arXiv subjects

Kei-ichi Maeda

Publications and source records attributed to Kei-ichi Maeda.

At least 73 records · Page 4Linked to original sources

arXiv2010

Black Hole in the Expanding Universe with Arbitrary Power-Law Expansion

We present a time-dependent and spatially inhomogeneous solution that interpolates the extremal Reissner-Nordström (RN) black hole and the Friedmann-Lemaître-Robertson-Walker (FLRW) universe with arbitrary power-law expansion. It is an exact solution of the $D$-dimensional Einstein-"Maxwell"-dilaton system, where two Abelian gauge fields couple to the dilaton with different coupling constants, and the dilaton field has a Liouville-type exponential potential. It is shown that the system satisfies the weak energy condition. The solution involves two harmonic functions on a $(D-1)$-dimensional Ricci-flat base space. In the case where the harmonics have a single-point source on the Euclidean space, we find that the spacetime describes a spherically symmetric charged black hole in the FLRW universe, which is characterized by three parameters: the steepness parameter of the dilaton potential $n_T$, the U$(1)$ charge $Q$, and the "nonextremality" $τ$. In contrast with the extremal RN solution, the spacetime admits a nondegenerate Killing horizon unless these parameters are finely tuned. The global spacetime structures are discussed in detail.

gr-qc↗

arXiv2010

Black Hole in the Expanding Universe from Intersecting Branes

We study physical properties and global structures of a time-dependent, spherically symmetric solution obtained via the dimensional reduction of intersecting M-branes. We find that the spacetime describes a maximally charged black hole which asymptotically tends to the Friedmann-Lemaître-Robertson-Walker (FLRW) universe filled by a stiff matter. The metric solves the field equations of Einstein-Maxwell-dilaton system, in which four Abelian gauge fields couple to the dilation with different coupling constants. The spacetime satisfies the dominant energy condition and is characterized by two parameters, $Q$ and $τ$, related to the Maxwell charge and the relative ratio of black-hole horizon radii, respectively. In spite of the nontrivial time-dependence of the metric, it turns out that the black hole event horizon is a Killing horizon. This unexpected symmetry may be ascribed to the fact that the 11-dimensional (11D) brane configurations are supersymmetric in the static limit. Finally, combining with laws of trapping horizon, we discuss the thermodynamic properties of the black hole. It is shown that the horizon possesses a nonvanishing temperature, contrary to the extremal Reissner-Nordstrøm (RN) solution.

hep-th↗

arXiv2010

Supersymmetric Intersecting Branes in Time-dependent Backgrounds

We construct a fairy general family of supersymmetric solutions in time- and space-dependent backgrounds in general supergravity theories. One class of the solutions are intersecting brane solutions with factorized form of time- and space-dependent metrics, the second class are brane solutions in pp-wave backgrounds carrying spacetime-dependence, and the final class are the intersecting branes with more nontrivial spacetime-dependence, and their intersection rules are given. Physical properties of these solutions are discussed, and the relation to existing literature is also briefly mentioned. The number of remaining supersymmetries are identified for various configurations including single branes, D1-D5, D2-D6-branes with nontrivial dilaton, and their possible dual theories are briefly discussed.

hep-th↗

arXiv2010

Supersymmetric Intersecting Branes on the Waves

We construct a general family of supersymmetric solutions in time- and space-dependent wave backgrounds in general supergravity theories describing single and intersecting p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. We discuss how many degrees of freedom we have in the solutions. We also propose that these solutions can be used to describe higher-dimensional time-dependent "black holes", and discuss their property briefly.

hep-th↗

arXiv2010

One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity

Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared (IR) divergence, we consider the IR regularization to obtain the finite value. We find that the loop corrections to the scalar perturbations are amplified by the e-folding; in other words there appear the logarithmic correction, just as discussed by M.Sloth et al. On the other hand, we find that the tensor perturbations do not suffer from infrared divergence.

hep-th↗

arXiv2009

Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.

astro-ph.HE↗

arXiv2009

The Bernstein Conjecture, Minimal Cones, and Critical Dimensions

Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular at the apex, may be used to provide counterexamples to the conjecture. The physical implications of these counterexamples in curved spacetimes are discussed from various points of view, ranging from classical general relativity, brane physics, and holographic models of fundamental interactions.

hep-th↗

arXiv2009

Dynamics of intersecting brane systems -- Classification and their applications --

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional supergravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations.

