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We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three-dimensional backgrounds, including the BTZ black hole in string theory and Lifshitz black hole solutions in conformal gravity and Hu-Sawicki $F(R)$ theory. The main properties of the selected black hole solutions is that their line elements are Weyl related to that of a homogeneous spacetime, whose spatial part possesses Lie symmetry, described by Lobachevsky-type geometry with arbitrary negative Gaussian curvature. Using the Weyl symmetry of massless Dirac action, we consider the perturbation equations of fermionic fields in relation to those of the homogeneous background, which having definite singularities, are transformed into Heun equation. We point out the existence of quasinormal modes labeled by the accessory parameter of the Heun function. The distribution of the quasinormal modes has been clarified to satisfy the boundary conditions that require ingoing and decaying waves at the event horizon and conformal infinity, respectively. It turned out that the procedure based on the Heun function, beside reproducing the previously known results obtained via hypergemetric function for the BTZ and Lifshitz black hole solution in conformal gravity, brings up new families of quasinormal frequencies, which can also contain purely imaginary modes. Also, the analysis of the quasinormal modes shows that with the negative imaginary part of complex frequencies $\omega=\omega_{Re}+i\omega_{Im}$, the fermionic perturbations are stable in this background.

We consider a $(2+1)$-dimensional spacetime whose two-dimensional space part is Weyl-related to a surface of arbitrary negative constant Gaussian curvature with symmetries of two-dimensional Lie algebra. It is shown that the geometry is a Lobachevsky-type geometry described by deformed hyperbolic function. At leading order string effective action with the source given by dilaton and antisymmetric $B$-field in the presence of central charge deficit term $\Lambda$, we obtained a solution whose line element is Weyl-related to this homogeneous spacetime with arbitrary negative Gaussian curvature. The solution can be transformed to the BTZ-like black hole by coordinate redefinition, while the BTZ black hole can be recovered by choosing a special set of parameters. The solutions appear to be in the high curvature limit $R\alpha'\gtrsim1$, with emphasis on including the higher order $\alpha'$ corrections. Considering the two-loop (first order $\alpha'$) $\beta$-function equations of $\sigma$-model, we also present the $\alpha'$-corrected black hole solutions.

In this paper, we present two new families of spatially homogeneous black hole solution for $z=4$ Ho\v{r}ava-Lifshitz Gravity equations in $(4+1)$ dimensions with general coupling constant $\lambda$ and the especial case $\lambda=1$, considering $\beta=-1/3$. The three-dimensional horizons are considered to have Bianchi types $II$ and $III$ symmetries, and hence the horizons are modeled on two types of Thurston $3$-geometries, namely the Nil geometry and $H^2\times R$. Being foliated by compact 3-manifolds, the horizons are neither spherical, hyperbolic, nor toroidal, and therefore are not of the previously studied topological black hole solutions in Ho\v{r}ava-Lifshitz gravity. Using the Hamiltonian formalism, we establish the conventional thermodynamics of the solutions defining the mass and entropy of the black hole solutions for several classes of solutions. It turned out that for both horizon geometries the area term in the entropy receives two non-logarithmic negative corrections proportional to Ho\v{r}ava-Lifshitz parameters. Also, we show that choosing some proper set of parameters the solutions can exhibit locally stable or unstable behavior., Comment: 28 pages, no figures

We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $(2+1)$-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge $B$-field, and central charge deficit term $\Lambda$. At the quantum level, solutions of Wheeler-DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm's mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level., Comment: 3 references added

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge $B$-field. Presence of the considered $B$-field leads to the unusual asymptotic behavior of solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston geometries of $E^3$, $S^3$, $H^3$, $H^2 \times E^1$, $\widetilde{{SL_2R}}$, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton hair is of the secondary type. Furthermore, for Bianchi type $V$, the $T$-dual black hole solution is obtained which carries no charge associated with $B$-field and possesses a dilaton hair of secondary kind. Also, the entropy turns to be invariant under the $T$-duality.

We present non-critical Bianchi type $I$ string cosmology solutions in the presence of central charge deficit term $\Lambda$. The leading order string frame curvature appears to be in the high curvature limit $R\alpha'\gtrsim1$, which underlines the necessity of including higher order $\alpha'$-corrections. We give new solutions of two-loop (order $\alpha'$) $\beta$-function equations of $\sigma$-model with non-zero $\Lambda$ and dilaton field in both cases of absence and presence of spatially homogeneous $H$-field ($H=dB$). Also, the evolution of solutions is studied in the Einstein frame, where the string effective action can transform to Gauss-Bonnet gravity model coupled to the dilaton field with potential. We study explicit examples in order $\alpha'$ with chosen values of appeared constants in the solutions and discuss the cosmological implications.

