6 problems

Let $g$ be the number of point masses in a single lens plane, and let the maximum number of images denote the largest number of images that such a lens can produce for a background…

An n-lens is a gravitational lens consisting of $n$ point masses, and a lensed image is an observed image produced by such a lens. Rhie's conjecture. The upper bound for the number…

No-hair conjecture. A black hole is entirely described by its mass $M$, angular momentum $J$, and electric charge $Q$, measurable at asymptotic infinity.

For a geodesic polygon in a black-hole spacetime, let $\mathring{\alpha}_{M}$ denote its Gaussian bending measure, and suppose that all vertices lie at the same distance $d$ from t…

In a single-plane point-mass lens with $g$ masses, the number of images is bounded above by the conjectured value $5(g-1)$. Rhie's conjecture. The upper bound for the single-plane…

Image-count conjecture. (i) The number of bright images lensed by an isothermal elliptical galaxy without shear is at most $6$. (ii) In the presence of a shear, the number of brigh…