Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed

Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times 10^{-5}$. The point-like mass solution contradicts this restriction. The condition $\tau=0$ satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and to the number of the external dimensions $d_0=3$. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.Comment: 8 pages, Revtex4, no figures, minor changes adde

Aspects of Horava-Lifshitz cosmology

We review some general aspects of Horava-Lifshitz cosmology. Formulating it in its basic version, we extract the cosmological equations and we use observational data in order to constrain the parameters of the theory. Through a phase-space analysis we extract the late-time stable solutions, and we show that eternal expansion, and bouncing and cyclic behavior can arise naturally. Concerning the effective dark energy sector we show that it can describe the phantom phase without the use of a phantom field. However, performing a detailed perturbation analysis, we see that Horava-Lifshitz gravity in its basic version suffers from instabilities. Therefore, suitable generalizations are required in order for this novel theory to be a candidate for the description of nature.Comment: 10 pages, 4 figures, invited talk given at the 2nd International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Assymetry, National Tsing Hua University, Hsinchu, Taiwan, November 5-6, 201

Semi-Classical Description of Antiproton Capture on Atomic Helium

A semi-classical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on Helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular momentum states of incident antiprotons which result in capture via single or double electron ionization, i.e. into [He$^{++}\,\bar p$ or He$^{+}\,\bar p$], and the distribution of energy and angular momentum states following the Auger cascade. These final states are discussed in light of recently reported, anomalously long-lived antiproton states observed in liquid He.Comment: 15 pages, 9 figures may be obtained from authors, Revte

The Roton Fermi Liquid

We introduce and analyze a novel metallic phase of two-dimensional (2d) electrons, the Roton Fermi Liquid (RFL), which, in contrast to the Landau Fermi liquid, supports both gapless fermionic and bosonic quasiparticle excitations. The RFL is accessed using a re-formulation of 2d electrons consisting of fermionic quasiparticles and $hc/2e$ vortices interacting with a mutual long-ranged statistical interaction. In the presence of a strong vortex-antivortex (i.e. roton) hopping term, the RFL phase emerges as an exotic yet eminently tractable new quantum ground state. The RFL phase exhibits a ``Bose surface'' of gapless roton excitations describing transverse current fluctuations, has off-diagonal quasi-long-ranged order (ODQLRO) at zero temperature (T=0), but is not superconducting, having zero superfluid density and no Meissner effect. The electrical resistance {\it vanishes} as $T \to 0$ with a power of temperature (and frequency), $R(T) \sim T^\gamma$ (with $\gamma >1$), independent of the impurity concentration. The RFL phase also has a full Fermi surface of quasiparticle excitations just as in a Landau Fermi liquid. Electrons can, however, scatter anomalously from rotonic "current fluctuations'' and "superconducting fluctuations'', leading to "hot" and "cold" spots. Fermionic quasiparticles dominate the Hall electrical transport. We also discuss instabilities of the RFL to a conventional Fermi liquid and a superconductor. Precisely {\it at} the instability into the Fermi liquid state, the exponent $\gamma =1$, so that $R(T) \sim T$. Upon entering the superconducting state the anomalous quasiparticle scattering is strongly suppressed. We discuss how the RFL phenomenology might apply to the cuprates.Comment: 43 page

Kaluza-Klein models: can we construct a viable example?

In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)\epsilon in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.Comment: 11 pages, Revtex4, no figures, appendix and references adde

The x ray reflectivity of the AXAF VETA-I optics

The x-ray reflectivity of the VETA-I optic, the outermost shell of the AXAF x-ray telescope, with a bare Zerodur surface, is measured and compared with theoretical predictions. Measurements made at energies of 0.28, 0.9, 1.5, 2.1, and 2.3 keV are compared with predictions based on ray trace calculations. The data were obtained at the x-ray calibrations facility at Marshall Space Flight Center with an electron impact x-ray source located 528 m from the grazing incidence mirror. The source used photoelectric absorption filters to eliminate bremsstrahlung continuum. The mirror has a diameter of 1.2 m and a focal length of 10 m. The incident and reflected x-ray flux are detected using two proportional counters, one located in the incident beam of x-rays at the entrance aperture of the VETA-I, and the other in the focal plane behind an aperture of variable size. Results on the variation of the reflectivity with energy as well as the absolute value of the reflectivity are presented. We also present a synchrotron reflectivity measurement with high energy resolution over the range 0.26 to 1.8 keV on a flat Zerodur sample, done at NSLS. We present evidence for contamination of the flat by a thin layer of carbon on the surface, and the possibility of alteration of the surface composition of the VETA-I mirror perhaps by the polishing technique. The overall agreement between the measured and calculated effective area of VETA-I is between 2.6 percent and 10 percent, depending on which model for the surface composition is adopted. Measurements at individual energies deviate from the best-fitting calculation to 0.3 to 0.8 percent, averaging 0.6 percent at energies below the high energy cutoff of the mirror reflectivity, and are as high as 20.7 percent at the cutoff. We also discuss the approach to the final preflight calibration of the full AXAF flight mirror