hep-th↗

arXiv2009

Black hole-black string phase transitions from hydrodynamics

We discuss the phase transitions between three states of a plasma fluid (plasma ball, uniform plasma tube, and non-uniform plasma tube), which are dual to the corresponding finite energy black objects (black hole, uniform black string, and non-uniform black string) localized in an asymptotically locally AdS space. Adopting the equation of state for the fluid obtained by the Scherk-Schwarz compactification of a conformal field theory, we obtain axisymmetric static equilibrium states of the plasma fluid and draw the phase diagrams with their thermodynamical quantities. By use of the fluid/gravity correspondence, we predict the phase diagrams of the AdS black holes and strings on the gravity side. The thermodynamic phase diagrams of the AdS black holes and strings show many similarities to those of the black hole-black string system in a Kaluza-Klein vacuum. For instance, the critical dimension for the smooth transition from the uniform to non-uniform strings is the same as that in the Kaluza-Klein vacuum in the canonical ensemble. The analysis in this paper may provide a holographic understanding of the relation between the Rayleigh-Plateau and Gregory-Laflamme instabilities via the fluid/gravity correspondence.

hep-th↗

arXiv2009

Attractor Universe in the Scalar-Tensor Theory of Gravitation

In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general formulation in terms of two-dimensional phase space. We show that there are two kinds of fixed points, one of which is an attractor depending on the coupling constant and equation of state. In the case with a power-law potential in the Jordan frame, we also find new type of inflation caused by the coupling to the matter fluid.

hep-th↗

arXiv2009

Can higher curvature corrections cure the singularity problem in f(R) gravity?

Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $μ\lesssim 10^{-19}$ GeV, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.

astro-ph↗

arXiv2008

Relativistic stars in f(R) gravity, and absence thereof

Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models.

astro-ph↗

arXiv2008

Liquid bridges and black strings in higher dimensions

Analyzing a capillary minimizing problem for a higher-dimensional extended fluid, we find that there exist startling similarities between the black hole-black string system (the Gregory-Laflamme instability) and the liquid drop-liquid bridge system (the Rayleigh-Plateau instability), which were first suggested by a perturbative approach. In the extended fluid system, we confirm the existence of the critical dimension above which the non-uniform bridge (NUB, i.e., {\it Delaunay unduloid}) serves as the global minimizer of surface area. We also find a variety of phase structures (one or two cusps in the volume-area phase diagram) near the critical dimension. Applying a catastrophe theory, we predict that in the 9 dimensional (9D) space and below, we have the first order transition from a uniform bridge (UB) to a spherical drop (SD), while in the 10D space and above, we expect the transition such that UB $\to$ NUB $\to$ SD. This gives an important indication for a transition in the black hole-black string system.

hep-th↗

arXiv2008

Entropy Function and Universality of Entropy-Area Relation for Small Black Holes

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy $S_{BH}$ of small black hole is proportional to its horizon area $A$. In particular we find a universal result that $S_{BH}=A/2G$, the ratio is two times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

hep-th↗

arXiv2007

Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon crossing time is smaller than some critical value ($\sim |$slow-roll parameter $|^{-1}$), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

hep-th↗

arXiv2007

Gravitational Wave Signals from Chaotic System: A Point Mass with A Disk

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase of the orbit in which particle motion becomes to be nearly regular (the so-called ``stagnant motion'') for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviours affect on observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviours of the orbit via the gravitational waves.

gr-qc↗

arXiv2007

Dynamics of colliding branes and black brane production

We study the dynamics of colliding domain walls including self-gravity. The initial data is set up by applying a BPS domain wall in five-dimensional supergravity, and we evolve the system determining the final outcome of collisions. After a collision, a spacelike curvature singularity covered by a horizon is formed in the bulk, resulting in a black brane with trapped domain walls. This is a generic consequence of collisions, except for non-relativistic weak field cases, in which the walls pass through one another or multiple bounces take place without singularity formation. These results show that incorporating the self-gravity drastically changes a naive picture of colliding branes.

gr-qc↗

arXiv2007

Fermions on Colliding Branes

We study the behaviour of five-dimensional fermions localized on branes, which we describe by domain walls, when two parallel branes collide in a five-dimensional Minkowski background spacetime. We find that most fermions are localized on both branes as a whole even after collision. However, how much fermions are localized on which brane depends sensitively on the incident velocity and the coupling constants unless the fermions exist on both branes.

hep-th↗