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We study cosmological application of the holographic energy density in the Brans-Dicke theory. Considering the holographic energy density as a dynamical cosmological constant, it is more natural to study it in the Brans-Dicke theory than in general relativity. Solving the Friedmann and Brans-Dicke field equations numerically, we clarify the role of Brans-Dicke field during evolution of the universe. When the Hubble horizon is taken as the IR cutoff, the equation of state ($w_{\Lmd}$) for the holographic energy density is determined to be 5/3 when the Brans-Dicke parameter $\omg$ goes infinity. This means that the Brans-Dicke field plays a crucial role in determining the equation of state. For the particle horizon IR cutoff, the Brans-Dicke scalar mediates a transition from $w_{\Lmd} = -1/3$ (past) to $w_{\Lmd} = 1/3$ (future). If a dust matter is present, it determines future equation of state. In the case of future event horizon cutoff, the role of the Brans-Dicke scalar and dust matter are turned out to be trivial, whereas the holographic energy density plays an important role as a dark energy candidate with $w_{\Lmd} =-1$., Comment: 10pages, 3figures, version to appear in PLB

We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and extremal BTZ black hole (EBTZ). Our method is based on the potential analysis and solving the wave equation to find the condition for the frequency $\omega$ exactly. In the NBTZ case, one finds the quasinormal (complex and discrete) modes which signals for a non-unitary evolution. Real and discrete modes are found for the PADS case, which means that it is unitary obviously. On the other hand, we find real and continuous modes for the two extremal black holes of MBTZ and EBTZ. It suggests that these could be candidates for the unitary system., Comment: 14 pages, contracted version to appear in MPLA

We study cosmological applications of the holographic energy density. Considering the holographic energy density as a dynamical cosmological constant, we need the Brans-Dicke theory as a dynamical framework instead of general relativity. In this case we use the Bianchi identity as a consistency relation to obtain physical solutions. It is shown that the future event horizon as the IR cutoff provides the dark energy in the Brans-Dicke theory. Furthermore the role of the Brans-Dicke scalar is clarified in the dark energy-dominated universe by calculating its equation of state., Comment: 9 pages

We calculate logarithmic corrections to the Bekenstein-Hawking entropy for three-dimensional BTZ black hole with J=0 and Kerr-de Sitter (KdS) space with J=0 including the Schwarzschild-de Sitter (SdS) solution due to thermal fluctuations. It is found that there is no distinction between the event horizon of the BTZ black hole and the cosmological horizon of KdS space. We obtain the same correction to the Cardy formula for BTZ, KdS, and SdS cases. We discuss AdS/CFT and dS/ECFT correspondences in connection with logarithmic corrections., Comment: 9 pages, version to appear in PLB. k-dependent analysis is withdrawn

We study a close relationship between the topological anti-de Sitter (TAdS)-black holes and topological de Sitter (TdS) spaces including the Schwarzschild-de Sitter (SdS) black hole in five-dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing $k$ by $-k$. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild-TdS space by substituting $m$ with $-m$. For this purpose we calculate thermal quantities of bulk, (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further we compute logarithmic corrections to the Bekenstein-Hawking entropy, Cardy-Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that the cosmological horizon of the TdS spaces is nothing but the event horizon of the TAdS black holes and the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes., Comment: 17 pages

We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences., Comment: 9 pages, version to appear in PLB

We investigate the relationship between the holographic temperature bound and the slow-roll inflation. For this purpose we introduce the holographic temperature bound for a radiation matter :$T \ge T_{\rm H}$. Here $T_{\rm H}$ is the Hubble temperature which arises from the cosmological holographic description of for a radiation-dominated universe. For the quasi-de Sitter phase of slow-roll inflation, we find that the holographic temperature bound of $T_{\rm GH} \ge T_{\rm H}$ is guaranteed with the Gibbons-Hawking temperature $T_{\rm GH}$. When $T_{\rm GH}= T_{\rm H}$, inflation ends., Comment: 9 pages, 1figure

