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Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

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REFERENCES 131<br />

For possible physical applications, one should calculate <strong>and</strong> us<strong>in</strong>g<br />

where From (47)–(51) we <strong>de</strong>duce [11, 13]:<br />

Parameter <strong>de</strong>pends upon ratios of physical parameters: <strong>and</strong><br />

does not <strong>de</strong>pend upon the quasi–Cartan matrix <strong>and</strong>, hence, upon <strong>in</strong>tersections<br />

of The parameter <strong>de</strong>pends upon ratios<br />

where are functions of GM, <strong>and</strong> The calculation of<br />

needs an exact solution for radial functions Relations (53) <strong>and</strong><br />

(54) co<strong>in</strong>ci<strong>de</strong> with those obta<strong>in</strong>ed <strong>in</strong> [7] for block–orthogonal case, when<br />

charges are co<strong>in</strong>cid<strong>in</strong>g <strong>in</strong>si<strong>de</strong> blocks. For most <strong>in</strong>terest<strong>in</strong>g<br />

solutions with <strong>and</strong> (53)<br />

implies<br />

Acknowledgments<br />

This work was supported <strong>in</strong> part by DFG grant 436 RUS 113/236/O(R),<br />

by RFBR, grant 98–02–16414, Project SEE <strong>and</strong> CONACYT, Mexico.<br />

VNM is grateful to Depto. <strong>de</strong> Fisica, CINVESTAV for their hospitality.<br />

References<br />

[1] D. Kramer, Acta Physica Polonica 2 (1969) 807.<br />

[2] G. Neugebauer <strong>and</strong> D. Kramer, Ann. <strong>de</strong>r Physik (Leipzig) 24 (1969) 62.<br />

[3] V.N.Melnikov, <strong>in</strong>: Cosmology <strong>and</strong> Gravitation, ed. M.Novello, (Editions Frontieres,<br />

S<strong>in</strong>gapore, 1994) pp.147.<br />

[4] V.N.Melnikov, <strong>in</strong>: Cosmology <strong>and</strong> Gravitation II. (Editions Frontieres, S<strong>in</strong>gapore,<br />

1996) pp.465.<br />

[5] V.D.Ivashchuk <strong>and</strong> V.N.Melnikov, <strong>in</strong>: Lecture Notes <strong>in</strong> Physics, v.537. Eds.<br />

S.Cotsakis <strong>and</strong> G.Gibbons, (Spr<strong>in</strong>ger, Berl<strong>in</strong>, 2000) pp.214.

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