arXiv subjects

Masato Nozawa

Publications and source records attributed to Masato Nozawa.

At least 19 recordsLinked to original sources

arXiv2025

Kerr-Schild transformation of the Benenti-Francaviglia metric

The Benenti-Francaviglia (BF) family of metrics provides the most general form of a spacetime metric that admits two mutually commuting Killing vectors and an irreducible Killing tensor. The geodesic equations for the BF family are thus completely integrable by separation of variables. Within this broad class, we explore the Kerr-Schild transformation of a degenerate subclass distinguished by the existence of a shear-free null geodesic congruence. By requiring the deformed metric to preserve the Killing symmetry and circularity, we demonstrate that the deformed metric again falls into the degenerate BF family, modulo the replacement of a single structure function. We apply the present algorithm to ${\cal N}=2$ gauged supergravity and obtain a dyonic generalization of the Chong-Cveti\v{c}-L\"u-Pope rotating black hole solution, by taking the background metric to be a solution of the Einstein-scalar gravity. The present prescription extends to five dimensions, provided that the constant of geodesic motion associated with the extra Killing direction vanishes. The same reasoning applies to the case where the background degenerate BF metric is distorted in a (non)conformal manner. Our formalism offers a unified perspective on the relation between seed and deformed metrics in the Kerr-Schild construction.

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arXiv2024

Supersymmetry of the Robinson-Trautman solution

The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the spacetime is algebraically special, we provide an exhaustive classification of supersymmetric Robinson-Trautman spacetimes in the four-dimensional ${\cal N}=2$ gauged supergravity. The differential constraints that arise from the integrability conditions of the Killing spinor equation enable us to systematically reconstruct the metric. We derive the explicit form of the Killing spinor either by directly integrating the Killing spinor equation or by casting the solution into the canonical form of supersymmetric solutions given in hep-th/0307022. In any case, the supersymmetric Robinson-Trautman solution generically exhibits a naked singularity.

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arXiv2024

Robinson-Trautman solutions with scalar hair and Ricci flow

The vacuum Robinson-Trautman solution admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. We perform a comprehensive classification of solutions exhibiting this property in Einstein's gravity with a massless scalar field, assuming that the solution belongs at least to Petrov-type II and some of the components of Ricci tensor identically vanish. We find that these solutions can be grouped into three distinct classes: (I-a) a natural extension of the Robinson-Trautman family incorporating a scalar hair satisfying the time derivative of the Ricci flow equation, (I-b) a novel non-asymptotically flat solution characterized by two functions satisfying Perelman's pair of the Ricci flow equations, and (II) a dynamical solution possessing ${\rm SO}(3)$, ${\rm ISO}(2)$ or ${\rm SO}(1,2)$ symmetry. We provide a complete list of all explicit solutions falling into Petrov type D for classes (I-a) and (I-b). Moreover, leveraging the massless solution in class (I-a), we derive the neutral Robinson-Trautman solution to the ${\cal N}=2$ gauged supergravity with the prepotential $F(X) =-iX^0X^1$. By flipping the sign of the kinetic term of the scalar field, the Petrov-D class (I-a) solution leads to a time-dependent wormhole with an instantaneous spacetime singularity. Although the general solution is unavailable for class (II), we find a new dynamical solution with spherical symmetry from the AdS-Roberts solution via AdS/Ricci-flat correspondence.

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arXiv2023

Wormhole $C$ metric

The C-metric in vacuum general relativity describes a pair of accelerated black holes supported by conical singularity. In this paper, we present a new family of exact solutions to the Einstein-phantom scalar system that describes accelerated wormholes in AdS. In the zero acceleration limit with a vanishing potential, the present solution recovers the asymptotically flat wormhole originally constructed by Ellis and Bronnikov. The scalar potential of the phantom field has an infinite number of critical points and is expressed in terms of the superpotential, which is obtained by suitable analytic continuation of one parameter family of the ${\cal N}=2$ gauged supergravity. As one traverses two asymptotic regions connected by throat, the scalar field evolves from AdS, corresponding to the origin of the potential, towards the neighboring AdS local minimum of the potential. We find that the flipping transformation, which interchanges the role of ``radial'' and "angular'' coordinates at the expense of double Wick rotation, is an immediate cause for the existence of two branches of static AdS wormholes discovered previously. Contrary to the ordinary C-metric, the conical singularity along the symmetry axis can be completely resolved, when the (super)potential is periodic or zero. We explore the global causal structure in detail.

