arXiv subjects

Norihiro Tanahashi

Publications and source records attributed to Norihiro Tanahashi.

At least 37 records · Page 2Linked to original sources

arXiv2019

Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime

We examine hidden symmetry and its relation to the separability of the Maxwell equation on the Wahlquist spacetime. After seeing that the Wahlquist spacetime is a type-D spacetime whose repeated principal null directions are shear-free and geodesic, we show that the spacetime admits three gauged conformal Killing-Yano (GCKY) tensors which are in a relation with torsional conformal Killing-Yano tensors. As a by-product, we obtain an ordinary CKY tensor. We also show that thanks to the GCKY tensors, the Maxwell equation reduces to three Debye equations, which are scalar-type equations, and two of them can be solved by separation of variables.

gr-qc↗

arXiv2019

Dyonic Catalysis in the KPV Vacuum Decay

We investigate catalysis induced by a dyonic impurity in the metastable vacuum studied by Kachru, Pearson and Verlinde, which can be relevant to vacuum decay in the KKLT scenario. The impurity is a D3-brane wrapping on $ \mathbb{S}^3$ in the Klebanov-Strassler geometry. The effect of the D3-brane can be encoded in the world-volume theory of an NS5-brane as an electromagnetic field on it. As the field strength becomes large, instability of the vacuum enhances. As a result, the lifetime of the metastable vacuum becomes drastically shorter.

hep-th↗

arXiv2019

Invertible field transformations with derivatives: necessary and sufficient conditions

We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications.

hep-th↗

arXiv2019

Separability of Maxwell equation in rotating black hole spacetime and its geometric aspects

Recently a new formalism for perturbations of Maxwell's equations on the background of the Kerr-NUT-(A)dS spacetime was proposed, with which the equations are reduced to a equation of motion of a scalar field that can be solved by separation of variables. In this formalism the differential operators that commute with the operators of the equations of motion, called symmetry operators, played a key role to establish the separable structure. In this work we propose a method to reproduce these commuting symmetry operators in terms of the geometric quantities associated to the hidden symmetry of the background spacetime.

gr-qc↗

arXiv2018

Chaos of Wilson Loop from String Motion near Black Hole Horizon

To find the origin of chaos near black hole horizon in string-theoretic AdS/CFT correspondence, we perform a chaos analysis of a suspended string in AdS black hole backgrounds. It has a definite CFT interpretation: chaos of Wilson loops, or in other words, sensitive time-evolution of a quark antiquark force in thermal gauge theories. Our nonlinear numerical simulation of the suspended Nambu-Goto string shows chaos, which would be absent in pure AdS background. The calculated Lyapunov exponent $λ$ satisfies the universal bound $λ\leq 2πT_{\rm H}$ for the Hawking temperature $T_{\rm H}$. We also analyze a toy model of a rectangular string probing the horizon and show that it contains a universal saddle characterized by the surface gravity $2πT_{\rm H}$. Our work demonstrates that the black hole horizon is the origin of the chaos, and suggests a close interplay between chaos and quark deconfinement.

hep-th↗

arXiv2017

Wave propagation and shock formation in the most general scalar-tensor theories

This work studies wave propagation in the most general scalar-tensor theories, particularly focusing on the causal structure realized in these theories and also the shock formation process induced by nonlinear effects. For these studies we use the Horndeski theory and its generalization to the two scalar field case. We show that propagation speeds of gravitational wave and scalar field wave in these theories may differ from the light speed depending on background field configuration, and find that a Killing horizon becomes a boundary of causal domain if the scalar fields share the symmetry of the background spacetime. About the shock formation, we focus on transport of discontinuity in second derivatives of the metric and scalar field in the shift-symmetric Horndeski theory. We find that amplitude of the discontinuity generically diverges within finite time, which corresponds to shock formation. It turns out that the canonical scalar field and the scalar DBI model, among other theories described by the Horndeski theory, are free from such shock formation even when the background geometry and scalar field configuration are nontrivial. We also observe that gravitational wave is protected against shock formation when the background has some symmetries at least. This fact may indicate that the gravitational wave in this theory is more well-behaved compared to the scalar field, which typically suffers from shock formation.

