منابع مشابه
The Goldberg-Sachs theorem in linearized gravity
The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized...
متن کاملA higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem
In more than four spacetime dimensions, a multiple Weyl-aligned null direction (WAND) need not be geodesic. It is proved that any higher-dimensional Einstein spacetime admitting a non-geodesic multiple WAND also admits a geodesic multiple WAND. All five-dimensional Einstein spacetimes admitting a non-geodesic multiple WAND are determined.
متن کاملq-ANALOGUE OF WILSON’S THEOREM
[n]q := 1− q 1− q = 1 + q + · · ·+ q . Clearly limq→1[n]q = 1, so we say that [n]q is a q-analogue of the integer n. Supposing that a ≡ b (mod n), we have [a]q = 1− q 1− q = 1− q + qb(1− q) 1− q ≡ 1− q 1− q = [b]q (mod [n]q). Here the above congruence is considered over the polynomial ring in the variable q with integral coefficients. And q-analogues of some arithmetical congruences have been s...
متن کاملThe Basic Analogue of Kummer’s Theorem
which has since been known as Kummer's theorem. This appears to be the simplest relation involving a hypergeometric function with argument ( — 1). All the relations in the theory of hypergeometric series rF8 which have analogues in the theory of basic series are those in which the argument is ( + 1 ) . Apparently, there has been no successful at tempt to establish the basic analogue of any form...
متن کاملAn analogue of the Baire category theorem
Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 1970
ISSN: 0022-2518
DOI: 10.1512/iumj.1971.20.20017