The two-loop (order $\alpha'$) $\beta$-function equations, which are equivalent to the equations of motion of $\alpha'$-corrected string effective action, are considered for anisotropic homogeneous space-times. These equations are solved for all Bianchi-type models in two schemes of effective action, namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then the metric, dilaton and $B$-field are found at $\alpha'$ perturbative corrections., Comment: 33 pages

We consider a string model at one-loop related to a $\sigma$-model whose antisymmetric tensor field is constructed as complex structure on the background manifold, specially on a manifold $R\times N$ where $N$ is a complex manifold. As an example, we consider a homogeneous anisotropic $(1+4)$-dimensional $\sigma$-model where space part of the background is a $4$-dimensional complex manifold. By solving the related one-loop $\beta$-functions we obtain a static solution so that by reduction of this solution to $(1+3)$-dimension we obtain a static solution of Einstein equation where the matter sector is effectively interpreted as an inhomogeneous, anisotropic and barotropic matter satisfying all the energy conditions. Finally, the $T$-dual background of the solution is investigated and it is shown that the duality transformation and reduction processes commute with each other., Comment: 11 pages

We study two different possibilities of constructing the energy-momentum tensors for non-commutative Abelian Proca field, by using (i) general Noether theorem and (ii) coupling to a weak external gravitational field. Both energy-momentum tensors are not traceless due to the violation of Lorentz invariance in non-commutative spaces. In particular, we show that the obtained energy density of the latter case coincides exactly with that of obtained by Dirac quantization method., Comment: 9 pages

We show that the conservation of energy-momentum tensor of a gravitational model with Einstein-Hilbert like action on a nearly Kahler manifold with the scalar curvature of a curvature-like tensor, is consistent with the nearly Kahler properties. In this way, the nearly Kahler structure is automatically manifested in the action as a induced matter field. As an example of nearly Kahler manifold, we consider the group manifold of R x II x S3 x S3 on which we identify a nearly Kahler structure and solve the Einstein equations to interpret the model. It is shown that the nearly Kahler structure in this example is capable of alleviating the well known fine tuning problem of the cosmological constant. Moreover, this structure may be considered as a potential candidate for dark energy., Comment: 15 pages

Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant. Then, the system of second class constraints is quantized by introducing Dirac brackets in the reduced phase space., Comment: 12 pages, minor revision

UNKNOWN

vast oceans inside most of the large Jovian and Saturnian icy moons, and Kuiper Belt Objects like Triton, Charon, and Pluto whose geologies are dominated by water and ammonia. Key pieces of the ocean-world science puzzle – which when completed may reveal whether life is widespread in the cosmos, why it exists where it does, and how it originates – are distributed among them. The eventual exploration of all these worlds will yield humanity’s total tangible knowledge about life in the universe, essentially forever. Thus, their exploration has existential significance for humanity’s self-regard, and indeed perhaps of our place in the natural scheme. The matter of planning how to pursue such a difficult and unprecedented exploration opportunity is therefore historic. The technical challenges are formidable, far harder than at Mars: missions to the Jovian and Saturnian ocean worlds are severely power-limited; trip times can be as much as a half decade and decade, respectively. And the science targets are global-scale oceans beneath kilometers of cryogenic ice. Reaching and exploring them would be a multi-generational undertaking, so again it is essential to plan and prepare. Today, we lack the instrumentation, subsystems, and remote operationalintelligence technologies needed to build and use exploration avatars as good as what we can envision needing.

NASA's newly restructured Mars Exploration Program (MEP) is finally on the way to Mars with the successful April 7 launch of the 2001 Mars Odyssey Orbiter. In addition, the announcement by the Bush Administration that the exploration of Mars will be a priority within NASA's Office of Space Science further cements the first decade of the new millennium as one of the major thrusts to understand the "new" Mars. Over the course of the past year and a half, an integrated team of managers, scientists, and engineers has crafted a revamped MEP to respond to the scientific as well as management and resource challenges associated with deep space exploration of the Red Planet. This article describes the new program from the perspective of its guiding philosophies, major events, and scientific strategy. It is intended to serve as a roadmap to the next 10-15 years of Mars exploration from the NASA viewpoint. [For further details, see the Mars Exploration Program web site (URL): http://mars.jpl.nasa.gov]. The new MEP will certainly evolve in response to discoveries, to successes, and potentially to setbacks as well. However, the design of the restructured strategy is attentive to risks, and a major attempt to instill resiliency in the program has been adopted. Mars beckons, and the next decade of exploration should provide the impetus for a follow-on decade in which multiple sample returns and other major program directions are executed. Ultimately the vision to consider the first human scientific expeditions to the Red Planet will be enabled. By the end of the first decade of this program, we may know where and how to look for the elusive clues associated with a possible martian biological record, if any was every preserved, even if only as "chemical fossils.".

We examine, from a multimission program perspective, key issues and recommended strategies for three aspects of telecommunications and navigation support to future Mars exploration missions.