arXiv subjects

Masato Minamitsuji

Publications and source records attributed to Masato Minamitsuji.

At least 55 records · Page 3Linked to original sources

arXiv2018

Stealth Schwarzschild solution in shift symmetry breaking theories

We find stealth Schwarzschild solutions with a nontrivial profile of the scalar field regular on the horizon in the Einstein gravity coupled to the scalar field with the k-essence and/or generalized cubic galileon terms, which is a subclass of the Horndeski theory breaking the shift symmetry, where the propagation speed of gravitational waves coincides with the speed of light. After deriving sufficient conditions for the shift symmetry breaking theory to allow a general Ricci-flat metric solution with a nontrivial scalar field profile, we focus on the stealth Schwarzschild solution with the scalar field with or without time dependence. For the profile $ϕ=ϕ_0(r)$, we explicitly obtain two types of stealth Schwarzschild solutions, one of which is regular on the event horizon. The linear perturbation analysis clarifies that the kinetic term of the scalar mode identically vanishes, indicating that the scalar mode is strongly coupled. The absence of the kinetic term of the scalar mode in the quadratic action would inevitably arise for the stealth Schwarzschild solutions in the theory with a general scalar field profile depending only on the spatial coordinates. On the other hand, for the time-dependent scalar field profile, we clarify that there does not exist a stealth Schwarzschild solution in the shift symmetry breaking theories.

gr-qc↗

arXiv2018

Black holes in quartic-order beyond-generalized Proca theories

The generalized Proca theories with second-order equations of motion can be healthily extended to a more general framework in which the number of propagating degrees of freedom remains unchanged. In the presence of a quartic-order nonminimal coupling to gravity arising in beyond-generalized Proca theories, the speed of gravitational waves $c_t$ on the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological background can be equal to that of light $c$ under a certain condition. By using this condition alone, we show that the speed of gravitational waves in the vicinity of static and spherically symmetric black holes is also equivalent to $c$ for the propagation of odd-parity perturbations along both radial and angular directions. As a by-product, the black holes arising in our beyond-generalized Proca theories are plagued by neither ghost nor Laplacian instabilities against odd-parity perturbations. We show the existence of both exact and numerical black hole solutions endowed with vector hairs induced by the quartic-order coupling.

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arXiv2018

General Relativity solutions in modified gravity

Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.

gr-qc↗

arXiv2018

Vector boson star solutions with a quartic order self-interaction

We investigate boson star (BS) solutions in the Einstein-Proca theory with the quartic order self-interaction of the vector field $λ(A^μ\bar{A}_μ)^2/4$ and the mass term $μ\bar{A}^μA_μ/2$, where $A_μ$ is the complex vector field and ${\bar A}_μ$ is the complex conjugate of $A_μ$, and $λ$ and $μ$ are the coupling constant and the mass of the vector field, respectively. The vector BSs are characterized by the two conserved quantities, the Arnowitt-Deser-Misner (ADM) mass and the Noether charge associated with the global $U(1)$ symmetry. We show that in comparison with the case without the self-interaction $λ=0$, the maximal ADM mass and Noether charge increase for $λ>0$ and decrease for $λ<0$. We also show that there exists the critical central amplitude of the temporal component of the vector field above which there is no vector BS solution, and for $λ>0$ it can be expressed by the simple analytic expression. For a sufficiently large positive coupling $Λ:=M_{pl}^2λ/(8πμ^2) \gg 1$, the maximal ADM mass and Noether charge of the vector BSs are obtained from the critical central amplitude and of ${\cal O}[\sqrtλM_{pl}^3/μ^2 \ln (λM_{pl}^2/μ^2)]$, which is different from that of the scalar BSs, ${\cal O}(\sqrt{λ_ϕ}M_{pl}^3/μ_ϕ^2)$, where $λ_ϕ$ and $μ_ϕ$ are the coupling constant and the mass of the complex scalar field.

