科研之友
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摘要
A classical computation of vector bremsstrahlung in ultrarelativistic gravitational-force collisions of massive point particles is presented in an arbitrary number d of extra dimensions. Our method adapts the post-linear formalism of General Relativity to the multidimensional case. The total emitted energy, as well as its angular and frequency distribution and characteristic values, are discussed in detail. %26lt;br%26gt;For an electromagnetic mediation propagated in the bulk, the emitted energy E (em) of scattering with impact parameter b has magnitude E (em) similar to e (4) e (%26apos;2)gamma (d+2) /(m (2) b (3d+3)), with dominant frequency omega (em) similar to gamma(2) /b. For the gravitational force the charge emits via vector field, propagated in the bulk, energy E (rad) similar to [G (D) m (%26apos;) e](2)gamma (d+2) /b (3d+3) for d a parts per thousand yen 2, with dominant frequency omega similar to gamma(2) /b; and energy E (rad) similar to [G (5) m (%26apos;) e (5)](2) gamma(3) ln gamma/b (6) for d = 1, with most of the energy coming from a wide frequency region omega a [(gamma/b), (gamma(2) /b)]. For the UED model with extra space volume V = (2 pi R) (d) the emitted energy is E (UED) similar to (b (d) /V)(2) E (rad). Finally, for the ADD model, including four dimensions, the electromagnetic field living on 3-brane, loses on emission the energy E (ADD) similar to [G (D) m (%26apos;) e](2) gamma(3) /(V b (2d+3)), with characteristic frequency omega (ADD) similar to gamma/b. %26lt;br%26gt;The contribution of the low frequency part of the radiation (soft photons) to the total radiated energy is shown to be negligible for all values of d. The domain of validity of the classical result is discussed. The result is analyzed from the viewpoint of the de Witt-Brehme-Hobbs equation (and corresponding equations in higher dimensions). The different frequency domains and their competition mentioned above, may be explained as coming from different terms in this equation. Thus the whole emission process may be naturally split in two sub-processes with drastically different spectral and temporal characteristics.
- 出版日期2014-1-21
