum. The presence of the non-zero stress-energy modifies key features of the black hole, such as the surface gravity, Regge-Wheeler equation, linear stability, and greybody factors in a rather nontrivial way. Working within the inverse-Cowling approximation, (effectively the test-field limit), we shall present general forms for the Regge-Wheeler equation for linearized spin 0, spin 1, and axial spin 2 perturbations on an arbitrary static spherically symmetric background spacetime. Using very general features of the background spacetime, (in particular the classical energy conditions for the stress-energy surrounding the black hole), we extract several interesting and robust bounds on the behaviour of such systems, including rigorous bounds on the greybody factors for dirty black holes.

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Three-form field can give rise to viable cosmological scenarios of dark energy with potentially observable signatures distinct from standard single scalar field models. In this study, the background dynamics of three-form cosmology are investigated. Our analysis suggests that the potential of three-form field should be runaway. We also investigate the possibility to solve the coincidence problem by using the coupling of three-form field to dark matter. Four types of coupling form are examined and we find that the coupling of the form Q = √ 6Γ(Ẋ + 3HX)/κ provides the possibility to solve the coincidence problem. ContentsRecently, dark energy from three-form field has been studied and it is found that three-form field can provide the accelerating universe [20]. However, the coincidence problem cannot be solved since there are no stable fixed points at which energy densities of dark matter and dark energy are comparable. According to interacting scalar models, there are three classes of coupling form,where subscript φ and c denote the contribution for the scalar field and cold dark matter respectively. For the first type, it cannot provide the standard evolution of the universe while with the same parameters the coincidence problem is solved [21]. For the second and third types with exponential potential and α φ = 0 case, the coincidence problem cannot be solved since there are no stable fixed points at which Ω φ /Ω c ∼ O(1) [12]. However, in the case of α φ = 0 and ω φ = constant, there are the fixed points which provide the possibility to solve the coincidence problem. Nevertheless, they also yield the negative energy density of the dark energy [22,23]. From many investigations of the interacting scalar field dark energy, it suggests that it is not easy to solve the coincidence problem with the proper behavior of the evolution. Therefore, it is worthwhile to investigate whether the interacting three-form field can provide the possibility to solve the coincidence with the proper behavior of the evolution and this is the aim of our paper.It is important to note that the coupled quintessence with growing matter, a matter consisting of particles with an increasing mass, provides one of the possible solutions to solve the coincidence problem [24]. The candidate of the growing matter is suggested as neutrinos and then the observed dark energy density and the equation of state parameter are determined by the neutrinos mass. Significant results of this model are investigated and compared with the observational data [25].We review dark energy from non-interacting three-form field in section 2. Our analysis suggests that the potential of the three-form field should be runaway. This suggestion is obtained by ensuring the well-behaved evolution of the universe. Analogous to scalar field dark energy, three types of simple coupling form of the three-form field with dark matter are examined for various runaway potentials in section 3. In order to provide the consistent perturbations in the models, three types of the coupling for...