gr-qc↗

arXiv2018

Relativistic stars in vector-tensor theories

We study relativistic star solutions in second-order generalized Proca theories characterized by a $U(1)$-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

gr-qc↗

arXiv2018

Black hole perturbations in vector-tensor theories: The odd-mode analysis

In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings $G_3(X)$, where $X=-A_μA^μ/2$ with a vector field $A_μ$, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component $A_1$, which originates from the coupling to the Einstein tensor $G^{μν}A_μA_ν$ equivalent to the quartic coupling $G_4(X)$ containing a linear function of $X$, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings $G_4(X) \supset β_4 X^n$ with the nonvanishing $A_1$, while the other branch with $A_1=0$ can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.

gr-qc↗

arXiv2017

Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits

Using a thin shell, the first law of thermodynamics, and a unified approach, we study the thermodymanics and find the entropy of a (2+1)-dimensional extremal rotating Bañados-Teitelbom-Zanelli (BTZ) black hole. The shell in (2+1) dimensions, i.e., a ring, is taken to be circularly symmetric and rotating, with the inner region being a ground state of the anti-de Sitter (AdS) spacetime and the outer region being the rotating BTZ spacetime. The extremal BTZ rotating black hole can be obtained in three different ways depending on the way the shell approaches its own gravitational or horizon radius. These ways are explicitly worked out. The resulting three cases give that the BTZ black hole entropy is either the Bekenstein-Hawking entropy, $S=\frac{A_+}{4G}$, or it is an arbitrary function of $A_+$, $S=S(A_+)$, where $A_+=2πr_+$ is the area, i.e., the perimeter, of the event horizon in (2+1) dimensions. We speculate that the entropy of an extremal black hole should obey $0\leq S(A_+)\leq\frac{A_+}{4G}$. We also show that the contributions from the various thermodynamic quantities, namely, the mass, the circular velocity, and the temperature, for the entropy in all three cases are distinct. This study complements the previous studies in thin shell thermodynamics and entropy for BTZ black holes. It also corroborates the results found for a (3+1)-dimensional extremal electrically charged Reissner-Nordström black hole.

hep-th↗

arXiv2017

Hairy black-hole solutions in generalized Proca theories

We present a family of exact black-hole solutions on a static spherically symmetric background in second-order generalized Proca theories with derivative vector-field interactions coupled to gravity. We also derive non-exact solutions in power-law coupling models including vector Galileons and numerically show the existence of regular black holes with a primary hair associated with the longitudinal propagation. The intrinsic vector-field derivative interactions generally give rise to a secondary hair induced by non-trivial field profiles. The deviation from General Relativity is most significant around the horizon and hence there is a golden opportunity for probing the Proca hair by the measurements of gravitational waves (GWs) in the regime of strong gravity.

gr-qc↗

arXiv2017

Proca stars with nonminimal coupling to the Einstein tensor

We investigate Proca star (PS) solutions, namely boson star (BS) type solutions for a complex vector field with mass and nonminimal coupling to the Einstein tensor. Irrespective of the existence of nonminimal coupling, PS solutions are mini-BS type, but the inclusion of it changes properties. For positive nonminimal coupling parameters, PS solutions do not exist for central amplitudes above some certain value due to the singular behavior of the evolution equations. For negative nonminimal coupling parameters, there is no such singular behavior but sufficiently enhanced numerical resolutions are requested for larger amplitudes. Irrespective of the sign of the nonzero nonminimal coupling parameter, PSs with the maximal Arnowitt-Deser-Misner mass and Noether charge are gravitationally bound. Properties of PSs are very similar to those of BSs in scalar-tensor theories including healthy higher-derivative terms.

gr-qc↗

arXiv2017

Black holes in vector-tensor theories

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic and quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.

gr-qc↗

arXiv2017

Thermodynamics of extremal rotating thin shells in an extremal BTZ spacetime and the extremal black hole entropy