hep-th↗

arXiv2016

Universality in Chaos of Particle Motion near Black Hole Horizon

Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, the Lyapunov exponent is subject to an inequality $λ\leq 2πT_{\rm BH}/\hbar$, which is identical to the bound recently discovered by Maldacena, Shenker and Stanford.

hep-th↗

arXiv2016

New Quasidilaton theory in Partially Constrained Vielbein Formalism

In this work we study the partially constrained vielbein formulation of the new quasidilaton theory of massive gravity which couples to both physical and fiducial metrics simultaneously via a composite effective metric. This formalism improves the new quasidilaton model since the Boulware-Deser ghost is removed fully non-linearly at all scales. This also yields crucial implications in the cosmological applications. We derive the governing cosmological background evolution and study the stability of the attractor solution.

hep-th↗

arXiv2015

The most general second-order field equations of bi-scalar-tensor theory in four dimensions

The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.

gr-qc↗

arXiv2015

Spherical Domain Wall Collapse in a Dust Universe

To clarify observational consequence of bubble nucleations in inflationary era, we analyse dynamics of a spherical domain wall in an expanding universe. We consider a spherical shell of the domain wall with tension $σ$ collapsing in a spherically-symmetric dust universe, which is initially separated into the open Friedmann-Lemaître-Robertson-Walker universe inside the shell and the Einstein-de Sitter universe outside. The domain wall shell collapses due to the tension, and sweeps the dust fluid. The universe after the collapse becomes inhomogeneous and is described by the Lemaître-Tolman-Bondi model. We construct solutions describing this inhomogeneous universe by solving dynamical equations obtained from Israel's junction conditions applied to this system. We find that a black hole forms after the domain wall collapse for any initial condition, and that the black hole mass at the moment of its formation is universally given by $M_{\rm BH}\simeq 17 σ/H_{\rm hc}$, where $H_{\rm hc}$ is the Hubble parameter at the time when the shell radius becomes equal to the Hubble radius. We also find that the dust fluid is distributed as $ρ\propto R^{3/2}$ near the central region after the collapse, where $R$ is the area radius. These features would provide observable signatures of a spherical domain wall generated in the early universe.

gr-qc↗

arXiv2015

Cosmology in bimetric theory with an effective composite coupling to matter

We study the cosmology of bimetric theory with a composite matter coupling. We find two possible branches of background evolution. We investigate the question of stability of cosmological perturbations. For the tensor and vector perturbations, we derive conditions on the absence of ghost and gradient instabilities. For the scalar modes, we obtain conditions for avoiding ghost degrees. In the first branch, we find that one of the scalar modes becomes a ghost at the late stages of the evolution. Conversely, this problem can be avoided in the second branch. However, we also find that the constraint for the second branch prevents the doubly coupled matter fields from being the standard ingredients of cosmology. We thus conclude that a realistic and stable cosmological model requires additional minimally coupled matter fields.

hep-th↗

arXiv2014

Causality and Hyperbolicity of Lovelock Theories

In Lovelock theories, gravity can travel faster or slower than light. The causal structure is determined by the characteristic hypersurfaces. We generalise a recent result of Izumi to prove that any Killing horizon is a characteristic hypersurface for all gravitational degrees of freedom of a Lovelock theory. Hence gravitational signals cannot escape from the region inside such a horizon. We investigate the hyperbolicity of Lovelock theories by determining the characteristic hypersurfaces for various backgrounds. First we consider Ricci flat type N spacetimes. We show that characteristic hypersurfaces are generically all non-null and that Lovelock theories are hyperbolic in any such spacetime. Next we consider static, maximally symmetric black hole solutions of Lovelock theories. Again, characteristic surfaces are generically non-null. For some small black holes, hyperbolicity is violated near the horizon. This implies that the stability of such black holes is not a well-posed problem.

