# Computational Relativistic Astrophysics

## Numerical relativity

To clarify the formation process of black holes and neutron stars and the merger process of black holes and neutron stars, we have to fully solve Einstein's equation together with the equations of motion for the matter in the presence of the matter fields. These equations are nonlinear, simultaneous, and partially differential equations, and hence, it is not feasible to get solutions analytically, in general. Therefore, numerical simulation using high-performance computers is the unique approach for the theoretical study. Numerical relativity is the field such that Einstein's equation is fully solved in computer. Since 1990s, we have been developing formulations and numerical methods in numerical relativity. For a solution of Einstein's equation, the numerical method is well established. It is also feasible to accurately solve hydrodynamics/magnetohydrodynamics equations and to approximately solve radiation hydrodynamics equations for neutrino transport. Using such developed infrastructure, we are now exploring a variety of dynamical and general relativistic phenomena like merger of binary neutron stars and black hole-neutron star binaries, stellar core collapse to a black hole and surrounding torus, formation of a supermassive black hole through the collapse of supermassive stars, evolution of black holes by accretion of matter, long-term evolution of rotating neutron stars, stability of higher-dimensional black hole, merger of binary neutron stars in scalar-tensor theory of gravity, and so on. These numerical-relativity simulations now play an important role for predicting gravitational waveforms for the detection by gravitational-wave detectors and for exploring high-energy phenomena such as gamma-ray bursts and supernova explosion. Numerical relativity also plays a role for exploring nonlinear nature of gravity theories.

## Predicting gravitational waveforms

Gravitational waves are emitted from general-relativistic and dynamical phenomena, if they are not in spherically symmetric systems. If a large amount of gravitational waves are emitted, they could be detected by gravitational-wave detectors such as LIGO, VIRGO, KAGRA(LCGT). In fact, advanced LIGO has already achieved the first direct detection of gravitational waves from binary black holes in September of 2015.

We may expect that a large number of gravitational-wave sources will be observed by the gravitational-wave detectors in the near future. After gravitational-waves are observed, we have to determine what the source of gravitational waves is. Specifically, we have to extract the information of the sources like mass, spin, distance from us, and so on. For this purpose, we have to prepare theoretical templates of gravitational waves emitted from the expected sources. We are now performing a large number of numerical-relativity simulations for the merger of binary neutron stars, black hole-neutron star binaries, stellar core collapse to a stellar-size and supermassive black hole, and so on, aiming at accurately predicting the gravitational waveforms.

## Merger of binary neutron stars

Merger of binary neutron stars is one of the most promising sources for gravitational-wave detectors like LIGO, VIRGO, KAGRA(LCGT). This phenomena is also the promising origin of short-hard gamma-ray bursts. To predict gravitational waveforms emitted by the binary neutron star merger and to theoretically explore the merger hypothesis of short-hard gamma-ray bursts, numerical-relativity is the unique approach. In addition, the merger of binary neutron stars and associated mass ejection process is proposed as the main site for the r-process nucleosynthesis. For exploring this hypothesis, numerical relativity is again the unique theoretical approach. We have been working in this problem in the last two decades and obtained a variety of knowledges for the merger process and resulting gravitational waveforms.

## Merger of black hole-neutron star binaries

Merger of black hole-neutron star binaries is also among the most promising sources of gravitational waves and a promising candidate for the central engine of short-hard gamma-ray bursts. For this system, broadly speaking, there are two possible fates. One is that the neutron star is simply swallowed by the companion black hole, and the other is that the neutron star is tidally disrupted during the merger process. In the case that the tidal disruption occurs, a wide variety of high-energy phenomena like gamma-ray bursts and mass ejection leading transient electromagnetic emission are expected. We are exploring these phenomena in numerical relativity.

## Gravitational collapse to a black hole

Massive stars are evolved through a series of nuclear burning and eventually, in their center, iron core is formed. If the mass of iron core (and surrounding layers) is sufficiently large, a black hole will be formed after the stellar core collapse. Massive stellar-size black holes recently discovered in binary black holes observed by advanced LIGO are likely to be formed in such process. However, the formation process of such black holes is not well understood yet.