We investigate the role of the cosmological constant in the holographic description of a radiation-dominated universe $C_2/R^4$ with a positive cosmological constant $\Lambda$. In order to understand the nature of cosmological term, we first study the newtonian cosmology. Here we find two aspects of the cosmological term: entropy ($\Lambda \to S_{\rm \Lambda}$) and energy ($\Lambda \to E_{\rm \Lambda}$). Also we solve the Friedmann equation parametrically to obtain another role. In the presence of the cosmological constant, the solutions are described by the Weierstrass elliptic functions on torus and have modular properties. In this case one may expect to have a two-dimensional Cardy entropy formula but the cosmological constant plays a role of the modular parameter $\tau(C_2,\Lambda)$ of torus. Consequently the entropy concept of the cosmological constant is very suitable for establishing the holographic entropy bounds in the early universe. This contrasts to the role of the cosmological constant as a dark energy in the present universe., Comment: 15 pages

We study the wave equation for a massive scalar field in three-dimensional AdS-black hole and dS (de Sitter) spaces to find what is the difference and similarity between two spaces. Here the AdS-black hole is provided by the J=0 BTZ black hole. To investigate its event (cosmological) horizons, we compute the absorption cross section, quasinormal modes, and study the AdS(dS)/CFT correspondences. Although there remains an unclear point in defining the ingoing flux near infinity of the BTZ black hole, quasinormal modes are obtained and the AdS/CFT correspondence is confirmed. However, we do not find quasinormal modes and thus do not confirm the assumed dS/CFT correspondence. This difference between AdS-black hole and dS spaces is very interesting, because their global structures are similar to each other., Comment: 23 pages, version to appear in CQG

We introduce the brane-bulk interaction to discuss a limitation of the cosmological Cardy-Verlinde formula which is useful for the holographic description of brane cosmology. In the presence of the brane-bulk interaction, we cannot find the entropy representation of the first Friedmann equation (the cosmological Cardy-Verlinde formula). In the absence of the interaction, the cosmological Cardy-Verlinde formula is established even for the time-dependent charged AdS background. Hence, if there exists a dynamic exchange of energy between the brane and the bulk (that is, if $\tilde T^t~_y \not=0$), we cannot achieve the cosmological holographic principle on the brane., Comment: 9 pages, REVTEX

We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The Kerr-de Sitter space describes the gravitational background of a point particle whose mass and spin are given by $1-M$ and $J$ and its curvature radius is given by $\ell$. In order to study the propagation of metric, dilaton, and Kalb-Ramond two-form, we perform the perturbation analysis in the southern diamond of Kerr-de Sitter space including a conical singularity. It reveals a mixing between the dilaton and other unphysical fields. Introducing a gauge-fixing, we can disentangle this mixing completely and obtain one decoupled dilaton equation. However it turns out to be a tachyon with $m^2=-8/\ell^2$. We compute the absorption cross section for the dilatonic tachyon to extract information on the cosmological horizon of Kerr-de Sitter space. It is found that there is no absorption of the dilatonic tachyon in the presence of the cosmological horizon of Kerr-de Sitter space., Comment: 16 pages, 2 eps figures

We study the wave equation for a minimally coupled massive scalar in D-dimensional de Sitter space. We compute the absorption cross section to investigate its cosmological horizon in the southern diamond. By analogy of the quantum mechanics, it is found that there is no absorption in de Sitter space. This means that de Sitter space is usually in thermal equilibrium, like the black hole in anti de Sitter space. It confirms that the cosmological horizon not only emits radiation but also absorbs that previously emitted by itself at the same rate, keeping the curvature radius of de Sitter space fixed., Comment: 11 pages, REVTEX

We introduce the relation between the holographic entropy bounds and the inflationary universe. First the holographic entropy bounds for radiation-dominated universe, radiation-dominated universe with a positive cosmological constant are introduced. For an exact de Sitter phase, we use the maximal entropy bound. We classify the inflation based on the quasi-de Sitter spacetime into three steps: slow-roll period of inflation, epoch of reheating, and radiation-dominated era. Then we study how to apply three entropy bounds to the three steps of the inflation. Finally we discuss our results., Comment: 16 pages, two eps figures

