arXiv subjects

Masato Minamitsuji

Publications and source records attributed to Masato Minamitsuji.

At least 19 recordsLinked to original sources

arXiv2026

Exact pp-wave solutions in shift-symmetric higher-order scalar-tensor theories

We investigate exact plane-fronted gravitational wave (pp-wave) solutions within the framework of shift-symmetric quadratic-order higher-order scalar--tensor (HOST) theories. These solutions represent fully nonlinear radiative spacetimes that extend beyond the linearized approximation. We demonstrate that under the algebraic conditions on the coupling functions, the gravitational field equations reduce to a two-dimensional Laplace equation for the wave profile, recovering the structural form of vacuum general relativity (GR). By adopting a scalar field ansatz that depends linearly on transverse coordinates and arbitrarily on the retarded null coordinate, we maintain a constant kinetic term of the scalar field. This configuration allows for a \emph{stealth pp-wave} solution, where a nontrivial scalar field profile coexists with the gravitational wave without backreacting on the spacetime geometry. We further show that these stealth configurations are fully compatible with the degeneracy conditions of Class-Ia DHOST theories and satisfy current observational constraints. Finally, we examine the behavior of these solutions under disformal transformations, revealing that while the Brinkmann form is preserved, the stealth property is generically lost due to the mixing of scalar and tensor degrees of freedom. These results establish the robustness of pp-wave solutions in viable DHOST frameworks and highlight their utility for probing nonlinear effects in modified gravity.

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arXiv2025

Stealth black hole solutions in higher-order Maxwell-Einstein theories

We study static and spherically symmetric black hole solutions in higher-order Maxwell-Einstein theories. We do not particularly focus on the degenerate classes of theories. For several specific choices of the coupling functions, we show that in the presence of the ordinary Maxwell kinetic term the Reissner-Nordstr\"om-(anti-)de Sitter solution in the pure Maxwell-Einstein theory can also be a solution in generic classes of higher-order Maxwell-Einstein theories, and in the absence of the ordinary Maxwell kinetic term the Schwarzschild-(anti-)de Sitter solution with the nonzero electric field can be obtained. This corresponds to a stealth black hole solution as the electric field does not affect the spacetime geometry. We then focus on several degenerate classes of higher-order Maxwell-Einstein theories, and find that the dyonic Reissner-Nordstr\"om-(anti-)de Sitter solution in the pure Maxwell-Einstein theory can be a solution.

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arXiv2024

Even-parity black hole perturbations in Minimal Theory of Bigravity

We study even-parity black hole perturbations in Minimal Theory of Bigravity (MTBG). We consider the Schwarzschild solution written in the spatially-flat coordinates in the self-accelerating branch as the background solution. We clarify the gauge transformations for the $\ell=0$, $1$, and $\geq2$ modes with $\ell$ being the angular multipole moments under the joint foliation-preserving diffeomorphism transformation. Requiring that the asymptotic regions in the physical and fiducial sectors share the same Minkowski vacua, the solution to the $\ell=0$ perturbations can be absorbed by a redefinition of the Schwarzschild background. In order to analyze the $\ell=1$ and $\geq 2$ modes, for simplicity we focus on the effectively massless case, where the constant parameter measuring the ratio of the proper times between the two sectors is set to unity and the effective mass terms in the equations of motion vanish. We also find that as a particular solution all the $\ell=1$ perturbations vanish by imposing their regularity at spatial infinity. For each of the $\ell\geq 2$ modes, in the effectively massless case, we highlight the existence of the expected two propagating modes and four instantaneous modes.

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arXiv2024

Angular and radial stabilities of spontaneously scalarized black holes in the presence of scalar-Gauss-Bonnet couplings