In a (2+1)-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter (AdS) spacetime, respectively. By applying the first law of thermodynamics to the extremal shell one shows that its entropy is an arbitrary function of the gravitational area $A_+$ alone, $S=S(A_+)$. When the shell approaches its own gravitational radius $r_+$ and turns into an extremal rotating BTZ black hole, it is found that the entropy of the spacetime remains such a function of $A_+$. It is thus vindicated, that extremal black holes, here extremal BTZ black holes, have different properties from the corresponding nonextremal black holes, which have the Bekenstein-Hawking entropy $S(A_+)= \frac{A_+}{4G}$, where $G$ is the gravitational constant. It is argued that for the extremal case $0\leq S(A_+)\leq \frac{A_+}{4G}$. Thus, rather than having just two entropies for extremal black holes, as previous results debated, 0 and $\frac{A_+}{4G}$, it is shown that extremal black holes may have a continuous range of entropies, limited by precisely those two entropies. Surely, the entropy that a particular extremal black hole picks must depend on past processes, notably on how it was formed. It is also found a remarkable relation between the third law of thermodynamics and the impossibility for a massive body to reach the velocity of light. In the procedure, it becomes clear that there are two distinct angular velocities for the shell, the mechanical and thermodynamic angular velocities. In passing, we clarify, for a static spacetime with a thermal shell, the meaning of the Tolman temperature formula at a generic radius and at the shell. (Abridged version).

hep-th↗

arXiv2016

Solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor

We investigate the static and spherically symmetric solutions in a class of the generalized Proca theory with the nonminimal coupling to the Einstein tensor. First, we show that the solutions in the scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor can be those in the generalized Proca theory with the vanishing field strength. We then show that when the field strength takes the nonzero value the static and spherically symmetric solutions can be found only for the specific value of the nonminimal coupling constant. Second, we investigate the first-order slow-rotation corrections to the static and spherically symmetric background. We find that for the background with the vanishing electric field strength the slowly rotating solution is identical to the Kerr- (anti-) de Sitter solutions in general relativity. On the other hand, for the background with the nonvanishing electric field strength the stealth property can realized at the first order in the slow-rotation approximation.

gr-qc↗

arXiv2016

Compact objects in Horndeski gravity

Horndeski gravity holds a special position as the most general extension of Einstein's theory of general relativity with a single scalar degree of freedom and second-order field equations. Because of these features, Horndeski gravity is an attractive phenomenological playground to investigate the consequences of modifications of general relativity in cosmology and astrophysics. We present a review of the progress made so far in the study of compact objects (black holes and neutron stars) within Horndeski gravity. In particular, we review our recent work on slowly rotating black holes and present some new results on slowly rotating neutron stars.

gr-qc↗

arXiv2016

Relativistic stars in scalar-tensor theories with disformal coupling

We present a general formulation to analyze the structure of slowly rotating relativistic stars in a broad class of scalar-tensor theories with disformal coupling to matter. Our approach includes theories with generalized kinetic terms, generic scalar field potentials and contains theories with conformal coupling as particular limits. In order to investigate how the disformal coupling affects the structure of relativistic stars, we propose a minimal model of a massless scalar-tensor theory and investigate in detail how the disformal coupling affects the spontaneous scalarization of slowly rotating neutron stars. We show that for negative values of the disformal coupling parameter between the scalar field and matter, scalarization can be suppressed, while for large positive values of the disformal coupling parameter stellar models cannot be obtained. This allows us to put a mild upper bound on this parameter. We also show that these properties can be qualitatively understood by linearizing the scalar field equation of motion in the background of a general-relativistic incompressible star. To address the intrinsic degeneracy between uncertainties in the equation-of-state of neutron stars and gravitational theory, we also show the existence of universal equation-of-state-independent relations between the moment of inertia and compactness of neutron stars in this theory. We show that in a certain range of the theory's parameter space the universal relation largely deviates from that of general relativity, allowing, in principle, to probe the existence of spontaneous scalarization with future observations.

