Hisaaki SHINKAI Homepage
Researches -- [pub. list] | [abstracts] | summary of topics [E] [J]

## Research Abstracts

My main interests are physics under strong gravity, described by general relativity. I have studied almost all areas in general relativity; compact stars (black holes, neutron stars, wormholes, etc), cosmology (inflation, expansion rate, etc), gravitational waves (waveform, event rate, etc), and test of general relativity (alternative theories, higher-dimensional spacetime). Some keywords can be listed as;

• General Relativity and Cosmology
Relativistic Objects, Relativistic Cosmology, Theories of Gravitation, Formulations for Numerical Analysis, Gravitational Waves

• Astrophysics
Gravitational Waves Event Rates, Formation of Supermassive Black Holes

• History of Science

Some Highlights
• My topics are particularly in their nonlinear natures which require numerical simulations. In general relativity, the methods for simulations are not simple and each steps of analysis (e.g, which formulation of the Einstein equations is better, how can we extract gravitational wave, how we treat black holes) have been obtained in long history. My name is well known in numerical relativity community, where I first proposed a formula expressing gravitational wave (Weyl scalar) from ADM quantities in 1994, which is now widely used in the codes of black hole simulations. I also conducted a series of work on formulation problem in numerical relativity, which was the problem why we faced an unexpected blow-up in numerical evolutions of the Einstein equation (1998-2003). I found the existence of error growing modes in the standard ADM formulation (now known as constraint violation modes), and also reported some recipes to get robust set of equations applying a way of Lagrange multipliers. This basic idea is now commonly applied as one of the necessary techniques in numerical simulation.
• My most cited article is on the structure of a black hole in Randall-Sundrum's brane-world model (2001). We pointed out a charged black hole exhibits pathological features in the bulk. The story was briefly mentioned in the general book by Lisa Randall, "Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions".
• My most famous article in public is on the dynamical features of the "traversable" Morris-Thorne's wormhole (2002). I am the first person to study the numerical simulation of wormhole structure, which I showed that wormholes with negative energy are unstable and the throat of wormhole will shrink (or expand) if positive (negative) energy is inserted. This result has been followed by several groups, and I also have generalized the study in higher-dimensional and in alternative gravity theories.
• My current interests are on gravitational wave and astrophysics. After the announcement of the discovery of GW150914 by the LIGO group, we are now on the starting line of new astronomy. As a member of KAGRA data analysis group (I personally joined since August 2015), I began working on event rates of gravitational waves, on the methods of testing general relativity, and also on the methods of extracting signals from noisy data. My latest publication is on a formation model of supermassive black holes, in which I mentioned that only our hierarchical formation scenario predicts a detection of black hole merger of its final mass over 100 solar mass (2017).
• I got my current position at Osaka Institute of Technology 10 years ago, and this university gives me a lot of the lectureships, which gives me a lot of chances of writing textbooks and general books. I also have many chances to talk with non-scientists, and I got a lot of experiences. When I prepared talk slides with some background history, I myself got excited to dig up some unknown stories in history of sciences. Recently, I wrote a report on Goryu Asada, a citizen scientist in Edo era, who is sometimes credited with the independent discovery of Kepler's third law.

Topic search
 Generality of the inflationary scenario in the early Universe 1991- Transformations of variables between 3+1 and 2+2 formulations 1993- Treatment of dynamics in the Ashtekar's connection approach 1994- Gravitational waves in Brans-Dicke theory of gravity 1995- Boson Stars in Scalar-Tensor theories 1997- Post-Newtonian treatent in Numerical Relativity 1997- Hyperbolic formulations and Numerical Relativity 1998- Higher dimensional cosmology 1999- Dual-null formulation, application to Gravitaional Waves, Wormholes, ... 1999- Asymptotically constrained systems and Numerical Relativity 2000- Standard testbeds for numerical relativity 2002- ... under updating ... 2004-

 Generality of the inflationary scenario in the early Universe

The Inflationary scenario solves many long-standing fundamental problems in the standard Big-bang model. However, whether inflation starts in anisotropic and/or inhomogeneous space-time and whether the space-time enters inflationary phase in general situation are not clear. By integrating the Einstein equations numerically in a plane-symmetric space-time, I show that even we set highly inhomogeneous scalar field (inflaton) or even if we assume locally strong gravitational wave packets, the space-time evolves into homogeneous de Sitter space-time. These results certify so-called Cosmic No-hair Conjecture", which states all initially expanding universes with cosmological constants approach de Sitter space-time asymptotically [1][2].
In 1995, Linde and Vilenkin proposed that topological defects themselves expand rapidly and may become sources of inflation (topological inflationary model"). I examine their models numerically for the case of planar domain wall and global monopole system and show the parameter ranges they work [3].

