# Program

All the talk are given in the “Conference Room” at ICISE.

The gravitational wave detectors LIGO/VIRGO have discovered the signals generated by the coalescence of binary black holes at astronomical distances. The theoretical and numerical works on the two-body problem in general relativity play a very important role when deciphering and interpreting the gravitational wave signals. In this talk we present the state-of-the-art on post-Newtonian (PN) methods in GR, applied to the gravitational waveform generated during the inspiralling phase of coalescing black hole binaries. In particular we discuss recent developments on the fourth post-Newtonian (4PN) approximation, both for the equations of motion [1]–[3] and the gravitational radiation field [4].

[1] Laura Bernard, Luc Blanchet, Alexandre Bohé,
Guillaume Faye and Sylvain Marsat, *Fokker action of
non-spinning compact binaries at the fourth post-Newtonian
approximation*, Phys. Rev. D, **93**, (2016).

[2] Laura Bernard, Luc Blanchet, Alexandre Bohé, Guillaume
Faye and Sylvain Marsat, *Energy and periastron advance of
compact binaries on circular orbits at the fourth post-Newtonian
order*, Phys. Rev. D, **95**, 044026 (2017).

[3] Laura Bernard, Luc Blanchet, Alexandre Bohé, Guillaume
Faye and Sylvain Marsat, *Dimensional regularization of the IR
divergences in the Fokker action of point-particle binaries at the
fourth post-Newtonian order*, submitted to Phys. Rev. D (2017).

[4] Tanguy Marchand, Luc Blanchet and Guillaume Faye, *Gravitational-wave tail effects to quartic non-linear order*,
Class. and Quant. Gravity **33**, 244003 (2016).

We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two non-spinning compact objects up to the 4PN order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near zone and far zone fields, and a consistent computation of the 4PN tail effect in d dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the model of point particles describing compact objects.

A newly born, proto-neutron star or a compact remnant of neutron stars binary merger are expected to rotate differentially and to be important sources of gravitational radiation. A highly accurate, multidomain spectral code is used in order to construct sequences of general relativistic, differentially rotating neutron stars in axisymmetry and stationarity. The high level of accuracy and stability of the code enable us to investigate the solution space corresponding to broad ranges of degree of differential rotation and stellar densities. We find new types of configurations, which were not considered in previous work, mainly due to numerical limitations. We review studies on properties of differentially rotating neutron stars and strange stars in GR.

We show that a massless canonical scalar field minimally coupled to general relativity can become a tachyonic ghost at low energies around a background in which the scalar's gradient is spacelike. By performing a canonical transformation we demonstrate that this low energy ghost can be recast, at the level of the action, in a form of a fluid that undergoes a Jeans-like instability affecting only modes with large wavelength. This illustrates that low energy tachyonic ghosts do not lead to a catastrophic quantum vacuum instability, unlike the usual high-energy ghost degrees of freedom.

In the context of a gauge theory nonminimally coupled to scalar-tensor gravity, we find a cosmological attractor solution that represents a de Sitter universe with a homogeneous magnetic field. The solution fully takes into account backreaction of the magnetic field to the geometry and the scalar field. Such a solution is made possible by scaling-type global symmetry and fine-tuning of two parameters of the theory. If the fine-tuning is relaxed then the solution is deformed to an axisymmetric Bianchi type-I universe with constant curvature invariants, a homogeneous magnetic field and a homogeneous electric field. Implications to inflationary magnetogenesis are briefly discussed.

[1] S.~Mukohyama, “Stealth magnetic field in de Sitter spacetime,” Phys.\ Rev.\ D **94**, no. 12, 121302 (2016) doi:10.1103/PhysRevD.94.121302 [arXiv:1607.07041 [hep-th]].

This talk is based on the study in collaboration with P.S. Joshi, J. Guo, P. Kocharlakota, H. Tagoshi, T. Harada, M. Patil and A. Krolak [1]. The superspinar proposed by Gimon and Hoava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable, and that the modes will decay in time. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.

[1] P.S. Joshi, J. Guo, P. Kocharlakota, H. Tagoshi, T. Harada, M. Patil and A. Krolak, arXiv: 1707.07242.

In our research [1], we construct solutions describing static and spherical relativistic stars in the minimal model of the de Rham-Gabadadz-Tolley (dRGT) massive gravity. A new equation, derived from consistency conditions, determines the behavior of a extra degree of freedom. By numerical calculation, we show that the maximal mass in massive gravity is smaller than that in general relativity for several equations of state. The results could be consistent with previous studies [2] on the energy scales in which non-linear kinetic terms appear. Moreover, we report the studies of relativistic stars in the non-minimal model of the theory.

