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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2423-2438 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Technical results are presented on motion in N(〉4)D manifolds to clarify the physics of brane theory, Kaluza–Klein theory, induced-matter theory, and string theory. The so-called canonical or warp metric in five dimensions (5D) effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force (per unit mass) parallel to the four-dimensional (4D) velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10−65 g or less, which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(〉4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2193-2200 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the modern version of 5-D general relativity where the fifth dimension induces matter in 4-D space–time, a choice of coordinates and its restrictions on the geometry (a gauge) dictates the physics of the gravitational, electromagnetic, and scalar fields (spin 2, 1, 0). We extend previous work by concentrating on two related problems. First, we use the lapse and shift formalism to carry out a (4+1) split of Kaluza–Klein theory valid in any gauge. Second, we use a conformal gauge to simplify the 5-D field equations, find a plane-wave solution, and identify the energy and momentum of the particle associated with it. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5195-5201 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be nonseparable functions of time and the extra coordinate l and the induced metric on l=const hypersurfaces has the form of a Friedmann–Robertson–Walker cosmology. The 5D manifold and 3D and 4D submanifolds are in general curved, which distinguishes this solution from previous ones in the literature. The singularity structure of the manifold is explored: some models in the class do not exhibit a big bang, while others exhibit a big bang and a big crunch. For the models with an initial singularity, the equation of state of the induced matter evolves from radiation-like at early epochs to Milne-like at late times and the big bang manifests itself as a singular hypersurface in 5D. The projection of comoving 5D null geodesics onto the 4D submanifold is shown to be compatible with standard 4D comoving trajectories, while the expansion of 5D null congruences is shown to be in line with conventional notions of the Hubble expansion. © 2001 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 6907-6914 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: When general relativity is extended from four to five dimensions, as in the theory of Kaluza and Klein, the relations for the classical tests are modified. The light-deflection problem shows a particularly interesting modification. We derive the general expression for light deflection by a massive body in the five-dimensional theory, and show that it can lead to significantly reduced deflection angles. © 1995 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3883-3887 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Following earlier work, it is inquired how far the 5-D Kaluza–Klein equations without sources may be reduced to the Einstein equations with sources. It is shown by algebraic means that this can be done, provided the extra part of the 5-D geometry is used appropriately to define an effective 4-D energy-momentum tensor. The latter has reasonable properties, but will require further detailed study.
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  • 6
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 232 (1971), S. 251-252 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] In considering the above points, it must be stated that the Lomnitz law has in its favour the fact that it can explain the range over which Q has been found constant in the Earth (1 1-25 s periods). Whether it is valid to use it in explaining this constancy is another matter, and one that is open ...
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Astrophysics and space science 31 (1974), S. 333-339 
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Clusters of galaxies are approximated by the Schwarzschild interior solution (with non-zero cosmological constant) embedded in a Robertson/Walker background. The conditions that the two metrics join up smoothly and that the cluster be stable imply either (a)k=−1 with Λ lying in the range −1.1×10−27≲Λ≲1.5×10−36 (s−2), or (b)k=0. Also, superclustering on a scale larger than 0.5 Mpc is unacceptable unless Λ〈0.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Astrophysics and space science 36 (1975), S. 363-382 
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Attention is given to the radiation of microwaves by charged dust in space. Presently-used particle distributions do not restrict the presence in space of large numbers of small (r〈10−6 cm) silicate grains, but it is shown that such densities (ϱ≈10−25–10−26 g cm−3) of small grains would produce a microwave background with an energy density of the same order of magnitude as the energy density of the (presumed) cosmological 3 K background. Limits set by the isotropy of the latter are: ϱ(HI clouds)≲10−26, ϱ(Galactic plane)≲10−30, ϱ(Halo)≲10−32, ϱ(Local Group)≲10−34 g cm−3. These limits imply that either there is a cutoff in particle distributions atr≃10−6 cm, or that the density of silicate grains in space has been generally overestimated, or that cosmic rays have broken up a lot of grains so that they now form a population of grains of very small size (≃10−7 cm) which are difficult to detect by conventional methods. One way to look for the latter population is by studying expected distortions of the 3 K spectrum to the short wavelength side of the portion hitherto observed (grains may have a size distribution able to give an approximate black-body curve for radiation from larger grains of 10−6 cm size), and by testing the effective energy density of the 3 K field in other galaxies.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Astrophysics and space science 57 (1978), S. 203-217 
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density σ and an angular velocity ω. Self-similarity as a statement of the absence of scales implies that σ and ω can be written asσ=αc 2/4πGr, ω=βc/r, and demands that α and β be pure numbers.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Astrophysics and space science 23 (1973), S. 227-255 
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This work is divided into 13 sections and 2 appendices, and aims to elucidate the accretion mechanism, which operates via image-theory forces, whenever two interstellar dust grains come close together. Section 1 is an introduction. Section 2 proposes that the distribution of interstellar grains be taken asn(r) ∝r −4 to avoid distortion of the 3K microwave background by radiation from spinning grains. Section 3 examines each of three types of image force accretion processes, finding them to be dominant compared to radiation or gravitational forces by at least a factor of 1019. Section 4 states that only grains made of conducting material (e.g., graphite, ice, iron) are involved in image theory. Section 5 presents reasons for believing that two grains should coalesce on impact. Section 6 examines the motion of charged interstellar grains in Hi and Hii regions. Section 7 demonstrates, by way of four examples involving dust grains ofr=10−7 cm up tor=10−4 cm, that the image effects on conducting grains are not trivial, and that the dynamics involved is not to be compared at all with elementary Coulomb interaction of two changes. Section 8 concludes that accretion with not take place in Hi clouds if thermal (equipartition) velocities prevail among the dust particles. section 9 examines grain interactions in Hii regions: here, following an argument due to Spitzer, consideration is given to the case of a population of dust grains all streaming in the direction of the local magnetic field B at velocities of order 0.1 km s−1. It is shown that accretion takes place effectively, leading to the formation of interstellar ‘grit’, meaning grains of mass 10−8 to 10−7 gm, radius ≃ 0.1 mm; and leaving also a population ofr≳10−6 cm grains, which are observed in polarization and extinction measurements. The existence of the latter is now a deduction and not an ad hoc postulate, as previously, and implies a distribution of the general formn(r) ∝r mean −3 , in approximate agreement with that of Section 2. Section 10 considers the accretion mechanism as a cascade process. Section 11 shows that the existence of grains in space ofr ≃ 10−6 cm rules out an origin in supernova or galactic explosions, and supports a passive origin, perhaps in red giants or Mira variables. Section 12 discusses the implications of the results found for polarization observations and cosmogony, the latter being given a new foundation in which planets of different composition form automatically from a solar nebula. Section 13 is a conclusion.
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