Recent observations have shown that large galaxies usually have a supermassive black hole (SMBH) of million to 10 billion solar mass in their center. However, the formation process of SMBH is still unknown: Actually, clarifying the formation process of SMBH has been a long- standing problem in astrophysics.

We are challenging these problems in the framework of numerical relativity. Specifically, we prepare a variety of plausible progenitor stars and perform a variety of numerical-relativity simulations aiming at clarifying the black-hole formation process. We then explore the possible signals of the black hole formation like gravitational waves, neutrinos, and electromagnetic waves, which may be detected in the future observations leading to clarifying the formation process of black holes.

## Instability of rotating neutron stars

Rotating neutron stars are often unstable. If they are rapidly rotating or differentially rotating with a high degree of differential rotation, they could be unstable to non-axisymmetric deformation. Such non-axisymmetric outcome could be the source of gravitational waves. Exploring the stability issues of neutron stars is one of the issues in our group.

## Magnetohydrodynamics simulation in General Relativity

There are a wide variety of phenomena in which magnetic fields play a crucial role for their processes. It is quite likely that magnetic-field instabilities play an important role in the merger of binary neutron stars and supernova explosion. For example, at the collision of two neutron stars, a shear layer is inevitably formed at the contact surface of two neutron stars. At such shear surface, it is known that the Kelvin-Helmholtz instability occurs and a number of small vortexes are generated. The vortex motion subsequently amplifies the magnetic-field strength by winding of the magnetic fields. After the significant amplification of the magnetic field, turbulence is likely to be excited, and then, the resulting turbulent viscosity could determine the evolution of the merger remnant because it contributes to angular momentum transfer and viscous heating. To clarify these processes, we have to perform a magnetohydrodynamics simulation in general relativity. Here, for the accurate study, we need to correctly take into account the Kelvin-Helmholtz instability in the simulation. However, this is not computationally an easy task because the fast-growing mode of the Kelvin-Helmholtz instability has very small scales and we have to resolve such a small-scale mode in numerical relativity. To date, no simulation has resolved this type of small-scale modes, and thus, no physical simulation has been done. In the future, we need to perform a extremely high-resolution simulation to fully clarify the merger process of binary neutron stars. Magnetic-field instabilities could also play a crucial role in supernova explosion, evolution of the merger remnants of black hole-neutron star binaries, and so on. There are many issues that should be attacked by magnetohydrodynamics simulations in general relativity.

## Viscous hydrodynamics

One phenomenological way to take into account angular momentum transport and turbulent viscosity is to employ viscous hydrodynamics. By this, we explore the merger remnant of binary neutron stars and a torus surround the central compact objects.

## Higher-dimensional black holes

There are a variety of gravity theories that predict that spacetime in our world may have dimensions larger than 4 and do not contradict any observation and experimental results. The nature of gravity theories is well reflected in the properties of black holes which are the most strongly self-gravitating object. We explore the nature of higher-dimensional black hole in the framework of general relativity. In 4 spacetime dimension, black holes in general relativity are known to be stable against any (linear) perturbation. However, in higher-dimension, this is not the case: We found that if a black hole is moderately rapidly rotating, it could be unstable to non-axisymmetric deformation. Subsequently, it emits gravitational waves, dissipates angular momentum, and eventually settles to a stable black hole with small spin parameter. We also found evidence that in higher-dimensional spacetime, naked singularity may be formed much more easily than in four dimension. For example, in the two black hole collision, such singularity may be generated.

## Binary neutron stars in scalar-tensor theory

We have not had any evidence that general relativity is violated. However, the tests of general relativity have been performed in relatively weakly gravitational environment like in the solar system and binary neutron stars of large orbital separation. If gravitational waves from neutron-star merger are detected, we will have a great opportunity for testing general relativity in a strongly gravitational environment. For this test, it is important to expect what happens in alternative theory of gravity in the strongly selfgravitating systems. As one effort, we performed simulations for the merger of binary neutron stars in a scalar-tensor theory of gravity.