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arXiv2023

New family of C-metrics in ${\cal N}=2$ gauged supergravity

We present a new family of charged C-metrics in ${\cal N}=2$ gauged supergravity in four dimensions. The double Wick rotation of the C-metric allows us to bring our solution into a different family of the C-metrics previously found by Lü and Vázquez-Poritz. In the case of zero acceleration limit, our solution with vanishing charges reduces to the scalar haired black holes in AdS with regular horizons. Nevertheless, it turns out that each family of neutral solutions fails to veil the curvature singularity by the event horizon, showing that neither of them represents the accelerated black holes with a scalar hair. Physical solutions without visible curvature singularities are obtained only in the case of nonvanishing charges. Causal structures of the solution are spelled out in detail. We also present conditions under which the solution preserves supersymmetry.

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arXiv2021

An alternative to the Simon tensor

The Simon tensor gives rise to a local characterization of the Kerr-NUT family in the stationary class of vacuum spacetimes. We find that a symmetric and traceless tensor in the quotient space of the stationary Killing trajectory offers a useful alternative to the Simon tensor. Our tensor is distinct from the spatial dual of the Simon tensor and illustrates the geometric property of the three dimensional quotient space more manifest. The reconstruction procedure of the metric for which the generalized Simon tensor vanishes is spelled out in detail. We give a four dimensional description of this tensor in terms of the Coulomb part of the imaginary selfdual Weyl tensor, which corresponds to the generalization of the three-index tensor defined by Mars. This allows us to establish a new and simple criterion for the Kerr-NUT family: the gradient of the Ernst potential becomes the non-null eigenvector of the Coulomb part of the imaginary selfdual Weyl tensor. We also discuss the ${\rm SU}(1,2)$ covariant extension of the obstruction tensor into the Einstein-Maxwell system as an intrinsic characterization of the Kerr-Newman-NUT family.

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arXiv2021

Static spacetimes haunted by a phantom scalar field: classification and global structure in the massless case

We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and an $(n-2)$-dimensional Einstein space $K^{n-2}$ with curvature $k=0, \pm 1$, and that the scalar field depends only on the radial variable, we present a complete classification of static solutions for both signs of kinetic term. Contrary to the case with a non-phantom scalar field, the Fisher solution is not unique, and there exist two additional metrics corresponding to the generalizations of the Ellis-Gibbons solution and the Ellis-Bronnikov solution. We explore the maximal extension of these solutions in detail by the analysis of null/spacelike geodesics and singularity. For the phantom Fisher and Ellis-Gibbons solutions, we find that there inevitably appear parallelly propagated (p.p) curvature singularities in the parameter region where there are no scalar curvature singularities. Interestingly, the areal radius blows up at these p.p curvature singularities, which are nevertheless accessible within a finite affine time along the radial null geodesics. It follows that only the Ellis-Bronnikov solution describes a regular wormhole in the two-sided asymptotically flat spacetime. Using the general transformation relating the Einstein and Jordan frames, we also present a complete classification of solutions with the same symmetry coupled to a conformal scalar field. Additionally, by solving the field equations in the Jordan frame, we prove that this classification is genuinely complete.

