Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8
We study static scalar and Maxwell fields created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for these field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation of the red-shift factor. Both transformations are determined by one function of the spatial coordinates. We show that in a case of higher dimensional spherically symmetric black holes one can find such a bi-conformal transformation that the symmetry of the D-dimensional metric is enhanced after its application. Namely, the metric becomes a direct sum of the metric on a unit sphere and the metric of the anti-de Sitter space. The method of the heat kernels allows one to obtain static Green functions in the original space of the static black hole. The general useful representation of static Green functions is obtained in the Schwarzschild-Tangherlini spacetimes of arbitrary dimension. Using this method we obtained the exact closed form for the potentials of massless scalar and Maxwell fields created by static charges near four- and five-dimensional charged black holes.
Jiří Bičák Oldřich Semerák