[1] Can Gravitational Waves Prevent Inflation?
with Kei-ichi Maeda (Waseda Univ.)
Physical Review D48, 3910-3913 (1993) Abstract

[2] Generality of Inflation in a Planar Universe
with Kei-ichi Maeda (Waseda Univ.)
Physical Review D49, 6367-6378 (1994) Abstract

[3] Dynamics of Topological Defects and Inflation
with Nobuyuki Sakai, Takashi Tachizawa and Kei-ichi Maeda (Waseda Univ.)
Physical Review D53, 655-661 (1996) Abstract

Note::
The results of [1] are reviewed in a subsection in
P. Anninos, Living Review of Relativity, 1998-2, http://www.livingreviews.org/Articles/Volume1/1998-2anninos
"Physical and Relativistic Numerical Cosmology"

 Transformations of variables between 3+1 and 2+2 formulations

The characteristic formulation of general relativity is attractive for treating gravitational waves. However, this formulation is not the best choice for numerical relativity, because it has focusing features. In order to extract and express some proper structure of gravitational field, I derive a transformation formula from the Weyl curvature $C_{\mu\nu\rho\sigma}$ to the Weyl scalar $\Psi_i$, using projections of Weyl curvature on 2-plane. Since I use a decomposition of the Weyl curvature into electric- and magnetic-parts, the formula has advantages for numerical relativists who work in ADM formulation [1].

One application is the proposal of a new method to present principal null directions pictorially. We can now easily see that the Petrov type of the space-time will damp to a simpler one according to the distance from a source (peeling-off theorem) even for a numerically generated (3+1) data. Another application is a new definition of a maximally polarized direction of propagating gravitational waves. Two modes of gravitational waves, +-mode and x-mode, are often mixed by non-linear term in Einstein equations, and those effects are called a gravitational Faraday effect' from an analogy in the electromagnetism. I applied my definition to a numerical simulation and show some examples of such a rotation of a polarized plane. (Details are in the thesis section 5.3).

[1] A 3+1' Method for Finding Principal Null Directions
with Laurens Gunnarsen and Kei-ichi Maeda (Waseda Univ.)
Classical and Quantum Gravity, 12, 133-140 (1995) Abstract
Note::
The formula for deriving NP quantities were immediately applied in Potsdam/WashU/NCSA group's numerical code, and now available as a module of their Cactus code (as thorn Psikadelia). The method is now also used in Texas/PennState group's code.

 Gravitational waves in Brans-Dicke theory of gravity

A direct observation of gravitational waves can be used as a tool of testing theory of gravity. We studied gravitational radiation in Brans-Dicke theory of gravity, which is an alternative theory to general relativity, and compared with those in general relativity. Analyzing test particles falling into a Kerr black hole, we estimated the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. By applying these results in non-spherical dust collapse, we found that the scalar modes dominate only for highly spherical collapse, and clarified in which parameter ranges we can expect to observe the scalar modes of gravitational waves.

Gravitational Waves in Brans-Dicke Theory : Analysis by Test Particles around a Kerr Black Hole
with Motoyuki Saijo and Kei-ichi Maeda (Waseda Univ.)
Phys. Rev. D56 (1997) 785-797 Abstract

Can We Detect Brans-Dicke Scalar Gravitational Waves in Gravitational Collapse?
with M. Saijo and K. Maeda (Waseda Univ.)
The 18th Texas Symposium on Relativistic Astrophysics, (1996 December, Chicago) [ps]

 Treatment of dynamics in the Ashtekar's connection approach

Motivated by a plan to apply the connection approach formulated by Ashtekar to classical numerical relativity, I show how to treat the constraints and reality conditions in the $SO(3)$-ADM (Ashtekar) version of general relativity. I clarify the difference between the reality conditions on the metric and on the triad from the point of the following the time developments of 3-hypersurfaces. Assuming the reality condition on the triad, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously, which, I think, will play as an alternative variable together with those of Capovilla-Dell-Jacobson's [1].