We study bouncing and cyclic universes from an (n+1)-dimensional brane in the (n+2)-dimensional charged AdS bulk background. In the moving domain wall (MDW) approach this picture is clearly realized with a specified bulk configuration, the 5D charged topological AdS (CTAdS_5) black hole with mass M and charge Q. The bulk gravitational dynamics induces the 4D Friedmann equations with CFT-radiation and exotic stiff matters for a dynamic brane. This provides bouncing universes for k=0, -1 and cyclic universe for k=1, even though it has an exotic stiff matter from the charge Q. In this work we use the other of the Binetruy-Deffayet-Langlos (BDL) approach with the bulk Maxwell field. In this case we are free to determine the corresponding mass M-tilde and charge Q-tilde because the mass term is usually included as an initial condition and the charge is given by an unspecified solution to the Maxwell equation under the BDL metric. Here we obtain only bouncing universes if one does not choose two CTAdS_5 black holes as the bulk spacetime. We provide a way of avoiding the exotic matter on the brane by introducing an appropriate local matter. Finally we discuss an important relation between the exotic holographic matter and Lorentz invariance violation., Comment: 20 pages, latex

We study the dynamical behavior of the dilaton in the background of three-dimensional Kerr-de Sitter space which is inspired from the low-energy string effective action. The perturbation analysis around the cosmological horizon of Kerr-de Sitter space reveals a mixing between the dilaton and other fields. Introducing a gauge (dilaton gauge), we can disentangle this mixing completely and obtain one decoupled dilaton equation. However it turns out that this belongs to the tachyon. The stability of de Sitter solution with J=0 is discussed. Finally we compute the dilaton absorption cross section to extract information on the cosmological horizon of de Sitter space., Comment: 11 pages, reference added and a version to appear in PLB

We study the wave equation for a minimally coupled massive scalar in three-dimensional de Sitter space. We compute the absorption cross section to investigate its cosmological horizon in the southern diamond. Although the absorption cross section is not defined exactly, we can be determined it from the fact that the low-energy $s(j=0)$-wave absorption cross section for a massless scalar is given by the area of the cosmological horizon. On the other hand, the low-temperature limit of $j\not=0$-mode absorption cross section is useful for extracting information surrounding the cosmological horizon. Finally we mention a computation of the absorption cross section on the CFT-side using the dS/CFT correspondence., Comment: 13 pages, version to appear in MPLA

We explore the dynamic dS/CFT correspondence using the moving domain wall(brane) approach in the brane cosmology. The bulk spacetimes are given by the Schwarzschild-de Sitter (SdS) black hole and the topological-de Sitter (TdS) solutions. We consider the embeddings of (Euclidean) moving domain walls into the (Euclidean) de Sitter spaces. The TdS solution is better to describe the static dS/CFT correspondence than the SdS black hole, while in the dynamic dS/CFT correspondence the SdS solution provides situation better than that of the TdS solution. However, we do not find a desirable cosmological scenario from the SdS black hole space., Comment: 13 pages, revised version including the new interpretation for energy terms in the Friedmann equation of the Euclidean space approach to appear in PLB

We review the relation between entropy bounds to rewrite Friedmann equation on the brane in terms of three entropy bounds: Bekenstein-Verlinde ($S_{BV}$); Bekenstein-Hawking bound ($S_{BH}$); Hubble bound ($S_H$). For a strongly coupled conformal field theory (CFT) with a dual 5-dimensional anti de Sitter Schwarzschild (AdSS$_5$) black hole, we can easily establish the connection between the Cardy-Verlinde formula on the CFT side and the entropy representation of Friedmann equation in cosmology. In this case its cosmological evolution for entropy is given by the semi-circle. However, for the matter-dominated case, we find that the cosmological evolution diagram takes a different form of the cycloid. Here we propose two different entropy relations for matter-dominated case. It turns out that the Verlinde's entropy relation so restricted that it may not be valid for the matter-dominated universe., Comment: 14 pages, Talk at the 7th Italian-Korean Symposium on Relativistic Astrophysics, Kimhae, Korea, 23-28 July 2001

We study the three dimensional Schwarzschild-de Sitter (SdS$_3$) black hole which corresponds essentially to a conical defect. We compute the mass of the SdS$_3$ black hole from the correct definition of the mass in asymptotically de Sitter space. Then we clarify the relation between the mass, entropy and temperature for this black hole without any ambiguity. Also we establish the SdS$_3$/CFT$_2$-correspondence for the entropy by applying the Cardy formula to a CFT with a central charge $c=3\ell/2G_3$. Finally we discuss the entropy bounds for the SdS$_3$ black hole., Comment: 6 pages and RevTex

