"2009-12-31+01:00"^^ . "Byly studov\u00E1ny vlastnosti a aplikace algebraick\u00E9 klasifikace Weylova tenzoru ve vy\u0161\u0161\u00EDch dimenz\u00EDch. Bylo dokon\u010Deno zobecn\u011Bn\u00ED Newmanova-Penroseova formalismu do vy\u0161\u0161\u00EDch dimenz\u00ED a tento formalismus byl v r\u016Fzn\u00FDch p\u0159\u00EDpadech pou\u017Eit."@cs . . "2011-06-14+02:00"^^ . "10"^^ . "10"^^ . . . "higher dimensional gravity; exact solutions; algebraic classification"@en . . "2009-04-28+02:00"^^ . "0"^^ . "1"^^ . . . "2007-01-01+01:00"^^ . . "Solutions of the Einstein equations in higher dimensions"@en . "0"^^ . . "One of the most important methods used for finding exact solutions of the Einstein equations in four dimensions (4D) is the Petrov classification. Recent rapid development of higher dimensional gravity was motivated by string theory and large extra dimensions scenarios. In our previous joint work with A. Coley and R. Milson, we developed a generalization of the Petrov classification for higher dimensions. This classification has been already used in differential geometry, high energy physics and higher dimensional gravity but in comparison with the situation in four dimensions, possible applications remain largely unexplored. We plan to focus on these applications. We want to study certain classes of spacetimes (the Kundt class, Kerr-Schild metrics) and generalize various 4D theorems to higher dimensions. We also plan to study algebraically special classes (types N, D). Besides vacuum solutions we also plan to study solutions of the Einstein-Maxwell-Chern-Simons equations."@en . "\u0158e\u0161en\u00ED Einsteinov\u00FDch rovnic ve vy\u0161\u0161\u00EDch dimenz\u00EDch" . " exact solutions" . . . . "Algebraic classification of the Weyl tensor in higher dimensions and its applications were studied. Generalization of the Newman-Penrose formalism was completed and the formalism was used in various cases."@en . . . "Jednou z nejd\u016Fle\u017Eit\u011Bj\u0161\u00EDch metod pou\u017E\u00EDvanou k hled\u00E1n\u00ED p\u0159esn\u00FDch \u0159e\u0161en\u00ED Einsteinov\u00FDch rovnic ve \u010Dty\u0159ech dimenz\u00EDch je tzv. Petrovova klasifikace. V posledn\u00EDch letech se za\u010Dal rychle rozv\u00EDjet z\u00E1jem i o \u0159e\u0161en\u00ED Einsteinov\u00FDch rovnic ve vy\u0161\u0161\u00EDch dimenz\u00EDch (D>4), motivovan\u00FD zejm\u00E9na teori\u00ED strun. V minul\u00FDch letech jsme ve spolupr\u00E1ci s A. Coleym a R. Milsonem vyvinuli zobecn\u011Bn\u00ED Petrovovy klasifikace i pro vy\u0161\u0161\u00ED dimenze. Tato nov\u00E1 klasifikace ji\u017E byla pou\u017Eita v diferenci\u00E1ln\u00ED geometrii, fyzice vysok\u00FDch energi\u00ED a v\u00EDcerozm\u011Brn\u00E9 gravitaci, doposud v\u0161ak byl ve srovn\u00E1n\u00ED se situac\u00ED ve \u010Dty\u0159ech dimenz\u00EDch zmapov\u00E1n pouh\u00FD zlomek mo\u017En\u00FDch pou\u017Eit\u00ED. Pr\u00E1v\u011B t\u011Bmito aplikacemi se chceme zab\u00FDvat. Chceme zkoumat r\u016Fzn\u00E9 t\u0159\u00EDdy p\u0159esn\u00FDch \u0159e\u0161en\u00ED (Kundtova t\u0159\u00EDda, Kerr-Schildovy metriky) a hledat zobecn\u011Bn\u00ED teor\u00E9m\u016F platn\u00FDch ve \u010Dty\u0159ech dimenz\u00EDch. D\u00E1le chceme zkoumat r\u016Fzn\u00E9 algebraicky speci\u00E1ln\u00ED t\u0159\u00EDdy (typy N a D). Krom\u011B vakuov\u00FDch \u0159e\u0161en\u00ED chceme studovat i \u0159e\u0161en\u00ED Einstein-Maxwellov\u00FDch rovnic s Chern-Simonsov\u00FDm \u010Dlenem." . . "higher dimensional gravity" . . . . . "http://www.isvav.cz/projectDetail.do?rowId=KJB100190702"^^ . "KJB100190702" . .