We examined also whether Ashtekar's formulation of general relativity has an advantage or not when we apply it in numerical relativity, especially on a tractability of degenerate points in dynamics. Assuming that all dynamical variables are finite, we concluded that an essential trick for such a continuous evolution is in complexifying fundamental variables. In order to restrict the complex region locally, we proposed some reality recovering' conditions on space-time. We showed that this idea works in an actual dynamical problem [2].

We checked the recent symmetric hyperbolic formulation in the Ashtekar's framework by Iriondo et al (1997), and found that their discussion was insufficient in the points that they did not mention characteristic speed and the consistency with the reality condition. We construct a symmetric hyperbolic system using the similar technique with theirs but use Hermitian matrix to characterize the system symmetric [4]. We also construct three levels of hyperbolic systems (weakly, strongly and symmetric) and discuss each gauge requirements and reality constraints [5]. From our numerical comparisons of these hyperbolic systems, we observe the strongly and symmetric hyperbolic system show better stability properties, but not so much difference between the latter two. Rather, we find that the symmetric hyperbolic system is not always the best for controlling stability. [7].

In order to make the evolution equations more robust against the violations of the constraint equations and reality conditions, we proposed a new system based on Ashtekar's variables. By extending the space and introducing a fictious dissipative forces, the system has its attractor in the constraint and real-valued surfaces. The obtained systems may be useful for future numerical studies using Ashtekar's variables [6]. Actually we performed numerical simulations and showed that this system works as expected [8] There we also proposed an alternative mechanism to obtain asymptotically constrained system, that will be explained here .

[1] Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
with Gen Yoneda (Waseda Univ.)
Classical and Quantum Gravity, 13, 783-790 (1996) Abstract

[2] Trick for Passing Degenerate Point in the Ashtekar Formulation
with Gen Yoneda and Akika Nakamichi (Waseda Univ.)
Physical Review D56 (1997) 2086-2093 Abstract

[3] Lorentzian dynamics in the Ashtekar gravity
with Gen Yoneda (Waseda Univ.)
The 8th Marcel Grossman Meeting (1997 June, Jerusalem)
Proceedings [ps]

[4] Symmetric hyperbolic system in the Ashtekar formulation
with Gen Yoneda (Waseda Univ.)
Physical Review Letters 82 (1999) 263 Abstract

[5] Constructing hyperbolic systems in the Ashtekar formulation of general relativity
with Gen Yoneda (Waseda Univ.)
Int. J. Mod. Phys. D. 9 (2000) 13. Abstract

[6] Asymptotically constrained and real-valued system based on Ashtekar's variables
with Gen Yoneda (Waseda Univ.)
Physical Review D 60 (1999) 101502 (Rapid Communication) Abstract

[7] Hyperbolic formulations and numerical relativity: Experiments using Ashtekar's connection variables
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 17 (2000) 4799 Abstract

[8] Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of Einstein equation
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 18 (2001) 441 Abstract

[9] Hyperbolic formulations and numerical relativity
with Gen Yoneda (Waseda Univ.)
The 9th Marcel Grossman Meeting (2000 July, Rome)
Proceedings Abstract, [ps]

Note::
The paper [5] was listed as a sample paper in the leaflet (year 2000) of Int. J. Mod. Phys. Journal.
The paper [8] was listed as a sample paper in the leaflet (year 2001) of Class. Quantum. Grav. Journal.
The paper [8] was chosen as one of the highlight papers on "Classical and Quantum Gravity" (by Institute of Physics). The journal has a special web page at http://www.iop.org/journals/cqg/extra/1, and you can download the article FREE.

 Boson Stars in Scalar-Tensor theories

In order to show some interesting features of scalar-tensor theory, I began studying a structure of boson stars. Boson stars are formed by complex scalar field. If we construct them in scalar-tensor theory of gravity in conformally transformed Einstein frame, then we just need to add one more scalar field in energy-momentum tensor.