We study the linear stability of spontaneously scalarized black holes (BHs) induced by a scalar field $\phi$ coupled to a Gauss-Bonnet (GB) invariant $R_{\rm GB}^2$. For the scalar-GB coupling $\xi(\phi)=(\eta/8) (\phi^2+\alpha \phi^4)$, where $\eta$ and $\alpha$ are constants, we first show that there are no angular Laplacian instabilities of even-parity perturbations far away from the horizon for large multipoles $l \gg 1$. The deviation of angular propagation speeds from the speed of light is largest on the horizon, whose property can be used to put constraints on the model parameters. For $\alpha \gtrsim -1$, the region in which the scalarized BH is subject to angular Laplacian instabilities can emerge. Provided that $\alpha \lesssim -1$ and $-1/2<\alpha \phi_0^2<-0.1155$, where $\phi_0$ is the field value on the horizon with a unit of the reduced Planck mass $M_{\rm Pl}=1$, there are scalarized BH solutions satisfying all the linear stability conditions throughout the horizon exterior. We also study the stability of spontaneously scalarized BHs in scalar-GB theories with a nonminimal coupling $-\beta \phi^2 R/16$, where $\beta$ is a positive constant and $R$ is a Ricci scalar. As the amplitude of the field on the horizon approaches an upper limit $|\phi_0|=4/\sqrt{\beta}$, one of the squared angular propagation speeds $c_{\Omega-}^2$ enters the instability region $c_{\Omega-}^2<0$. So long as $|\phi_0|$ is smaller than a maximum value determined for each $\beta$ in the range $\beta>5$, however, the scalarized BHs are linearly stable in both angular and radial directions.

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arXiv2024

Black hole thermodynamics in generalized Proca theories

We investigate thermodynamics of static and spherically symmetric black holes (BHs) in generalized Proca (GP) theories by applying the Iyer-Wald prescription. BH solutions in GP theories are divided into the two classes. The first class corresponds to the solutions obtained by the direct promotion of the BH solutions in shift-symmetric Horndeski theories, while the second class consists of the solutions which are obtained only in GP theories and contain a nonzero electromagnetic field. For BH solutions in the first class, we confirm that the BH entropy and its thermodynamic mass remain the same as those in the counterpart solution in shift-symmetric Horndeski theories. We also calculate the thermodynamical variables of the several static and spherically-symmetric BH solutions in the second class, and investigate the thermodynamical stability when there exist two BH solutions.

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arXiv2023

Exact solution for rotating black holes in parity-violating gravity

It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.

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arXiv2023

Black hole thermodynamics in Horndeski theories

We investigate thermodynamics of static and spherically symmetric black holes (BHs) in the Horndeski theories. Because of the presence of the higher-derivative interactions and the nonminimal derivative couplings of the scalar field, the standard Wald entropy formula may not be directly applicable. Hence, following the original formulation by Iyer and Wald, we obtain the differentials of the BH entropy and the total mass of the system in the Horndeski theories, which lead to the first-law of thermodynamics via the conservation of the Hamiltonian. Our formulation covers the case of the static and spherically symmetric BH solutions with the static scalar field and those with the linearly time-dependent scalar field in the shift-symmetric Horndeski theories. We then apply our results to explicit BH solutions in the Horndeski theories. In the case of the conventional scalar-tensor theories and the Einstein-scalar-Gauss-Bonnet theories, we recover the BH entropy obtained by the Wald entropy formula. In the shift-symmetric theories, in the case of the BH solutions with the static scalar field we show that the BH entropy follows the ordinary area law even in the presence of the nontrivial profile of the scalar field. On the other hand, in the case of the BH solutions where the scalar field linearly depends on time, i.e., the stealth Schwarzschild and Schwarzschild-(anti-) de Sitter solutions, the BH entropy also depends on the profile of the scalar field. By use of the entropy, we find that there exists some range of the parameters in which Schwarzschild$-$(AdS) BH with non-trivial scalar field is thermodynamically stable than Schwarzschild$-$(AdS) BH without scalar field in general relativity.

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arXiv2023

Instability of scalarized compact objects in Einstein-scalar-Gauss-Bonnet theories

We investigate the linear stability of scalarized black holes (BHs) and neutron stars (NSs) in the Einstein-scalar-Gauss-Bonnet (GB) theories against the odd- and even-parity perturbations including the higher multipole modes. We show that the angular propagation speeds in the even-parity perturbations in the $\ell \to \infty$ limit, with $\ell$ being the angular multipole moments, become imaginary and hence scalarized BH solutions suffer from the gradient instability. We show that such an instability appears irrespective of the structure of the higher-order terms in the GB coupling function and is caused purely due to the existence of the leading quadratic term and the boundary condition that the value of the scalar field vanishes at the spatial infinity.~This indicates that the gradient instability appears at the point in the mass-charge diagram where the scalarized branches bifurcate from the Schwarzschild branch. We also show that scalarized BH solutions realized in a nonlinear scalarization model also suffer from the gradient instability in the even-parity perturbations. Our result also suggests the gradient instability of the exterior solutions of the static and spherically-symmetric scalarized NS solutions induced by the same GB coupling functions.