We clarify a mechanism to obtain a massless gauge boson from the Kaluza-Klein approach of the Randall-Sundrum(RS) brane world. This corresponds exactly to the same mechanism of achieving a localization of the gauge boson by adding both the bulk and brane mass terms. Accordingly this work puts another example for a localization-mechanism of the gauge boson on the brane., Comment: 7 pages, typo corrected and comments added

We study issues of the quintessence in the brane cosmology. The initial bulk spacetime consists of two 5D topological anti de Sitter black hole joined by the brane (moving domain wall). Here we do not introduce any conventional radiation and matter. Instead we include a localized scalar on the brane as a stress-energy tensor, and thus we find the quintessence which gives an accelerating universe. Importantly, we obtain a $\rho^2$-term as well as a holographic matter term of $\alpha/a^4$ from the masses of the topological black holes. We discuss a possibility that in the early universe, $\rho^2$-term makes a large kinetic term which induces a decelerating universe. This may provide a hint of avoiding from the perpetually accelerating universe of the present-day quintessence. If a holographic matter term exists, it will plays the role of a CFT-radiation in the early universe., Comment: 12page, version to appear in MPLA

We discuss the possibility of quintessence in the dilatonic domain walls including the Randall-Sundrum brane world. We obtain the zero mode effective action for gravitating objects in the dilatonic domain wall. First we consider the four dimensional (4D) gravity and the Brans-Dicke graviscalar with a potential. This can be further rewritten as a minimally coupled scalar with the Liouville-type potential in the Einstein frame. However this model fails to induce the quintessence on the dilatonic domain wall because the potential is negative. Second we consider the 4D gravity with the dilaton. In this case we find also a negative potential. Any negative potential gives us negative energy density and positive pressure, which does not lead to an accelerating universe. Consequently it turns out that the zero mode approach of the dilatonic domain wall cannot accommodate the quintessence in cosmology., Comment: 10 pages, some ambiguity in mathematical expressions corrected and references added

We study the holographic principle in the brane cosmology. Especially we describe how to accommodate the 5D anti de Sitter Schwarzschild (AdSS$_5$) black hole in the Binetruy-Deffayet-Langlois (BDL) approach of brane cosmology. It is easy to make a connection between a mass $M$ of the AdSS$_5$ black hole and a conformal field theory (CFT)-radiation dominated universe on the brane in the moving domain wall approach. But this is not established in the BDL approach. In this case we use two parameters $C_1, C_2$ in the Friedmann equation. These arise from integration and are really related to the choice of initial bulk matter. If one chooses a bulk energy density $\rho_B$ to account for a mass $M$ of the AdSS$_5$ black hole and the static fifth dimension, a CFT-radiation term with $\rho_{CFT} \sim M/a^{4}$ comes out from the bulk matter without introducing a localized matter distribution on the brane. This means that the holographic principle can be established in the BDL brane cosmology., Comment: 9 pages, a version to appear in PRD

We discuss the brane cosmology in the 5D anti de Sitter Reissner-Nordstrom (AdSRN$_5$) spacetime. A brane with the tension $\sigma$ is defined as the edge of an AdSRN$_5$ space with mass $M$ and charge $Q$. In this case we get the CFT-radiation term $(\rho_{CFT})$ from $M$ and the charged dust $(-\rho^2_{cd})$ from $Q^2$ in the Friedmann-like equation. However, this equation is not justified because it contains $\rho_{cd}^2$-term with the negative sign. This is unconventional in view of the standard cosmology. In order to resolve this problem, we introduce a localized dust matter which satisfies $P_{dm}=0$. If $\rho_{dm}=\fr{\sqrt 3}{2}\rho_{cd}$, the unwanted $-\rho_{cd}^2$ is cancelled against $\rho_{dm}^2$ and thus one recovers a standard Friedmann-Robertson-Walker universe with CFT-radiation and dust matter. For the stiff matter consideration, we can set $\rho_{csti}\sim Q^2$ with the negative sign. Here we introduce a massless scalar which plays the role of a stiff matter with $P_{sca}=\rho_{sca}$ to cancel $-\rho_{csti}$. In this case, however, we find a mixed version of the standard and brane cosmologies., Comment: 8 pages, Latex, version to appear in MPLA

We consider the perturbation of giant gravitons in the background of dilatonic D-branes whose geometry is not of a conventional form of ${\rm AdS}_m \times {\rm S}^n$. We use the quadratic approximation to the brane action to investigate their vibrations around the equilibrium configuration. We found the normal modes of small vibrations of giant gravitons and these vibrations are turned out to be stable., Comment: 11 pages, LaTex, typos corrected, some points are clarified with comments