I show a sequence of equiilibrium configuration of boson star in both Brans-Dicke theory and Damour-Nordtvedt's quadratic coupling model. I found that if we pose an observational constraint for the theories, then the solutions are identical with those of general relativity. Applying a catastrophe theory, I also discuss their stability. What is interesting, I found that there are no stable sequence of boson stars in the earlier cosmological era if we work in quadratic coupling model [1].

By integrating the dynamical equations of this system numerically, I checked the above stability discussion in Brans-Dicke case. I also compared the scalar emissions from this system with GR [2,3].

[1] Generation of Scalar-Tensor Gravity Effects in Equilibrium State Boson Stars
with G.L. Comer (St.Louis Univ.)
Classical and Quantum Gravity 15 (1998) 669 Abstract

[2] Dynamical evolution of boson star in Brans-Dicke theory
with J. Balakrishna (Washington Univ.)
Physical Review D58 (1998) 044016 Abstract

[3] Dynamical evolution of boson stars
with J. Balakrishna, G.L. Comer, E. Seidel and W-M. Suen
The proceedings of Numerical Astrophysics 98 (1998 March, Tokyo) [ps]

Note::
The debates starting from [1] are summarized in A.W.Whinnett, Phys. Rev. D. 61 (2000) 124014, concluding that the results in [1] are confirmed.

 Post-Newtonian treatment in Numerical Relativity

One of the most important problem in simulating coalescing binary neutron star is to prepare physically satisfactoral initial data. Towards this problem in fully general relativistic (GR) hydrodynamical simulations, I am working to apply the post-Newtonian (PN) approach to construct initial data.
As a preliminary step, I showed that the discountinuous matching surface of the PN and GR in the vacuum region will be smmothe dout in fully relativistic evolution in a particular slicing condition [1].
I also tested a post-Newtonian approach by constructing a single neutron star model. I show how the PN approximation converges together with mass-radius relations for several polytropic equation of state. By solving the Hamiltonian constraint equation with these density profiles as trial functions, I examine the differences in the final metric. We conclude the second post-Newtonian' approximation is close enough to describe general relativistic single star [2].

[1] Newtonian and post-Newtonian binary neutron star mergers
with E.Y.M. Wang, F.D. Swesty, W-M. Suen, M. Tobias and C.M. Will
The 8th Marcel Grossman Meeting (1997 June, Jerusalem)
Proceedings [ps]

[2] Truncated post-Newtonian neutron star model
Physical Review D60 (1999) 067504 Abstract

Note::
The contents of [1] are applied for justifing the Pade approximation in A. Gupta, A. Gopakumar, B.R. Iyer, S. Iyer, Phys. Rev. D.62 (2000)044038.

 Hyperbolic formulations and Numerical relativity

Re-formulating the Einstein equations into hyperbolic form is extensively studied by several groups in these years. We started using Ashtekar's connection formulation, constructed three levels of hyperbolic forms, and compared their numerical differences systematically. We are trying to feed back these results into the standard ADM systems.

We checked the recent symmetric hyperbolic formulation in the Ashtekar's framework by Iriondo et al (1997), and found that their discussion was insufficient in the points that they did not mention characteristic speed and the consistency with the reality condition. We construct a symmetric hyperbolic system using the similar technique with theirs but use Hermitian matrix to characterize the system symmetric [1]. We also construct three levels of hyperbolic systems (weakly, strongly and symmetric) and discuss each gauge requirements and reality constraints [2]. From our numerical comparisons of these hyperbolic systems, we observe the strongly and symmetric hyperbolic system show better stability properties, but not so much difference between the latter two. Rather, we find that the symmetric hyperbolic system is not always the best for controlling stability. [3,6].

In order to make the evolution equations more robust against the violations of the constraint equations and reality conditions, we proposed a new system based on Ashtekar's variables. By extending the space and introducing a fictious dissipative forces, the system has its attractor in the constraint and real-valued surfaces. The obtained systems may be useful for future numerical studies using Ashtekar's variables [4]. Actually we performed numerical simulations and showed that this system works as expected [5,6] There we also proposed an alternative mechanism to obtain asymptotically constrained system, that is explained here.

