Hisa-aki Shinkai

Fate of the first traversible wormhole: Black hole collapse or inflationary expansion

We study numerically the stability of the first Morris-Thorne traversible wormhole, shown previously by Ellis to be a solution for a massless ghost Klein-Gordon field. Our code uses a dual-null formulation for spherically symmetric space-time integration, and the numerical range covers both universes connected by the wormhole. We observe that the wormhole is unstable against Gaussian pulses in either exotic or normal massless Klein-Gordon fields. The wormhole throat suffers a bifurcation of horizons and either explodes to form an inflationary universe or collapses to a black hole if the total input energy, is, respectively, negative or positive. As the perturbations become small in total energy, there is evidence for critical solutions with a certain black-hole mass or Hubble constant. The collapse time is related to the initial energy with an apparently universal critical exponent. For normal matter, such as a traveller traversing the wormhole, collapse to a black hole always results. However, carefully balanced additional ghost radiation can maintain the wormhole for a limited time. The black-hole formation from a traversible wormhole confirms the recently proposed duality between them. The inflationary case provides a mechanism for inflating, to macroscopic size, a Planck-sized wormhole formed in space-time foam.

Towards standard testbeds for numerical relativity

In recent years, many different numerical evolution schemes for Einsteins equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einsteins equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step towards building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources and can be used with many different approaches used in the relativity community.

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.

Gravitational Waves from Merging Intermediate-Mass Black Holes

The discovery of an intermediate-mass black hole (IMBH) supports a runaway path of supermassive black hole (SMBH) formation in galactic nuclei. No concrete model to explain all the steps of this bottom-up scenario for SMBHs is yet known, but here we propose to use gravitational radiation to probe the merging history of IMBHs. Collisions of black holes of mass 103-106 M☉ will produce gravitational radiation of 10-1 to 102 Hz in their final merging phase. We assume that a thousand 103 M☉ IMBHs form a 106 M☉ black hole in each galaxy via two different merging histories—hierarchical growth and monopolistic growth—using a theoretical model of quasar formation having a peak at z 2.5. We find that there would be 22-67 IMBH merging events per year in the universe and that the event numbers of the two models apparently differ in the frequency of gravitational radiation. Most of the bursts by these events will be detectable by currently proposed space gravitational wave antennas, such as LISA or DECIGO. We conclude that the statistics of the signals would provide both a galaxy distribution and a formation model of SMBHs.

Constraint propagation in the family of ADM systems

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on ‘‘asymptotically constrained’’ systems, we here present constraint propagation equations and their eigenvalues for the ArnowittDeser-Misner ~ADM! evolution equations with additional constraint terms ~adjusted terms! on the right-hand side. We conjecture that the system is robust against violation of constraints if the amplification factors ~eigenvalues of the Fourier component of the constraint propagation equations! are negative or purely imaginary. We show that such a system can be obtained by choosing multipliers of the adjusted terms. Our discussion covers Detweiler’s proposal and Frittelli’s analysis, and we also mention the so-called conformaltraceless ADM systems.

Advantages of a modified ADM formulation: Constraint propagation analysis of the Baumgarte-Shapiro-Shibata-Nakamura system

Several numerical relativity groups are using a modified Arnowitt-Deser-Misner ~ADM! formulation for their simulations, which was developed by Nakamura and co-workers ~and widely cited as the BaumgarteShapiro-Shibata-Nakamura system!. This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this reformulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using an eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other systems in our series of works. We derive the full set of the constraint propagation equations, and study it in the flat background space-time. We carefully examine how the replacements and adjustments in the equations change the propagation structure of the constraints, i.e., whether violation of constraints ~if it exists! will decay or propagate away. We conclude that the better stability of the BSSN system is obtained by their adjustments in the equations, and that the combination of the adjustments is in a good balance, i.e., a lack of their adjustments might fail to obtain the present stability. We further propose other adjustments to the equations, which may offer more stable features than the current BSSN equations.

Wormholes in higher dimensional space-time: Exact solutions and their linear stability analysis

We derive the simplest traversable wormhole solutions in

Generation of scalar-tensor gravity effects in equilibrium state boson stars

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Trick for passing degenerate points in the Ashtekar formulation

-dimensional general relativity, assuming static and spherically symmetric spacetime with a ghost scalar field. This is the generalization of the Ellis solution (or the so-called Morris-Thornes traversable wormhole) into a higher-dimension. We also study their stability using linear perturbation analysis. We obtain the master equation for the perturbed gauge-invariant variable and search their eigenvalues. Our analysis shows that all higher-dimensional wormholes have an unstable mode against the perturbations with which the throat radius is changed. The instability is consistent with the earlier numerical analysis in four-dimensional solution.

Dynamical evolution of boson stars in Brans-Dicke theory

Boson stars in zero-, one- and two-node equilibrium states are modelled numerically within the framework of scalar-tensor gravity. The complex scalar field is taken to be both massive and self-interacting. Configurations are formed in the case of a linear gravitational scalar coupling (the Brans-Dicke case) and a quadratic coupling which has been used previously in a cosmological context. The coupling parameters and asymptotic value for the gravitational scalar field are chosen so that the known observational constraints on scalar-tensor gravity are satisfied. It is found that the constraints are so restrictive that the field equations of general relativity and scalar-tensor gravity yield virtually identical solutions. We then use catastrophe theory to determine the dynamically stable configurations. It is found that the maximum mass allowed for a stable state in scalar-tensor gravity in the present cosmological era is essentially unchanged from that of general relativity. We also construct boson star configurations appropriate to earlier cosmological eras and find that the maximum mass for stable states is smaller than that predicted by general relativity, and the more so for earlier eras. However, our results also show that if the cosmological era is early enough then only states with positive binding energy can be constructed.