BEGIN:VCALENDAR VERSION:2.0 PRODID:-//linuxsoftware.nz//NONSGML Joyous v1.4//EN BEGIN:VEVENT SUMMARY:_Solving the Teukolsky Equation with spectral methods DTSTART:20251118T140000Z DTEND:20251118T160000Z DTSTAMP:20260610T190905Z UID:0a38dda2-536a-4f71-89b2-e29195307058 SEQUENCE:2 CREATED:20251117T094140Z DESCRIPTION:General Relativity is to this date the best theory of gravity we have and probing the very nature of Black Holes is possible through eve nts such as Gravitational Waves. In this work we describe our time domain solver of the 1+1D homogeneous Teukolsky equation\, an equation that encod es the physics of linear perturbations in Kerr spacetime. We solve it in h yperboloidal slices to be able to extract the signals at $\\mathcal{I^+}$ without the need for extrapolation. To do so we developed a code that empl oys two different kinds of spectral methods: a known pseudo-spectral schem e with collocation and a novel fully spectral scheme without collocation. With this second approach we obtain more accurate late-time power-law tail s\, as well as their decay rates\, and we have achieved results for negati ve spin-weights without the use of quad precision that many suggest is nec essary. Our results are in agreement with analytical and empirical general izations of Price’s Law for Kerr Black Holes. Then we proceed with a stu dy of the convergence properties of both spectral schemes and of the time- symmetric integrator we use. This integrator is implicit and it shows adva ntages relative to the more usual explicit integrators mainly in terms of efficiency\, but possibly also in terms of accuracy whenever we introduce source terms into the equation. Thus\, this work marks a first step to sol ve the full Teukolsky system and thus evolve Extreme-Mass Ratio Inspirals simulations accurately and efficiently. LAST-MODIFIED:20251117T094150Z LOCATION:Sala P3 (Piso 1 do Pavilhão de Matemática) do IST URL:http://df.vps.tecnico.ulisboa.pt/pt/eventos/_solving-the-teukolsky-equ ation-with-spectral-methods/ X-ALT-DESC;FMTTYPE=text/html:

General Relativity is to this date the best theory of gravity we have and probing the very na ture of Black Holes is possible through events such as Gravitational Waves . In this work we describe our time domain solver of the 1+1D homogeneous Teukolsky equation\, an equation that encodes the physics of linear pertur bations in Kerr spacetime. We solve it in hyperboloidal slices to be able to extract the signals at $\\mathcal{I^+}$ without the need for extrapolat ion.

To do so we developed a code that employs two different kin ds of spectral methods: a known pseudo-spectral scheme with collocation an d a novel fully spectral scheme without collocation. With this second appr oach we obtain more accurate late-time power-law tails\, as well as their decay rates\, and we have achieved results for negative spin-weights witho ut the use of quad precision that many suggest is necessary.

Our results are in agreement with analytical and empirical generalizations of Price’s Law for Kerr Black Holes. Then we proceed with a study of the c onvergence properties of both spectral schemes and of the time-symmetric i ntegrator we use. This integrator is implicit and it shows advantages rela tive to the more usual explicit integrators mainly in terms of efficiency\ , but possibly also in terms of accuracy whenever we introduce source term s into the equation. Thus\, this work marks a first step to solve the full Teukolsky system and thus evolve Extreme-Mass Ratio Inspirals simulations accurately and efficiently.

END:VEVENT END:VCALENDAR