[1] Symmetric hyperbolic system in the Ashtekar formulation
with Gen Yoneda (Waseda Univ.)
Physical Review Letters 82 (1999) 263 Abstract

[2] Constructing hyperbolic systems in the Ashtekar formulation of general relativity
with Gen Yoneda (Waseda Univ.)
Int. J. Mod. Phys. D. 9 (2000) 13. Abstract

[3] Asymptotically constrained and real-valued system based on Ashtekar's variables
with Gen Yoneda (Waseda Univ.)
Physical Review D 60 (1999) 101502 (Rapid Communication) Abstract

[4] Hyperbolic formulations and numerical relativity: Experiments using Ashtekar's connection variables
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 17 (2000) 4799 Abstract

[5] Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of Einstein equation
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 18 (2001) 441 Abstract

[6] Hyperbolic formulations and numerical relativity
with Gen Yoneda (Waseda Univ.)
The 9th Marcel Grossman Meeting (2000 July, Rome)
Proceedings Abstract, [ps]

Note::
The paper [2] was listed as a sample paper in the leaflet (year 2000) of Int. J. Mod. Phys. Journal.
The paper [5] was listed as a sample paper in the leaflet (year 2001) of Class. Quantum. Grav. Journal.
The paper [5] was chosen as one of the highlight papers on "Classical and Quantum Gravity" (by Institute of Physics). The journal has a special web page at http://www.iop.org/journals/cqg/extra/1, and you can download the article FREE.

 Higher dimensional cosmology

According to the recent development of string theories and related studies, our 4-dimensional spacetime was reduced from higher dimensional spacetime via a sort of compactifications. Such dimensional reductions are not yet well understood, and we do not have fundumental consensus in hand. However, we studied the following two topics based on the latest plausible scenario.

1. Stability of 5-dimensional Kaluza-Klein bubble spacetime [1].
The stability of 4-dimensional spacetime can be judged by the positiveness of its total energy. However, Brill-Horowitz's solution, which was found as a momentarily static initial data in 5-dimensional Kaluza-Klein spacetime, allows arbitrary negative total mass, and that negative mass solution is conjectured as a stable (expanding) solution by Corley-Jacobson. We show numerically that such a negative energy bubble will collapse and form a naked singularity, while the evolution start expanding.
In our analysis, we simply use 5-dimensional Einstein equations. If we apply the recent `brane-world' scenario, the fundamental equations are not the conventional Einstein's ones therefore our results might not directly proceed understanding of the higher dimensional cosmology. We, however, are quite interested in the fact that the stability of spacetime can be judged simply by the positiveness of its total energy even in the higher dimensional spacetime.
2. The 5th dimensional structure of the charged black holes on the brane [2].
According to the recent model by Randall and Sundrum (of ther second model 1999), Our 4-dimensional spacetime might be a domain wall in the 5-dimensional balk which contains negative cosmological constant. We studied a changed black holes withing this scenario, and discuss its global structure especially its 5th dimensional direction. We here considered both tidal charge which is arised from the bulk Weyl tensor and electric charge from a gauge field, and we assumed both are trapped on the wall. We showed that a Reissner-Nordstrom geometry is induced on the wall when only Weyl charge is present. However, we show that such solutions exhibit pathological features in the bulk.

[1] Fate of Kaluza-Klein bubble
with T. Shiromizu
Physical Review D 62 (2000) 024010 Abstract

[2] Charged brane-world black holes
with A. Chamblin, H.S. Reall, T. Shiromizu
Physical Review D63 (2001) 064015 Abstract

 Dual-null formulation for describing space-time geometry

Evolving space-time with dual-null ($2+2$) formulation has many advantages than the traditional space and time decomposition ($3+1$ formulation), but still a challenging project.

Proposal of the new approximation of space-time: Quasi-spherical approach [1]
We proposed a new approximation scheme in a dual-null decomposition of space-time, and report its numerical test on its validity. This proposal is with the aim of providing a computationally inexpensive estimate of the gravitational waveforms produced by a black-hole or neutron-star collision, given a full numerical simulation up to (or close to) coalescence, or an analytical model thereof. The scheme truncates the Einstein equations by removing second-order terms which would vanish in a spherically symmetric space-time. We numerically implemented this scheme, testing it against angular momentum by applying it to Kerr black holes. As error measures, we take the conformal strain and specific energy due to spurious gravitational radiation. The strain is found to be monotonic rather than wavelike. The specific energy is found to be at least an order of magnitude smaller than the 1 % level expected from typical black-hole collisions, for angular momentum up to at least 70 % of the maximum, for an initial surface as close as $r=3m$.