hep-th↗

arXiv2014

Shock Formation in Lovelock Theories

We argue that Lovelock theories of gravity suffer from shock formation, unlike General Relativity. We consider the propagation of (i) a discontinuity in curvature, and (ii) weak, high frequency, gravitational waves. Such disturbances propagate along characteristic hypersurfaces of a "background" spacetime and their amplitude is governed by a transport equation. In GR the transport equation is linear. In Lovelock theories, it is nonlinear and its solutions can blow up, corresponding to the formation of a shock. We show that this effect is absent in some simple cases e.g. a flat background spacetime, and demonstrate its presence for a plane wave background. We comment on weak cosmic censorship, the evolution of shocks, and the nonlinear stability of Minkowski spacetime, in Lovelock theories.

hep-th↗

arXiv2014

Exact black hole solutions in shift symmetric scalar-tensor theories

We derive a variety of exact black hole solutions in a subclass of Horndeski's scalar-tensor theory possessing shift symmetry, $ϕ\toϕ+c$, and reflection symmetry, $ϕ\to-ϕ$. The theory admits two arbitrary functions of $X:=-(\partialϕ)^2/2$, and our solutions are constructed without specifying the concrete form of the two functions, implying that black hole solutions in specific scalar-tensor theories found in the literature can be extended to a more general class of theories with shift symmetry. Our solutions include a black hole in the presence of an effective cosmological constant, the Nariai spacetime, the Lifshitz black hole, and other nontrivial solutions, all of which exhibit nonconstant scalar-field profile.

gr-qc↗

arXiv2014

Viable cosmology in bimetric theory

We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained.

hep-th↗

arXiv2014

Dynamical Meson Melting in Holography

We discuss mesons in thermalizing gluon backgrounds in the N=2 supersymmetric QCD using the gravity dual. We numerically compute the dynamics of a probe D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background thermalizing from zero to finite temperatures by energy injection. In static backgrounds, it has been known that there are two kinds of brane embeddings where the brane intersects the black hole or not. They correspond to the phases with melted or stable mesons. In our dynamical setup, we obtain three cases depending on final temperatures and injection time scales. The brane stays outside of the black hole horizon when the final temperature is low, while it intersects the horizon and settles down to the static equilibrium state when the final temperature is high. Between these two cases, we find the overeager case where the brane dynamically intersects the horizon although the final temperature is not high enough for a static brane to intersect the horizon. The interpretation of this phenomenon in the dual field theory is meson melting due to non-thermal effects caused by rapid energy injection. In addition, we comment on the late time evolution of the brane and a possibility of its reconnection.

hep-th↗

arXiv2014

Cosmological matching conditions and galilean genesis in Horndeski's theory

We derive the cosmological matching conditions for the homogeneous and isotropic background and for linear perturbations in Horndeski's most general second-order scalar-tensor theory. In general relativity, the matching is done in such a way that the extrinsic curvature is continuous across the transition hypersurface. This procedure is generalized so as to incorporate the mixing of scalar and gravity kinetic terms in the field equations of Horndeski's theory. Our matching conditions have a wide range of applications including the galilean genesis and the bounce scenarios, in which stable, null energy condition violating solutions play a central role. We demonstrate how our matching conditions are used in the galilean genesis scenario. In doing so, we extend the previous genesis models and provide a unified description of the theory admitting the solution that starts expanding from the Minkowski spacetime.

hep-th↗

arXiv2013

Multi-field G-inflation

We propose a multi-field extension of (generalized) G-inflation, based on covariant multi-galileons and their generalization preserving second-order field equations. We compute the quadratic action for cosmological perturbations. By comparing the formulas for cosmological perturbations, it is highlighted that multi-field DBI galileon inflation is not included in the multi-field version of generalized G-inflation. Our result indicates that the generalized covariant multi-galileon theory is not the most general multi-scalar-tensor theory with second-order field equations.

hep-th↗