General Relativistic Smoothed Particle Hydrodynamics (GR-SPH) - PowerPoint PPT Presentation

General Relativistic Smoothed Particle Hydrodynamics (GR-SPH) David Liptai Supervisors: Daniel Price and Paul Lasky

Motivations Neutron star mergers! SPH perfect for NS-merger simulations - No preferred geometry - Resolution follows mass - No need for background density floor - Except…. ☹ - No GR National Science Foundation/LIGO/Sonoma State University/A. Simonnet

Motivations Bonnerot et al. (2016) Fake GR ☹ Tidal Disruption Events Tearing Discs and QPOs

Motivations Paredes-Fortuny et al. (2015) Credit: Hotaka Shiokawa Event Horizon Telescope Relativistic Pulsar Winds

Equations of relativistic hydrodynamics d t = − ρ ∗ ∂ v i d ρ ∗ Continuity: ∂ x i | {z } ∂ ( √− gP ) √− g ✓ ◆ d p i d t = − 1 T µ ν ∂ g µ ν + Momentum: ∂ x i ∂ x i 2 ρ ∗ ρ ∗ | {z } | {z } “GR” ∂ ( √− gPv i ) + −√− g ✓ ◆ d e d t = − 1 T µ ν ∂ g µ ν Energy: ∂ x i 2 ρ ∗ ρ ∗ ∂ t | {z } “Hydro”

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Equations of relativistic hydrodynamics d ρ ∗ d t = 1 b ) ∂ W ab ( h a ) X X a m b ( v i a − v i a = m b W ab ( h a ) ρ ∗ , ∂ x i Continuity: Ω a b b | {z }  √− g a P a √− g b P b d p a � ∂ W ab ( h a ) ∂ W ab ( h b ) X i + f a Momentum: d t = − + m b i , Ω b ρ ∗ 2 ∂ x i ∂ x i Ω a ρ ∗ 2 a b b | {z } | {z } “GR”  √− g a P a v i √− g b P b v i � d e a ∂ W ab ( h a ) ∂ W ab ( h b ) Energy: X a b d t = − + + Λ a , m b Ω b ρ ∗ 2 ∂ x i ∂ x i Ω a ρ ∗ 2 a b b | {z } “Hydro”