Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.Comment: 18 pages, 4 tables, 4 figure
Greybody factors in black hole physics modify the naive Planckian spectrum that is predicted for Hawking radiation when working in the limit of geometrical optics. We consider the Schwarzschild geometry in (3+1) dimensions, and analyze the Regge-Wheeler equation for arbitrary particle spin s and wave-mode angular momentum ℓ, deriving rigourous bounds on the greybody factors as a function of s, ℓ, wave frequency ω, and the black hole mass m.
While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric amplification and the related quantum phenomenon of particle production (as encoded in the Bogoliubov coefficients), or bounds on transmission and reflection coefficients. Modifying and streamlining an approach developed by one of the present authors [Phys. Rev. A 59 (1999) 427-438], we investigate this question by developing a formal but exact solution for the appropriate second-order linear ODE in terms of a time-ordered exponential of 2x2 matrices, then relating the Bogoliubov coefficients to certain invariants of this matrix. By bounding the matrix in an appropriate manner, we can thereby bound the Bogoliubov coefficients.Comment: 25 pages, plain LaTe
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.
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