Britgrav 16

Relativistic burning on neutron stars

Alice Harpole

Supervisors: Ian Hawke & Nils Andersson

\partial_{t} D + \partial_{i} (D U^{i}) = - D Γ_{μ ν}^{μ} U^{ν}

\partial_{t} (D h) + \partial_{i} (U^{i} D h) = u^{0} \frac{D p_{0}}{D t} - D h Γ_{μ ν}^{μ} U^{ν}

\partial_{t} U_{j} + U^{i} \partial_{i} U_{j} = - U_{j} \frac{D \ln u^{0}}{D t} + Γ_{ρ ν j} U^{ν} U^{ρ} - \frac{1}{D h u^{0}} (\partial_{j} p_{0} + ξ \partial_{j} [\frac{π}{ξ}])

\partial_{i} (ζ U^{i}) = ζ (S - \frac{1}{Γ_{1} p_{0}} \frac{\partial p_{0}}{\partial t})

ζ (r, t) = ζ (0, t) \exp [\int_{0}^{r} d r' \frac{1}{Γ_{1} p_{0}} \frac{\partial p_{0}}{\partial r'}]