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arXiv2023

Effective description of generalized disformal theories

Generalized disformal transformations enable us to construct the generalized disformal Horndeski theories, which form the most general class of ghost-free scalar-tensor theories to this date. We extend the effective field theory (EFT) of cosmological perturbations to incorporate these generalized disformal Horndeski theories. The main difference from the conventional EFT is that our extended EFT involves operators with higher spatial derivatives of the lapse function. Our EFT also accommodates the generalized disformal transformation of U-DHOST theories.

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arXiv2023

Gravitational collapse and odd-parity black hole perturbations in Minimal Theory of Bigravity

In the former part, we study the gravitational collapse of pressureless dust and find special solutions, where, in both the physical and fiducial sectors, the exterior and interior spacetime geometries are given by the Schwarzschild spacetimes and the Friedmann-Lema\^itre-Robertson-Walker universes dominated by pressureless dust, respectively, with specific time slicings. In the case where the Lagrange multipliers are trivial and have no jump across the matter interfaces in both the physical and fiducial sectors, the junction conditions across them remain the same as those in general relativity (GR). For simplicity, we foliate the interior geometry by homogeneous and isotropic spacetimes. For a spatially flat interior universe, we foliate the exterior geometry by a time-independent flat space, while for a spatiallycurved interior universe, we foliate the exterior geometry by a time-independent space with deficit solid angle. Despite the rather restrictive choice of foliations, we find interesting classes of exact solutions that represent gravitational collapse in MTBG. In the spatially flat case, under a certain tuning of the initial condition, we find exact solutions of matter collapse in which the two sectors evolve independently. In the spatially closed case, once the matter energy densities and the Schwarzschild radii are tuned between the two sectors, we find exact solutions that correspond to the Oppenheimer-Snyder model in GR. In the latter part, we study odd-parity perturbations of the Schwarzschild$-$de Sitter solutions written in the spatially flat coordinates. For the higher-multipole modes $\ell\geq2$, we find that, in general, the system reduces to that of four physical modes, where two of them are dynamical and the remaining two are shadowy, i.e., satisfying only elliptic equations.

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arXiv2022

Highly compact Proca stars with quartic self-interactions

We study self-gravitating bound states of a complex vector field, known as Proca stars, with a new type of quartic-order self-interaction which does not exist in the case of either a complex scalar field or a real vector field. Depending on the sign of the coupling constant, this quartic self-interaction can yield a distinct feature of Proca stars from the previously investigated self-interaction of the vector field. We find that self-gravitating solutions can be so compact that the photon sphere could form. However, we also show that the self-interaction gives rise to a ghost instability for the stars whose compactness is close that for the formation of a photon sphere, which might invalidate the formation of the photon sphere.

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arXiv2022

Generalized disformal Horndeski theories: cosmological perturbations and consistent matter coupling

Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabilities for tensor and scalar perturbations. We also investigate the conditions under which a matter field can be consistently coupled to these theories without introducing unwanted extra degrees of freedom.

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arXiv2022

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field $\phi$ nonminimally coupled to the Ricci scalar $R$ of the form $F(\phi)R$. The scalar field has a self-interacting potential and sits at its vacuum expectation value $\phi_v$ far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value $\phi_c$ close to $0$. This allows the existence of scalarized NS solutions connecting $\phi_v$ with $\phi_c$ whose difference is significant, whereas the field is located in the vicinity of $\phi=\phi_v$ for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field $\phi$ finally approaches the asymptotic value $\phi_v$ without spoiling a successful cosmological evolution. After $\phi$ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