[1] Taishi Katsuragawa, Shin'ichi Nojiri, Sergei D. Odintsov, and Masashi Yamazaki,
*Relativistic stars in de Rham-Gabadadze-Tolley massive gravity*,
Phys. Rev. D 93, 124013.

[2] Sébastien Renaux-Petel,
*On the Vainshtein mechanism in the minimal model of massive gravity*,
JCAP 1403 (2014) 043

We discuss the wave scattering by a Kerr black hole. We assume that the wave source is a point source emitting a massless scalar wave, and the wavelength is much shorter than the size of the black hole. In the scattered wave, we see two diamond-shaped optical caustics associated with two different wave modes, which correspond to geodesic motions in the Kerr spacetime: direct light rays of which impact parameters are sufficient large and reach an observer, and winded light rays which wind around the photon sphere, then reach an observer. By taking the Fourier transform of the scattered waves, we obtain the images of the point source. Then, we discuss the relation between the position of the observer and the number of image. References

[1] Y. Nambu, S Noda, ”Wave optics in the black hole spacetimes: Schwarzschild case”, Class. Quant. Grav. 33, 75011 (2016) [gr-qc/1502.05468].

[2] S Noda, Y Nambu ”Wave optics in the black hole spacetimes: Kerr case” in prep,

The search for a consistent theory of finite-range gravity is a longstanding problem and well motivated by both theoretical and observational considerations. On the theoretical side, whether there exists such a consistent extension of general relativity by a mass term is a basic question of classical field theory. On the observational side, continuing experimental probes of gravity have revealed new unexpected phenomena at large scales. One of the most profound discovery is the cosmic acceleration, which was found in 1998. The extremely tiny energy-scale associated with the cosmic acceleration hints that gravity might need to be modified at long distances. The massive gravity is one of the most interesting attempts in this direction. In this talk, after briefly reviewing the history of massive gravity, I will describe cosmological solutions and their stability, including some recent updates such as the status of quasidilaton theories and Lorentz-violating massive gravity.

[1] A. De Felice and S. Mukohyama, “Graviton mass might reduce tension between early and late time cosmological data,” Phys. Rev. Lett. **118**, no. 9, 091104 (2017) doi:10.1103/PhysRevLett.118.091 [arXiv:1607.03368 [astro-ph.CO]].

[2] A. De Felice, S. Mukohyama and M. Oliosi, “Minimal theory of quasidilaton massive gravity,” Phys. Rev. D **96**, no. 2, 024032 (2017) doi:10.1103/PhysRevD.96.024032 [arXiv:1701.01581 [hep-th]].

[3] C. Mazuet, S. Mukohyama and M. S. Volkov, “Anisotropic deformations of spatially open cosmology in massive gravity theory,” JCAP **1704**, no. 04, 039 (2017)doi:10.1088/1475-7516/2017/04/039 [arXiv:1702.04205 [hep-th]].

[4] A. De Felice, S. Mukohyama and J. P. Uzan, “Extending bimetric models of massive gravity to avoid to rely on the Vainshtein mechanism on local scales and the Higuchi bound on cosmological scales,” arXiv:1702.04490 [hep-th].

[5] A. E. Gumrukcuoglu, K. Koyama and S. Mukohyama, “Stable cosmology in ghost-free quasidilaton theory,” arXiv:1707.02004 [hep-th].

I will talk about a recent progress of numerical modeling of binary neutron star mergers. Specifically, I will review a merger process composed of the inspital-late inspiral phase, the merger phase, and the post-merger phase and scientific targets of each phases.

The first direct detection of gravitational waves (GW) in GW150914 by advanced LIGO, opened the door to the era of gravitational-wave astronomy in which the universe is explored by means of GW. Binary neutron star (NS) systems, such as binary neutron stars and black hole-neutron star binaries, are also ones of the promising candidates of GW sources. If observed, GW from these NS binaries will present very exciting prospects.GW can be probes of the equation of state of NS matter which is still poorly understood.A long-standing puzzle on the central engine of short gamma-ray bursts could be resolvedif GW from a NS binary and a gamma-ray burst are observed simultaneously.Furthermore, the mergers of NS binaries also attract attention as a r-process nucleosynthesis sitewhich proceeds in the neutron-rich materials ejected in the merger.This is also important as a possible electro-magnetic counterpart to GW, because the ejecta will heated by the radioactive decay and fission of these r-process elements and would shine atoptical and infra-red bands in 1‚àí10 days after the merge.Motivated by these facts, we have performed numerical relativity simulations of mergers of NS binaries.I will talk recent developments on some topics listed above in our group and discuss future prospects.

