Regularization of static self-forces

Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the regularization method that enjoys the best justification is that of Detweiler and Whiting, which is based on a four-dimensional Green's function. We establish the connection between these methods and find that they are all equivalent, in the sense that they all lead to the same static self-force. For general static spacetimes, we compute local expansions of the Green's functions on which the various regularization methods are based. We find that these agree up to a certain high order, and conjecture that they might be equal to all orders. We show that this equivalence is exact in the case of ultrastatic spacetimes. Finally, our computations are exploited to provide regularization parameters for a static particle in a general static and spherically-symmetric spacetime.Comment: 23 pages, no figure

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

A simple analytical model for dark matter halo structure and adiabatic contraction

A simple analytical model for describing inner parts of dark matter halo is considered. It is assumed that dark matter density is power-law. The model deals with dark matter distribution function in phase space of adiabatic invariants (radial action and angular momentum). Two variants are considered for the angular part of the distribution function: narrow and broad distribution. The model allows to describe explicitly the process of adiabatic contraction of halo due to change of gravitational potential caused by condensation of baryonic matter in the centre. The modification of dark matter density in the centre is calculated, and is it shown that the standard algorithm of adiabatic contraction calculation overestimates the compressed halo density, especially in the case of strong radial anisotropy.Comment: 5 pages, 3 figures. v3 - major improvements, another halo model introduced, discussion extende