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arXiv2022

Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings

In Horndeski theories containing a scalar coupling with the Gauss-Bonnet (GB) curvature invariant $R_{\rm GB}^2$, we study the existence and linear stability of neutron star (NS) solutions on a static and spherically symmetric background. For a scalar-GB coupling of the form $\alpha \xi(\phi) R_{\rm GB}^2$, where $\xi$ is a function of the scalar field $\phi$, the existence of linearly stable stars with a nontrivial scalar profile without instabilities puts an upper bound on the strength of the dimensionless coupling constant $|\alpha|$. To realize maximum masses of NSs for a linear (or dilatonic) GB coupling $\alpha_{\rm GB}\phi R_{\rm GB}^2$ with typical nuclear equations of state, we obtain the theoretical upper limit $\sqrt{|\alpha_{\rm GB}|}<0.7~{\rm km}$. This is tighter than those obtained by the observations of gravitational waves emitted from binaries containing NSs. We also incorporate cubic-order scalar derivative interactions, quartic derivative couplings with nonminimal couplings to a Ricci scalar besides the scalar-GB coupling and show that NS solutions with a nontrivial scalar profile satisfying all the linear stability conditions are present for certain ranges of the coupling constants. In regularized 4-dimensional Einstein-GB gravity obtained from a Kaluza-Klein reduction with an appropriate rescaling of the GB coupling constant, we find that NSs in this theory suffer from a strong coupling problem as well as Laplacian instability of even-parity perturbations. We also study NS solutions with a nontrivial scalar profile in power-law $F(R_{\rm GB}^2)$ models, and show that they are pathological in the interior of stars and plagued by ghost instability together with the asymptotic strong coupling problem in the exterior of stars.

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arXiv2022

Resolving the pathologies of self-interacting Proca fields: A case study of Proca stars

It has been argued that a self-interacting massive vector field is pathological due to a dynamical formation of a singular effective metric of the vector field, which is the onset of a gradient or ghost instability. We discuss that this singularity formation is not necessarily a fundamental problem but a breakdown of the effective field theory (EFT) description of the massive vector field. By using a model of ultraviolet (UV) completion of the massive vector field, we demonstrate that a Proca star, a self-gravitating condensate of the vector field, continues to exist even after the EFT suffers from a gradient instability without any pathology at UV, in which the EFT description is still valid and the gradient instability in EFT may be interpreted as a standard dynamical instability of a high-density boson star from the UV perspective. On the other hand, we find that the EFT description is broken before the ghost instability appears. This suggests that a heavy degree of freedom may be spontaneously excited to cure the pathology of the EFT as the EFT dynamically tends to approach the onset of the ghost instability.

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arXiv2022

Linear stability of black holes with static scalar hair in full Horndeski theories: generic instabilities and surviving models

In full Horndeski theories, we show that the static and spherically symmetric black hole (BH) solutions with a static scalar field~$\phi$ whose kinetic term~$X$ is nonvanishing on the BH horizon are generically prone to ghost/Laplacian instabilities. We then search for asymptotically Minkowski hairy BH solutions with a vanishing $X$ on the horizon free from ghost/Laplacian instabilities. We show that models with regular coupling functions of $\phi$ and $X$ result in no-hair Schwarzschild BHs in general. On the other hand, the presence of a coupling between the scalar field and the Gauss-Bonnet (GB) term $R_{\rm GB}^2$, even with the coexistence of other regular coupling functions, leads to the realization of asymptotically Minkowski hairy BH solutions without ghost/Laplacian instabilities. Finally, we find that hairy BH solutions in power-law $F(R_{\rm GB}^2)$ gravity are plagued by ghost instabilities. These results imply that the GB coupling of the form $\xi(\phi)R_{\rm GB}^2$ plays a prominent role for the existence of asymptotically Minkowski hairy BH solutions free from ghost/Laplacian instabilities.

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arXiv2022

Static and spherically symmetric general relativity solutions in Minimal Theory of Bigravity

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlev\'e (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates.

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arXiv2022

Linear stability of black holes in shift-symmetric Horndeski theories with a time-independent scalar field

We study linear perturbations about static and spherically symmetric black holes with a time-independent background scalar field in shift-symmetric Horndeski theories, whose Lagrangian is characterized by coupling functions depending only on the kinetic term of the scalar field $X$. We clarify conditions for the absence of ghosts and Laplacian instabilities along the radial and angular directions in both odd- and even-parity perturbations. For reflection-symmetric theories described by a k-essence Lagrangian and a nonminimal derivative coupling with the Ricci scalar, we show that black holes endowed with nontrivial scalar hair are unstable around the horizon in general. This includes nonasymptotically flat black holes known to exist when the nonminimal derivative coupling to the Ricci scalar is a linear function of $X$. We also investigate several black hole solutions in nonreflection-symmetric theories. For cubic Galileons with the Einstein-Hilbert term, there exists a nonasymptotically flat hairy black hole with no ghosts/Laplacian instabilities. Also, for the scalar field linearly coupled to the Gauss-Bonnet term, asymptotically flat black hole solutions constructed perturbatively with respect to a small coupling are free of ghosts/Laplacian instabilities.

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