By analytically solving the Teukolsky gravitational wave equation for the spacetime of an ultracompact star of constant density, we derive exact and simple formulae that completely describe weakly damped oscillations trapped inside such stars. No similar complete analytic solution was known before, despite several attempts to find it. Our solution is cast in terms of the quasi normal modes of oscillations, which are eigenfunctions of the Teukolsky equation, subjected to proper boundary conditions. We give explicit coordinate form for these eigenfunctions. Each mode is characterized by a complex eigenfrequency. Its real part corresponds to the oscillation frequency f and inverse of its imaginary part to the mode characteristic damping time τ. Both f and τ are observables: they directly govern the behaviour of the “ringdonw” phase of the gravitational wave events, detected by the LIGO-Virgo-Kagra interferometers. We give explicit analytic formulae that express the mass M and radius R of the compact star in terms of the observed ringdown values f, τ . By comparing these to the values actually measured for ringdowns in specific 17 events reported by LIGO, we argue that in 13 of these 17 events the final merged object could not be an ultracompact star.
This shows a practical usefulness of our method and its possible extensions to other hypothetical black hole alternatives: the LIGO-Virgo-Kagra data may be directly used to reject some of these alternatives as being sources of the observed ringdowns.
BIO
Marek Abramowicz is Professor Emeritus at the Physics Department of Gothenburg University (Sweden) and works part time as a professor at the N. Copernicus Astronomical Centre in Warsaw (Poland) and at the Physics Department of Silesian University in Opava (Czechia). He is a Member Academia Scientiarum et Artium Europea (欧洲科学与艺术学院士). His main field of research is theory of black hole accretion disks. Together with collaborators he discovered and/or developed models of Polish Doughnuts, slim disks, adafs, magnetically arrested disks (MAD). After his Ph.D. in 1974 under Andrzej Trautman he was a postdoctoral fellow at Stanford (with Robert Wagoner) and at Austin, Texas (with John Archibald Wheeler and Dennis Sciama). Later, he kept profesorial positions in Oxford, Trieste (Sissa and ICTP), Copenhagen (Nordita) and Gothenburg (GU and Chalmers). He supervised about 30 master and doctoral theses. Several Chinese professors were his students or students of his students.
