Conference

In the context of the AdS/CFT correspondence, I will discuss model-independent properties shared by bulk theories of gravity with consistent dual descriptions. I will then discuss the prospects of extending these ideas to non-conformal theories, in particular to attempts to realize cosmological theories holographically. I will address the status of in-principle falsifiability of various holographic proposals through internal consistency conditions of the boundary theory.

FRW/CFT duality is a proposal for a holographic dual description for universe created by bubble nucleation. For (3+1) dimensional universe, the dual theory is defined on 2-sphere at the boundary of open universe. I will study correlation functions and explain essential features of FRW/CFT duality: One bulk field corresponds to a tower of CFT operators The boundary theory contains 2D gravity, and the Liouville field plays the role of time. Energy-momentum tensor has dimension 2, as required from the 2D conformal symmetry.

Nonlinear numerical relativistic elasticity may be necessary for simulations including neutron star crusts. Basic simulations of large deformations in relativistic elastic matter will be detailed, and issues necessary for more realistic simulations covered. This work is in collaboration with Carsten Gundlach.

I present a relativistic study of axisymmetric magnetohydrodynamic Bondi--Hoyle accretion onto a moving Kerr black hole. The equations of general relativistic magnetohydrodynamics are solved using high resolution shock capturing methods, involving the use of linearised Riemann solvers. In this study I use the ideal MHD limit, which assumes no viscosity and infinite conductivity. The fluid flow is completely specified by the adiabatic constant $Gamma$, the asymptotic speed of sound $c_s^infty$, and the plasma beta parameter $beta_P$. In particular I restrict the investigation to asymptotically supersonic flows where $v_infty ge c_rms^infty$. To determine the stability of the flow I measure the accretion rates of the energy, and mass. The models presented in this study exhibit a matter density depletion in the downstream region of the black hole which tends to vacuum in convergence tests. This is a feature due to the presence of the magnetic field, more specifically the magnetic pressure, which is not seen in purely hydrodynamic studies. The models investigated present a tendency towards a steady state, which is in agreement with previous studies performed by Font and Iban'ez (1998) using a purely hydrodynamic model.

Alfven oscillations of strongly magnetized neutron stars coupled to shear modes in the solid crust could possibly explain the quasi-periodic oscillations (QPOs) observed in the giant flares of soft gamma repeaters. We present results of two-dimensional simulations of Alfven torsional oscillations in magnetars, modeled as relativistic stars with a dipolar magnetic field. We use a general relativistic magnetohydrodynamics code in the anelastic approximation, which allows for an effective suppression of fluid modes and an accurate description of the Alfven waves. We discuss the coupling of the neutron star interior with the magnetosphere and the observational consequences.

I will discuss the techniques that can be used to include arbitrary equations of state in MHD simulations, particularly the ways in which one may perform conservative to primitive variable conversion numerically for such simulations.