The Dimensional-Reduction Anomaly

In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a (D-n)-dimensional space and an n-dimensional homogeneous ``internal'' space, a field can be decomposed into modes. As a result of this mode decomposition, the main objects which characterize the free quantum field, such as Green functions and heat kernels, can effectively be reduced to objects in a (D-n)-dimensional spacetime with an external dilaton field. We study the problem of the dimensional reduction of the effective action for such spacetimes. While before renormalization the original D-dimensional effective action can be presented as a ``sum over modes'' of (D-n)-dimensional effective actions, this property is violated after renormalization. We calculate the corresponding anomalous terms explicitly, illustrating the effect with some simple examples

Absorption of dark matter by a supermassive black hole at the Galactic center: role of boundary conditions

The evolution of the dark matter distribution at the Galactic center is analyzed, which is caused by the combination of gravitational scattering on Galactic bulge stars and absorption by a supermassive black hole at the center of the bulge. Attention is focused on the boundary condition on the black hole. It is shown that its form depends on the energy of dark matter particles. The modified flux of dark matter particles onto the black hole is calculated. Estimates of the amount of dark matter absorbed show that the fraction of dark matter in the total mass of the black hole may be significant. The density of dark matter at the central part of the bulge is calculated. It is shown that recently observed gamma radiation from the Galactic center can be attributed to the annihilation of dark matter with this density.Comment: 5 page

Scalar and electromagnetic fields of static sources in higher dimensional Majumdar-Papapetrou spacetimes

We study scalar massless and electromagnetic fields from static sources in a static higher dimensional spacetime. Exact expressions for static Green's functions for such problems are obtained in the background of the Majumdar-Papapetrou solutions of the Einstein-Maxwell equations. Using this result we calculated the force between two scalar or electric charges in the presence of one or several extremely charged black holes in equilibrium in the higher dimensional spacetime.Comment: Added two references, typos correcte

Self-energy of a scalar charge near higher-dimensional black holes

We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin the conformal anomalies in quantum field theory in even dimensional spacetimes.Comment: 9 page