This talk is based on the study in collaboration with Hirotada Okawa and Kei-ichi Maeda [1]. Energy extraction from a rotating or charged black hole is one of fascinating issues in general relativity. The collisional Penrose process is one of such extraction mechanisms and has been reconsidered actively since the publication of Ref.~[Banados2009]. In order to get results analytically, the test particle approximation is adopted so far. Successive works based on this approximation scheme have not yet revealed the upper bound on the efficiency of the energy extraction[Zaslavskii2012,Nemoto2013,Berti2014]. In this paper, we investigate the collisional Penrose process of infinitesimally thin charged shells in the Reissner-Nordstr\"{o}m spacetime by fully taking into account the self-gravity of the shells, and show that there is an upper bound on the extracted energy, which is consistent to the area law of the black hole. We also show a particular scenario in which the almost maximum energy extraction is achieved.

[1] K. Nakao, H. Okawa and K. Maeda,
*Nonlinear collisional Penrose process*, in preparation.
%ys. Rept. 261 (1995) 1 [Erratum ibid 281 (1997) 399] [hep-ph/9501369].

[Banados2009]
M. Banados, J. Silk and S. M. West,
Phys. Rev. Lett. **103**, 111102 (2009), [0909.0169].

[Zaslavskii2012]
O. B. Zaslavskii,
Phys. Rev. D **86**, 124039 (2012), [1207.5209].
%%CITATION = ARXIV:1207.5209;%%

[Nemoto2013]
H. {Nemoto}, U. {Miyamoto}, T. {Harada} and T. {Kokubu},
Phys. Rev. D **87**, 127502 (2013), [1212.6701].

[Berti2014]
E. Berti, R. Brito and V. Cardoso,
Phys. Rev. Lett. **114**, 251103 (2015), [1410.8534].

Though the expansion of a simple FLRW dust ball always decelerates in Newtonian gravitational dynamics, in GR, when the dust ball's radius insufficiently exceeds the Schwarzschild value, its expansion instead accelerates because the dominant gravitational time-dilation braking of its expansion speed weakens as it expands. But in “comoving coor dinates” the fixing of to unity eliminates all gravitational time dilation, producing the purely Newtonian Friedmann dust-ball equation of motion in those “coordinates”. For a particular initial condition Oppenheimer and Snyder remedied the GR-inconsistent purely- Newtonian dust-ball behavior in “comoving coordinates” by their famed analytic transformation to GR-compatible “standard” coordinates. Recent extension of their transformation to arbitrary dust- ball initial conditions enables the derivation of GR-consistent non- Newtonian equations of motion in “standard” coordinates for all shell radii of any simple FLRW dust ball. These show not only that a dust ball's expansion always accelerates when its radius insufficient ly exceeds the Schwarzschild value, but also that for a range of ini tial conditions a dust ball's expansion never ceases to accelerate (although that acceleration asymptotically decreases toward zero), ap parently eliminating any need for a nonzero “dark energy” cosmologi cal constant.

The direct detection of gravitational waves from binary black hole mergers by the advanced Laser Interferometer Gravitational-Wave Observatories has ushered astrophysics into a new era of observing cosmic events that were previously invisible. Using results for around two thousand star cluster models simulated using well-tested the MOCCA Monte Carlo code for star cluster evolution we determine the astrophysical properties and the local and comological merger rate densities for coalescing binary black holes (BBHs) originating from globular clusters. Our models cover different initial parameters (masses,metalicities, densities etc). We extracted information for all coalescing binary black holes (BBHs) that merge via gravitational radiation from these Globular Cluster (GC) models and for those BHs that collide due to 2-body, 3-body and 4-body dynamical interactions. In my talk I will focus on the importance of BBH mergers originating from GC for gravitational wave observations. The impact of the intermediate black holes that are dynamically formed in 30% GC models will be discussed.

