Wai-Mo Suen

Wave propagation in gravitational systems: Late time behavior

It is well known that the dominant late time behavior of waves propagating on a Schwarzschild spacetime is a power-law tail; tails for other spacetimes have also been studied. This paper presents a systematic treatment of the tail phenomenon for a broad class of models via a Greens function formalism and establishes the following. (i) The tail is governed by a cut of the frequency Greens function Gifmmode tilde{}else ~{}fi{}(ensuremath{omega}) along the -Imensuremath{omega} axis, generalizing the Schwarzschild result. (ii) The ensuremath{omega} dependence of the cut is determined by the asymptotic but not the local structure of space. In particular it is independent of the presence of a horizon, and has the same form for the case of a star as well. (iii) Depending on the spatial asymptotics, the late time decay is not necessarily a power law in time. The Schwarzschild case with a power-law tail is exceptional among the class of the potentials having a logarithmic spatial dependence. (iv) Both the amplitude and the time dependence of the tail for a broad class of models are obtained analytically. (v) The analytical results are in perfect agreement with numerical calculations.

Three Dimensional Numerical General Relativistic Hydrodynamics ; 1, Formulations, Methods, and Code Tests

This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and convergence of our general relativistic hydrodynamic treatment and its coupling to the spacetime evolutions described by the full set of Einstein equations with a perfect fluid source. The numerical treatment of the general relativistic hydrodynamic equations is based on high resolution shock capturing schemes. These schemes rely on the characteristic information of the system. A spectral decomposition for general relativistic hydrodynamics suitable for a general spacetime metric is presented. Evolutions based on three different approximate Riemann solvers coupled to four different discretizations of the Einstein equations are studied and compared. The coupling between the hydrodynamics and the spacetime (the right and left hand side of the Einstein equations) is carried out in a treatment which is second order accurate in {it both} space and time. Convergence tests for all twelve combinations with a variety of test beds are studied, showing consistency with the differential equations and correct convergence properties. The test-beds examined include shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of self-gravitating compact (TOV) stars, and evolutions of relativistically boosted TOV stars. Special attention is paid to the numerical evolution of strongly gravitating objects, e.g., neutron stars, in the full theory of general relativity, including a simple, yet effective treatment for the surface region of the star (where the rest mass density is abruptly dropping to zero).

Towards a realistic neutron star binary inspiral: Initial data and multiple orbit evolution in full general relativity

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.

Dynamical Evolution of Boson Stars

We study the dynamical properties of self-gravitating complex scalar field configurations (boson stars) in general relativity (GR) and in scalar tensor (ST) gravity, for scalar fields both with and without self couplings. We compare the stability and scalar field emissions from this system in both gravity theories. We also simulate the formation of boson stars.

Wave propagation in gravitational systems: Completeness of quasinormal modes.

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM’s) of the Klein-Gordon (KG) equation with different effective potentials V (x). In this paper we present a systematic study of the relation between the structure of the QNM’s of the KG equation and the form of V (x). In particular, we determine the requirements on V (x) in order for the QNM’s to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM’s do not form a complete set. For such systems, we show that a complete set of QNM’s can often be obtained by introducing an infinitesimal change in the effective potential.

Shapiro conjecture: Prompt or delayed collapse in the head-on collision of neutron stars?

We study the question of prompt versus delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out.

Damping of the cosmological constant by a classical scalar field

Abstract The dynamical damping of a cosmological constant Λ by a classical scalar field is investigated. The field is free, massless, and non-minimally coupled to gravity via a term ξRφ2. The cosmological constant is damped if ξ 0 and ξ> 1 2 , Λ , and the decay is stable against small spatially homogeneous perturbations. For other values of Λ and ξ, damping solutions either do not exist, are unstable, or lead to recollapse of the universe.

Perturbative approach to the quasinormal modes of dirty black holes

Using a recently developed perturbation theory for quasinormal modes (QNMs), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasistatic perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.