We discuss the brane cosmology in the 5D anti de Sitter Schwarzschild (AdSS$_5$) spacetime. A brane with the tension $\sigma$ is defined as the edge of an AdSS$_5$ space. We point out that the location of the horizon is an apparently, singular point at where we may not define an embedding of the AdSS$_5$ spacetime into the moving domain wall (MDW). We resolve this problem by introducing a radially infalling brane (RIB) in AdSS$_5$ space, where an apparent singularity turns out to be a coordinate one. Hence the CFT/FRW-cosmology is well-defined at the horizon. As an example, an universal Cardy formula for the entropy of the CFT can be given by the Friedmann equation at the horizon., Comment: 9 pages, REVTEX

We include the brane curvature scalar to study its cosmological implication in the brane world cosmology. This term is usually introduced to obtain the well-defined stress-energy tensor on the boundary of anti de Sitter-Schwarzschild space. Here we treat this as the perturbed term for cosmological purpose. We find corrections to the well-known equation of the brane cosmology. It contains new interesting terms which may play the important role in the brane cosmology., Comment: 9 pages, comments and references added, version to appear in PLB

We prove that in anti de Sitter space, there is no van Dam-Veltman-Zakharov discontinuity in the graviton propagator. Here we obtain the mass term of $M^2\propto \Lambda^2$ from the Gauss-Bonnet term, which is a ghost-free one. The condition that the massless limit is smooth is automatically satisfied for this case., Comment: 5 pages, comments and references added

We prove the no-go theorem that the gravivector $(h_{5\mu})$ and graviscalar $(h_{55})$ cannot have any on-shell propagation on the Randall-Sundrum (RS) brane. For this purpose, we analyze all of their linearized equations with the de Donder gauge (5D transverse-tracefree gauge). But we do not introduce any matter source. We use the Z$_2$-symmetry argument and their ($h_{5\mu}, h_{55}$) compatibility conditions with the tensor $h_{\mn}$-equation. It turns out that $h_{55}$ does not have any bulk (massive) and brane (massless) propagations. Although $h_{5\mu}$ has a sort of massive propagations, they do not belong to the physical solution. Hence we confirm that the Randall-Sundrum gauge suffices the on-shell brane physics., Comment: 9 pages, comments and references added

The question of whether the Kaluza-Klein (KK) graviphoton $h_{5\mu}$ and graviscalar $h_{55}$ are localized or not on the brane is one of the important issues. In this letter, we address this problem in five dimensions. Here we consider the massless (zero-mode) propagations without requiring the Z$_2$-symmetry on $h_{5\mu}$. We obtain the graviton $h_{\mu\nu}$, graviphoton, and graviscalar exchange amplitudes on shell. We find that the graviscalar has a tachyonic mass. It turns out that $h_{5\mu}$ admits the localized zero-modes on the brane while $h_{55}$ does not have a localized zero-mode. This is contrasted to the fact that the bulk spin-0 field has a localized zero-mode on the brane but the bulk spin-1 field does not have a localized solution in five dimensions., Comment: 10 pages, comments and references added

We investigate the zero mode dimensional reduction of the Kaluza-Klein unifications in the presence of a single brane in the infinite extra dimension. We treat the brane as fixed, not a dynamical object, and do not require the orbifold symmetry. It seems that, contrary to the standard Kaluza-Klein models, the 4D effective action is no longer invariant under the U(1) gauge transformations due to the explicit breaking of isometries in the extra dimension by the brane. Surprisingly, however, the linearized perturbation analysis around the RS vacuum shows that the Kaluza-Klein gauge field does possess the U(1) gauge symmetry at the linear level. In addition, the graviscalar also behaves differently from the 4D point of view. Some physical implications of our results are also discussed., Comment: 10 pages, revtex, no figure, version to appear in Phys. Rev. D, possible caveats of our results due to the zero mode ansatz we used are explained in more detail