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arXiv2021

Static spacetimes haunted by a phantom scalar field II: dilatonic charged solutions

We present a method to generate static solutions in the Einstein-Maxwell system with a (phantom) dilaton field in $n(\ge 4)$-dimensions, based upon the symmetry of the target space for the nonlinear sigma model. Unlike the conventional Einstein-Maxwell-dilaton system, there appears a critical value of the coupling constant for a phantom dilaton field. In the noncritical case, the target space is $\mathbb R\times {\rm SL}(2,\mathbb R)/H$ with the maximal subgroup $H=\{{\rm SO}(2), {\rm SO}(1,1)\}$, whereas in the critical case the target space becomes a symmetric pp-wave and the corresponding Killing vectors form a non-semisimple algebra. In either case, we apply the formalism to charge up the neutral solutions and show the analytical expression for dilatonic charged versions of (i) the Fisher solution, (ii) the Gibbons solution, and (iii) the Ellis-Bronnikov solution. We discuss global structures of these solutions in detail. It turns out that some solutions contained in the Fisher and Gibbons classes possess the parallelly propagated (p.p) curvature singularities in the parameter region where all the scalar curvature invariants remain bounded. These p.p curvature singularities are not veiled by a horizon, thrusting them into physically untenable nakedly singular spacetimes. We also demonstrate that the dilatonic-charged Ellis-Bronnikov solution admits a parameter range under which the solution represents a regular wormhole spacetime in the two-sided asymptotically flat regions.

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arXiv2021

Static spacetimes haunted by a phantom scalar field III: asymptotically (A)dS solutions

The static and spherically symmetric solutions in $n(\ge 4)$-dimensional Einstein-phantom-scalar system fall into three family: (i) the Fisher solution, (ii) the Ellis-Gibbons solution, and (iii) the Ellis-Bronnikov solution. We exploit these solutions as seed to generate a bunch of corresponding asymptotically (A)dS spacetimes, at the price of introducing the potential of the scalar field. Despite that the potentials are different for each solution, each potential is expressed in terms of the superpotential as in supergravity. We discuss the global structure of these solutions in detail and spell out the domain of parameters under which each solution represents a black hole/wormhole. The Ellis-Bronnikov class of solutions presents novel examples of spherical traversable wormholes that interpolate two different (A)dS critical points of the (super)potential.

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arXiv2020

All the three dimensional Lorentzian metrics admitting three Killing vectors

We obtain all the three-dimensional Lorentzian metrics which admit three Killing vectors. The classification has been done with the aid of the formalism which exploits the obstruction criteria for the Killing equations recently developed by present authors. The current classification method does not rely on the transitivity property of the isometry group. It turns out that the Lorentzian manifold harbors a much richer spectrum of metrics with various Segre types, compared to the Riemannian case.

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arXiv2019

6D (1,1) Gauged Supergravities from Orientifold Compactifications

We study dimensional reductions of M-theory/type II strings down to 6D in the presence of fluxes and spacetime filling branes and orientifold planes of different types. We classify all inequivalent orientifold projections giving rise to $\mathcal{N}=(1,1)$ supergravities in 6D and work out the embedding tensor/fluxes dictionary for each of those. Finally we analyze the set of vacua for the different classes of reductions and find an abundance of "no-scale" type Minkowski vacua, as well as a few novel examples of (A)dS extrema.

hep-th↗

arXiv2019

Counting the number of Killing vectors in a 3D spacetime

We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the values of differential invariants arising from the compatibility conditions of the Killing equation. As illustrating examples, we classify the Lifshitz and pp-wave spacetimes into a hierarchy based on their level of symmetry. A complete classification of spacetimes admitting 4 Killing vectors is also presented.

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arXiv2018

Divergence equations and uniqueness theorem of static black holes

Equations of divergence type in static spacetimes play a significant role in the proof of uniqueness theorems of black holes. We generalize the divergence equation originally discovered by Robinson in four dimensional vacuum spacetimes into several directions. We find that the deviation from spherical symmetry is encoded in a symmetric trace-free tensor $H_{ij}$ on a static timeslice. This tensor is the crux for the construction of the desired divergence equation, which allows us to conclude the uniqueness of the Schwarzschild black hole without using Smarr's integration mass formula. In Einstein-Maxwell(-dilaton) theory, we apply the maximal principle for a number of divergence equations to prove the uniqueness theorem of static black holes. In higher $(n\ge 5)$ dimensional vacuum spacetimes, a central obstruction for applicability of the current proof is the integration of the $(n-2)$-dimensional scalar curvature over the horizon cross-section, which has been evaluated to be a topological constant by the Gauss-Bonnet theorem for $n=4$. Nevertheless, it turns out that the $(n-1)$-dimensional symmetric and traceless tensor $H_{ij}$ is still instrumental for the modification of the uniqueness proof based upon the positive mass theorem, as well as for the derivation of the Penrose-type inequality.