We present results from a controlled numerical experiment investigating the effect of stellar density gas on the coalescence of binary black holes (BBHs) and the resulting gravitational waves (GWs). This investigation is motivated by the proposed stellar core fragmentation scenario for BBH formation and the associated possibility of an electromagnetic counterpart to a BBH GW event. We employ full numerical relativity coupled with general-relativistic hydrodynamics and set up a BBH (motivated by GW150914) inside gas with realistic stellar densities. Our results show that at densities dynamical friction between the BHs and gas changes the coalescence dynamics and the GW signal in an unmistakable way. We show that for GW150914, LIGO observations conclusively rule out BBH coalescence inside stellar gas of . Typical densities in the collapsing cores of massive stars are in excess of this density. This excludes the fragmentation scenario for the formation of GW150914.

We derive the first law of binary point-particle mechanics for generic bound (i.e. eccentric) orbits at the fourth post-Newtonian (4PN) order, accounting for the non-locality in time of the dynamics due to the occurence of a gravitational-wave tail effect at that order. Using this first law, we show how the periastron advance of the binary system can be related to the averaged redshift of one of the two bodies, in the circular orbit limit. Combining this expression with existing analytical self-force results for the averaged redshift, we recover the known 4PN expression for the circular-orbit periastron advance, to linear order in the mass ratio.

We will present basic results of our recent studies on the fate of Hawking's cosmic no-hair conjecture in the framework of anisotropically inflating model proposed by Kanno, Soda, and Watanabe. In particular, we will point out that the cosmic no-hair conjecture seems to be generally violated in the Kanno-Soda-Watanabe model for both canonical and non-canonical scalar fields due to the existence of an unusual coupling term . However, we will show that the cosmic no-hair conjecture will remain its validity once a phantom scalar field , whose kinetic energy term is negative definite, is introduced into the Kanno-Soda-Watanabe model.

We present a model of the analog geometry in a MHD flow (magnetoacoustic geometry) based on [1]. To investigate the properties of the magnetoacoustic geometry, we consider a two-dimensional axisymmetric inflow and examine the behavior of magnetoacoustic rays which is a counterpart of the MHD waves in the eikonal limit. We find that the magnetoacoustic geometry is classified into three types depending on two parameters characterizing the background flow: analog spacetimes of rotating black holes, ultra spinning stars with ergoregions which can evoke ergoregion instability, and spinning stars without ergoregions.

[1] S. Noda, Y. Nambu and M. Takahashi, ”Analog rotating black holes in a magnetohydrodynamic inflow”, Phys. Rev. D. 95, 104055 (2017) [gr-qc /1610.06690].

[2] W. G. Unruh, ”Experimental black-hole evaporation?”, Phys. Rev. Lett. 46, (1981) 1351–1353.

[3] C. Barcelo, S. Liberati, and M. Visser, ”Analogue Gravity”, Living Rev. Rel. 8, 12 (2005) [Living Rev. Rel. 14, 3 (2011)] [gr-qc/0505065].

We will present main results of our recent investigations on higher dimensional massive gravity~[1] and bi-gravity~[2]. In particular, we will show an effective method based on the well-known Cayley-Hamilton theorem to construct higher dimensional massive interaction terms. Then, we will focus on five-dimensional massive (bi-)gravity as specific demonstrations. In particular, we will show the corresponding Einstein and constraint equations for five-dimensional massive (bi-)gravity. Then, a number of cosmological solutions of five-dimensional massive (bi-)gravity will be presented accordingly.

[1]
T.Q. Do, *Higher dimensional nonlinear massive gravity*,
Phys. Rev. D { 93} (2016) 104003,
PhysRevD.93.104003
[arXiv:1602.05672].

[2]
T.Q. Do, *Higher dimensional massive bigravity*,
Phys. Rev. D { 94} (2016) 044022,
PhysRevD.94.044022
[arXiv:1604.07568].

Because the Einstein equation can't uniquely determine the metric, it must be supplemented by additional metric constraints. Since the Einstein equation can be derived in a purely special-relativistic context, those constraints (which can't be generally covariant) should be Lorentz-covariant; moreover, for the effect of the constraints to be natural from the perspective of observational and empirical physical scientists, they should also constrain the general coordinate transformations (which are compatible with the unconstrained Einstein equation) so that the constrained transformations manifest a salient feature of the Lorentz transformations. The little-known Einstein-Schwarzschild coordinate condition, which requires the metric's determinant to have its -1 Minkowski value, thereby constrains coordinate transformations to have unit Jacobian, and for that reason causes tensor densities to transform as true tensors, which is a salient feature of the Lorentz transformations. The Einstein-Schwarzschild coordinate condition also allows the static Schwarzschild solution's singular radius to be exactly zero; though another coordinate condition that allows zero Schwarzschild radius exists, it isn't Lorentz-covariant.