We discuss the compatibility between the weaker energy condition and the stability of Gregory, Rubakov and Sibiryakov (GRS) model. Because the GRS spacetime violates the weak energy condition, it may cause the instability. In the GRS model, the four dimensional gravity can be described by the massive KK modes with the resonance. Hence, instead of considering the weaker energy condition, we require for the stability of this model: no tachyon and no ghost condition for graviton modes ($h_{\mu\nu}$). No tachyonic condition ($m^2_h \geq 0$) is satisfied because the lowest state $m_h=0$ is supersymmetric vacuum state. Further, no ghost state condition is achieved if one requires some relations for the matter source: $2T_{55}= T^{\mu}_{\mu}=3(T_{22}+T_{33})$. It turns out that, although the GRS spacetime does not satisfy the weaker energy condition, it is stable against small perturbation., Comment: Revtex, 1 figure, 10 pages, a wrong citation corrected

We discuss the role of the trace part of metric fluctuations $h_{MN}$ in the Randall-Sundrum scenario of gravity. Without the matter, this field ($h=\eta^{MN}h_{MN}$) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source $\tilde{T}_{MN}$, this field satisfies the linearized equation $\Box_4 h =16\pi G_5 T^{\mu}_{\mu}$. This may correspond to the scalar $\xi^5$ in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations ($h_{5\mu} =h_{55}=0$), one finds the source relation $\tilde{T}^{\mu}_{\mu}=2\tilde{T}_{55}$, which leads to the ghost states in the massive modes. In addition, if one requires $T_{44}=2(T_{22}+T_{33})$, it is found that in the limit of $m^2_h \to 0$ we have the massless spin-2 propagation without the ghost state. This exactly corresponds to the same situation as in the intermediate scales of Gregory-Rubakov-Sibiryakov (GRS) model., Comment: 7 pages, no figure, the version to appear in PLB, comments on the matter source and references added, main results unchanged

In the dilatonic domain wall model, we study the Schwarzschild black hole as a solution to the Kaluza-Klein (KK) zero mode effective action which is equivalent to the Brans-Dicke (BD) model with a potential. This can describe the large Randall-Sundrum (RS) black hole whose horizon is to be the intersection of the black cigar with the brane. The black cigar located far from the AdS$_5$-horizon is known to be stable, but any explicit calculation for stability of the RS black hole at $z=0$ is not yet performed. Here its stability is investigated against the $z$-independent perturbations composed of odd, even parities of graviton ($h_{\mu\nu}$) and BD scalar($h_{44} = 2\phi $). It seems that the RS black hole is classically unstable because it has a potential instability at wavelength with $\lambda > 1/(2k)$. However, this is not allowed inside an AdS$_5$-box of the size with $1/(2k)$. Thus the RS black hole becomes stable. The RS black hole can be considered as a stable remnant at $z=0 $ of the black cigar., Comment: 10 pages, title changed, a crucial comment on the brane world black hole added, and to appear in Phys. Rev. D

We discuss the Randall-Sundrum (RS) choice for $h_{MN}$ in the brane-world. We begin with the de Donder gauge (transverse-tracefree) including scalar($h_{55}$), vector($h_{5\mu}$) and tensor($h_{\mu\nu}$) in five dimensions for comparison. One finds that $h_{55}=0$ and $h_{5\mu}=0$. This leads to the RS choice. It appears that the RS choice is so restrictive for the five massless states, whereas it is unique for describing the massive states. Furthermore, one can establish the stability of the RS solution with the RS choice only., Comment: corrected some typographical mistakes, 11 pages with ReVTeX, no figure

Recently, Ivanov and Volovich (hep-th/9912242) claimed that the perturbation of $h_{\mu\nu}$ with nonvanishing transverse components $h_{5\mu}$ is not localized on the brane because $h_{\mu\nu}$ depends on the fifth coordinate $z$ linearly. Consequently, it may indicate that the effective theory is unstable. However, we point out that such linear dependence on $z$ can be {\it gauged away}. Hence the solution does not belong to the physical one. Therefore, even if one includes $h_{5\mu}$, Randall and Sundrum's argument for the localized gravity on the brane remains correct., Comment: 4 pages, revtex