gr-qc↗

arXiv2016

Neutron stars in Horndeski gravity

Horndeski's theory of gravity is the most general scalar-tensor theory with a single scalar whose equations of motion contain at most second-order derivatives. A subsector of Horndeski's theory known as "Fab Four" gravity allows for dynamical self-tuning of the quantum vacuum energy, and therefore it has received particular attention in cosmology as a possible alternative to the $Λ$CDM model. Here we study compact stars in Fab Four gravity, which includes as special cases general relativity ("George"), Einstein-dilaton-Gauss-Bonnet gravity ("Ringo"), theories with a nonminimal coupling with the Einstein tensor ("John") and theories involving the double-dual of the Riemann tensor ("Paul"). We generalize and extend previous results in theories of the John class and were not able to find realistic compact stars in theories involving the Paul class.

gr-qc↗

arXiv2015

Slowly rotating black hole solutions in Horndeski gravity

We study black hole solutions at first order in the Hartle-Thorne slow-rotation approximation in Horndeski gravity theories. We derive the equations of motion including also cases where the scalar depends linearly on time. In the Hartle-Thorne formalism, all first-order rotational corrections are described by a single frame-dragging function. We show that the frame-dragging function is exactly the same as in general relativity for all known black hole solutions in shift symmetric Horndeski theories, with the exception of theories with a linear coupling to the Gauss-Bonnet invariant. Our results extend previous no-hair theorems for a broad class of Horndeski gravity theories.

gr-qc↗

arXiv2015

Thermodynamics of rotating thin shells in the BTZ spacetime

We investigate the thermodynamic equilibrium states of a rotating thin shell, i.e., a ring, in a (2+1)-dimensional spacetime with a negative cosmological constant. The inner and outer regions with respect to the shell are given by the vacuum anti-de Sitter and the rotating Bañados-Teitelbom-Zanelli spacetimes, respectively. The first law of thermodynamics on the thin shell, together with three equations of state for the pressure, the local inverse temperature and the thermodynamic angular velocity of the shell, yields the entropy of the shell, which is shown to depend only on its gravitational radii. When the shell is pushed to its own gravitational radius and its temperature is taken to be the Hawking temperature of the corresponding black hole, the entropy of the shell coincides with the Bekenstein-Hawking entropy. In addition, we consider simple ansätze for the equations of state, as well as a power-law equation of state where the entropy and the thermodynamic stability conditions can be examined analytically.

hep-th↗

arXiv2015

The Initial State of a Primordial Anisotropic Stage of Inflation

We investigate the possibility that the inflationary period in the early universe was preceded by a primordial stage of strong anisotropy. In particular we focus on the simplest model of this kind, where the spacetime is described by a non-singular Kasner solution that quickly evolves into an isotropic de Sitter space, the so-called Kasner-de Sitter solution. The initial Big Bang singularity is replaced, in this case, by a horizon. We show that the extension of this metric to the region behind the horizon contains a timelike singularity which will be visible by cosmological observers. This makes it impossible to have a reliable prediction of the quantum state of the cosmological perturbations in the region of interest. In this paper we consider the possibility that this Kasner-de Sitter universe is obtained as a result of a quantum tunneling process effectively substituting the region behind the horizon by an anisotropic parent vacuum state, namely a $1+1$ dimensional spacetime compactified over an internal flat torus, $T_2$, which we take it to be of the form ${de Sitter}_2 \times T_2$ or ${Minkowski}_2 \times T_2$. As a first approximation to understand the effects of this anisotropic initial state, we compute the power spectrum of a massless scalar field in these backgrounds. In both cases, the spectrum converges at small scales to the isotropic scale invariant form and only present important deviations from it at the largest possible scales. We find that the decompactification scenario from $M_2 \times T_2$ leads to a suppressed and slightly anisotropic power spectrum at large scales which could be related to some of the anomalies present in the current CMB data. On the other hand, the spectrum of the universe with a $dS_2 \times T_2$ parent vacuum presents an enhancement in power at large scales not consistent with observations.

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