Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure

Climate Evolution Through the Onset and Intensification of Northern Hemisphere Glaciation

The Pliocene Epoch (~5.3-2.6 million years ago, Ma) was characterized by a warmer than present climate with smaller Northern Hemisphere ice sheets, and offers an example of a climate system in long-term equilibrium with current or predicted near-future atmospheric CO2 concentrations (pCO2). A long-term trend of ice-sheet expansion led to more pronounced glacial (cold) stages by the end of the Pliocene (~2.6 Ma), known as the “intensification of Northern Hemisphere Glaciation” (iNHG). We assessed the spatial and temporal variability of ocean temperatures and ice-volume indicators through the late Pliocene and early Pleistocene (from 3.3 to 2.4 Ma) to determine the character of this climate transition. We identified asynchronous shifts in long-term means and the pacing and amplitude of shorter-term climate variability, between regions and between climate proxies. Early changes in Antarctic glaciation and Southern Hemisphere ocean properties occurred even during the mid-Piacenzian warm period (~3.264- 3.025 Ma) which has been used as an analogue for future warming. Increased climate variability subsequently developed alongside signatures of larger Northern Hemisphere ice sheets (iNHG). Yet, some regions of the ocean felt no impact of iNHG, particularly in lower latitudes. Our analysis has demonstrated the complex, non-uniform and globally asynchronous nature of climate changes associated with the iNHG. Shifting ocean gateways and ocean circulation changes may have pre-conditioned the later evolution of ice sheets with falling atmospheric pCO2. Further development of high-resolution, multi-proxy reconstructions of climate is required so that the full potential of the rich and detailed geological records can be realized