Narrow Results

We discuss the hypothesis that the constituents of dark matter in the galactic halo are primordial intermediate-mass black holes (PIMBHs). The status of axions and weakly interacting massive particles (WIMPs) is discussed, as are the methods for detecting PIMBHs with emphasis on microlensing. The role of the angular momentum ${𝒥}$ of the PIMBHs in their escaping previous detection is considered.

It is known that superpotentials of so-called higher-order theories of gravitation and Einstein theories with a cosmological constant are different in the "Palatini" formulation. However, these theories share a number of solutions, the energy of which should be defined out of superpotentials. We shall check that using augmented variational principles, recently introduced by us, the energy of a solution is defined regardless of the theory, and hence regardless of the superpotential used.

We discuss the hypothesis that the constituents of dark matter in the galactic halo are primordial intermediate-mass black holes (PIMBHs). The status of axions and weakly interacting massive particles (WIMPs) is discussed, as are the methods for detecting PIMBHs with emphasis on microlensing. The role of the angular momentum $\mathcal{J}$ of the PIMBHs in their escaping previous detection is considered.

We re-express the Kerr metric in standard Bondi-Saches coordinate near null infinity . Using the uniqueness result of characteristic initial value problem, we prove the Kerr metric is the only asymptotic flat, stationary, axial symmetric, algebraic special solution of vacuum Einstein equation.

In this article based on the plenary talk of one of the authors, we review recent results on the geometry of the two-surface r = 0, t = const in various stationary black-hole spacetimes which, contrary to the general belief, turns out to be different from that of a disk generically. The sources of the historically erroneous interpretation of that surface are pointed out, and a novel approach to performing analytical extensions of the known black-hole stationary solutions is outlined.