Dynamical properties of traversible wormholes [2]
Wormholes are known as a kind of solution of the Einstein equations, and have become a popular research topic, raising theoretical possibilities of rapid interstellar travel, time machines and warp drives. These topics sound like science fiction, but after an influential study of traversible wormholes by Morris amp; Thorne (1988), it became widely accepted as a scientific topic.
We study numerically the stability of Morris \& Thorne's traversible wormhole. We observe that the wormhole throat 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. For normal matter, such as a traveller traversing the wormhole, collapse to a black hole always results. However, 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.

[1] Quasi-spherical approximation for rotating black holes
with S.A. Hayward
Physical Review D 64 (2001) 044002. Abstract

[2] Fate of the first traversible wormhole: black-hole collapse or inflationary expansion
with S.A. Hayward
Physical Review D 66 (2002) 044005 Abstract

 Asymptotically constrained systems and Numerical relativity

In order to perform long-term stable numerical integration of the Einstein equations, we studied the direction of hyperbolic formulation as I described above. Then we found that the mathematical notion of the hyperbolicity may not be enough to discuss the Einstein equations since it ignores the contribution of the non-principal parts.

We proceeded an idea of constructing an "asymptotically constrained" system, without a notion of hyperbolicity. By analyzing the procedure of adjusting constraints to the dynamical equations and their constraint propagation equations, we conjectured that eigenvalue analysis of the homogenized constraint propagation equations indicates asymptotically constrained feature. The idea certainly worked and numerically confirmed for the Maxwell system and the Ashtekar formulation [1]. We also show that this idea is applicable to the ADM evolution equations by adjusting them with constraints [2]. We predicted several possibilites based on the ADM formulation for the Schwarzschild spacetime [3]. The generalization for higher dimensional space-time is also presented [6].
We further applied the same idea to the so-called BSSN (Baumgarte-Shapiro-Shibata-Nakamura) version of ADM formulation, and succeeded to show what part of the modifications contributes to give us stable evolution system, and proposed similar systems which are expected to be better than the current set of equations [4].
The series of above analysis provided us to analyze the stability of reformulations of the constraint dynamics systematically. However, the conditions for stability should be supported by mathematical prooves. In [5], we classified asymptotical behaviors of constraint-violation into three (asymptotically constrained, asymptotically bounded, and diverge), and gave their necessary and sufficient conditions. We find that degeneracy of eigenvalues sometimes leads constraint evolution to diverge (even if its real-part is not positive), and conclude that it is quite useful to check the diagonalizability of constraint propagation matrix.

[1] Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of Einstein equation
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 18 (2001) 441 Abstract

[2] Constraint propagation in the family of ADM systems
with Gen Yoneda (Waseda Univ.)
Physical Review D 63 (2001) 124019 (9 pages) Abstract

[3] Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
with Gen Yoneda (Waseda Univ.)
Class. Quantum Grav. 19 (2002) 1027-1049 Abstract

[4] Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
with Gen Yoneda (Waseda Univ.)
Physical Review D 66 (2002) 124003 Abstract

[5] Diagonalizability of constraint propagation matrix
with Gen Yoneda (Waseda Univ.)
Class. Quantum Gravity 20 (2003) L31-36 Abstract

[6] Constraint propagation in N+1 dimensional space-time
with Gen Yoneda (Waseda Univ.)
Gen. Rel. Grav. 36 (2004) 1931-1937 Abstract

 Standard testbeds for numerical relativity

In recent years, many different numerical evolution schemes for Einstein's 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. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. [1]

[1] Towards standard testbeds for numerical relativity
with Mexico Numerical Relativity Workshop 2002 Participants
M. Alcubierre, G. Allen, C. Bona, D. Fiske, T. Goodale, F.S. Guzman, I. Hawke, S. Hawley, S. Husa, M. Koppitz, C. Lechner, D. Pollney, D. Rideout, M. Salgado, E. Schnetter, E. Seidel, H. Shinkai, D. Shoemaker, B. Szilagyi, R. Takahashi, and J. Winicour
Class. Quant. Gravity 21 (2004) 589-613 Abstract