On the supergravity side, we study the propagation of the RR scalar and the dilaton in the D3-branes with NS $B$-field. To obtain the noncommutative effect, we consider the case of $B\to \infty(\theta \to\pi/2)$. We approximate this as the smeared D1-brane background with $F_5=H=0$. In this background, the RR scalar induces an instability of the near-horizon geometry. However, it turns out that the RR scalar is nonpropagating, while the dilaton is a physically propagating mode. We calculate the s-wave absorption cross section of the dilaton. One finds $\sigma_0^\phi |_{B\to\infty} \sim (\tilde \omega \tilde R_{\pi \over 2})^{8.9} / \omega^5$ in the leading-order while $\sigma_0^\phi|_{B=0} \sim (\tilde \omega R_0)^{8}/\omega^5$ in the D3-branes without $B$-field. This means that although the dilaton belongs to a minimally coupled scalar in the absence of $B$-field, it becomes a sort of fixed scalar in the limit of $B \to \infty$., Comment: added some discussions, 20 pages with one embedded eps figure, RevTeX

We calculate the effect of noncommutative spacetime on the greybody factor on the supergravity side. For this purpose we introduce a system of D3-branes with a constant NS $B$-field along their world volume directions ($x_2, x_3$). Considering the propagation of minimally coupled scalar with non-zero momentum along($x_2, x_3$), we derive an exact form of the greybody factor in $B$ field. It turns out that $\sigma^{B\ne0}_l > \sigma^{B=0}_l$. This means that the presence of $B$-field (the noncommutativity) suppresses the potential barrier surrounding the black hole. As a result, it comes out the increase of greybody factor., Comment: some discussions and references are added, 10 pages, no figure, ReVTeX

We propose the two formalisms for obtaining the noncommutative spacetime in a magnetic field. One is the first-order formalism and the other is the second-order formalism. Although the noncommutative spacetime is realized manifestly in the first-order formalism, the second-order formalism would be more useful for calculating the physical quantities in the noncommutative geometry than the first-order one. Several interesting points for string theory and fractional quantum Hall effect are discussed. In particular, we point out that the noncommutative geometry is closely related to the fractional quantum Hall effect(FQHE)., Comment: some references were added, 7 pages, no figure in RevTeX

We consider an easy way to get the noncommutative spacetime in Minkowski space. This corresponds to introducing a magnetic field ${\rm\bf B} = B \hat {\rm\bf k}$ in the plane. We construct a green's function in coordinate space which includes a Moyal phase factor. The projection to the lowest Landau level(LLL) is necessary for a simple calculation. Using this green's function and a second quantized formalism, we study the thermodynamic property of the anyons on the noncommutative geometry. It turns out that the Moyal phase factors contribute to the thermodynamic potential $\Omega$ as opposed to the free-particle nature., Comment: 19 pages in ReVTeX, 3 embedded eps figures, minor correction was made between eq.(50) and (51), one reference is added

We obtain the BTZ black hole (AdS$_3 \times$S$^3$) as a non-dilatonic solution from type 0B string theory. Analyzing the perturbation around this black hole background, we show that the tachyon is not a propagating mode., Comment: some detailed explanations are added, modified version will be appeared in Physics Letters B, 11 pages in RevTeX, no figures

In the type 0B string theory, we discuss the role of tachyon($T$) and fixed scalars($\nu,\lambda$). The issue is to explain the difference between tachyon and fixed scalars in the D$5_{\pm}$-D$1_{\pm}$ black hole background. For this purpose, we perform the semiclassical calculation. Here one finds a mixing between ($\nu, \lambda, T$) and the other fields. Using the decoupling procedure, one finds the linearized equation for the tachyon. From the potential analysis, it turns out that $\nu$ plays a role of test field well, while the tachyon induces an instability of Minkowski space vacuum. But the roles of $\nu$ and $T$ are the same in the near-horizon geometry. Finally we discuss the stability problem., Comment: 15 pages including embedded 2 eps figures, RevTeX3.0

We study the relationship between the gauge boson coupled to spin 2 operator and the singleton in three-dimensional anti-de Sitter space(AdS$_3$). The singleton can be expressed in terms of a pair of dipole ghost fields $A$ and $B$ which couple to $D$ and $C$ operators on the boundary of AdS$_3$. These operators form the logarithmic conformal field theory(LCFT$_2$). Using the correlation function for logarithmic pair, we calculate the greybody factor for the singleton. In the low temperature limit of $\omega \gg T_{\pm}$, this is compared with the result of the bulk AdS$_3$ calculation of the gauge boson. We find that the gauge boson cannot be realized as a model of the AdS$_3$/LCFT$_2$ correspondence., Comment: 9 pages, no figures, previous version should be replaced with this, the result was reversed