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arXiv2017

Euclidean supersymmetric solutions with the self-dual Weyl tensor

We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of ${\cal N}=2$ minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski-Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski-Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski-Tod form. This formalism enables us to show that the self-dual Reissner-Nordström-Taub-NUT-AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski-Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing-Yano tensor.

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arXiv2016

Supersymmetric black lenses in five dimensions

We present an asymptotically flat supersymmetric black lens solution with the horizon topology L(n,1)=S^3/Z_n in the five-dimensional minimal ungauged supergravity. We show that the black lens carries a mass, two independent angular momenta, electric charge and (n-1) magnetic fluxes, among which only the (n+1) quantities are independent.

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arXiv2016

Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution

We explore various aspects of the self-dual Plebański-Demiański family in the Euclidean Einstein-Maxwell-$Λ$ system. The Killing-Yano tensor which was recently found by Yasui and one of the present authors allows us to prove that the self-dual Plebański-Demiański metric can be brought into the self-dual Carter metric by an orientation-reversing coordinate transformation. We show that the self-dual Plebański-Demiański solution admits two independent Killing spinors in the framework of $N=2$ minimal gauged supergravity, whereas the non-self-dual solution admits only a single Killing spinor. This can be demonstrated by casting the self-dual Plebański-Demiański metric into two distinct Przanowski-Tod forms. As a by-product, a new example of the three-dimensional Einstein-Weyl space is presented. We also prove that the self-dual Plebański-Demiański metric falls into two different Calderbank-Pedersen families, which are determined by a single function subjected to a linear equation on the two dimensional hyperbolic space. Furthermore, we consider the hyper-Kähler case for which the metric falls into the Gibbons-Hawking class. We find that the condition for the nonexistence of Dirac-Misner string enforces the solution with a nonvanishing acceleration parameter to the Eguchi-Hanson space.

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arXiv2015

Black holes in an expanding universe and supersymmetry

This paper analyzes the supersymmetric solutions to five and six-dimensional minimal (un)gauged supergravities for which the bilinear Killing vector constructed from the Killing spinor is null. We focus on the spacetimes which admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal dimensional reduction along the Killing vector corresponding to the boost, we show that the solution in the ungauged case describes a charged, nonextremal black hole in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe with an expansion driven by a massless scalar field. For the gauged case, the solution corresponds to a charged, nonextremal black hole embedded conformally into a Kantowski-Sachs universe. It turns out that these dimensional reductions break supersymmetry since the bilinear Killing vector and the Killing vector corresponding to the boost fail to commute. This represents a new mechanism of supersymmetry breaking that has not been considered in the literature before.

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arXiv2015

Lovelock black holes with non-constant curvature horizon

This paper studies a class of $D=n+2(\ge 6)$ dimensional solutions to Lovelock gravity that is described by the warped product of a two-dimensional Lorentzian metric and an $n$-dimensional Einstein space. Assuming that the angular part of the stress-energy tensor is proportional to the Einstein metric, it turns out that the Weyl curvature of an Einstein space must obey two kinds of algebraic conditions. We present some exact solutions satisfying these conditions. We further define the quasilocal mass corresponding to the Misner-Sharp mass in general relativity. It is found that the quasilocal mass is constructed out of the Kodama flux and satisfies the unified first law and the monotonicity property under the dominant energy condition. Making use of the quasilocal mass, we show Birkhoff's theorem and address various aspects of dynamical black holes characterized by trapping horizons.

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