On Black Hole Stability in Critical Gravities

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition.Comment: 16 pages, minor corrections, further comments and references adde

Interacting Intersections

Intersecting p-branes can be viewed as higher-dimensional interpretations of multi-charge extremal p-branes, where some of the individual p-branes undergo diagonal dimensional oxidation, while the others oxidise vertically. Although the naive vertical oxidation of a single p-brane gives a continuum of p-branes, a more natural description arises if one considers a periodic array of p-branes in the higher dimension, implying a dependence on the compactification coordinates. This still reduces to the single lower-dimensional p-brane when viewed at distances large compared with the period. Applying the same logic to the multi-charge solutions, we are led to consider more general classes of intersecting p-brane solutions, again depending on the compactification coordinates, which turn out to be described by interacting functions rather than independent harmonic functions. These new solutions also provide a more satisfactory interpretation for the lower-dimensional multi-charge p-branes, which otherwise appear to be nothing more than the improbable coincidence of charge-centres of individual constituents with zero binding energy.Comment: 20 pages, Latex, references adde

Rotating Black Holes in Higher Dimensions with a Cosmological Constant

We present the metric for a rotating black hole with a cosmological constant and with arbitrary angular momenta in all higher dimensions. The metric is given in both Kerr-Schild and Boyer-Lindquist form. In the Euclidean-signature case, we also obtain smooth compact Einstein spaces on associated S^{D-2} bundles over S^2, infinitely many for each odd D\ge 5. Applications to string theory and M-theory are indicated.Comment: 8 pages, Latex. Short version, with more compact notation, of hep-th/0404008. To appear in Phys. Rev. Let

Brane Worlds in Collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed universe is one of a number of colliding D3-branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3-branes the metric remains static during and after the collision. We also obtain a general class of solutions representing $p$-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and negative-tension 3-brane.Comment: RevTex, 4 pages, 1 figure, typos and minor errors correcte

Hole spin relaxation in semiconductor quantum dots

Hole spin relaxation time due to the hole-acoustic phonon scattering in GaAs quantum dots confined in quantum wells along (001) and (111) directions is studied after the exact diagonalization of Luttinger Hamiltonian. Different effects such as strain, magnetic field, quantum dot diameter, quantum well width and the temperature on the spin relaxation time are investigated thoroughly. Many features which are quite different from the electron spin relaxation in quantum dots and quantum wells are presented with the underlying physics elaborated.Comment: 10 pages, 10 figure

Harmonic superpositions of non-extremal p-branes

The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or non-extremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multi-centre solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of non-extremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multi-scalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, and we discuss general procedures for constructing the solutions, and studying their symmetries.Comment: Latex, 23 page

Branching ratio and CP asymmetry of Bs→π+π−B_s \to \pi^+ \pi^- decays in the perturbative QCD approach

In this paper, we calculate the decay rate and CP asymmetry of the $B_s \to \pi^+\pi^-$ decay in perturbative QCD approach with Sudakov resummation. Since none of the quarks in final states is the same as those of the initial $B_s$ meson, this decay can occur only via annihilation diagrams in the standard model. Besides the current-current operators, the contributions from the QCD and electroweak penguin operators are also taken into account. We find that (a) the branching ratio is about $4 \times 10^{-7}$; (b) the penguin diagrams dominate the total contribution; and (c) the direct CP asymmetry is small in size: no more than $3$; but the mixing-induced CP asymmetry can be as large as ten percent testable in the near future LHC-b experiments.Comment: 12 pages, 4 figures included, RevTe

Study of color suppressed modes B0→Dˉ(∗)0η(′)B^0 \to \bar D^{(*)0} \eta^{(\prime)}

The color suppressed modes $B^0 \to \bar D^{(*)0} \eta^{(\prime)}$ are analyzed in perturbative QCD approach. We find that the dominant contribution is from the non-factorizable diagrams. The branching ratios calculated in our approach for $B^0 \to \bar D^{(*)0} \eta$ agree with current experiments. By neglecting the gluonic contribution, we predict the branching ratios of $B^0 \to \bar D^{(*)0} \eta'$ are at the comparable size of $B^0 \to \bar D^{(*)0} \pi^0$, but smaller than that of $B^0 \to \bar D^{(*)0} \eta$.Comment: revtex, 5 pages, axodraw.st

Cosmological Solutions in String Theories

We obtain a large class of cosmological solutions in the toroidally-compactified low energy limits of string theories in $D$ dimensions. We consider solutions where a $p$-dimensional subset of the spatial coordinates, parameterising a flat space, a sphere, or an hyperboloid, describes the spatial sections of the physically-observed universe. The equations of motion reduce to Liouville or $SL(N+1,R)$ Toda equations, which are exactly solvable. We study some of the cases in detail, and find that under suitable conditions they can describe four-dimensional expanding universes. We discuss also how the solutions in $D$ dimensions behave upon oxidation back to the $D=10$ string theory or $D=11$ M-theory.Comment: Latex, 21 pages, a reference adjuste

f(R) Gravities, Killing Spinor Equations, "BPS" Domain Walls and Cosmology

We derive the condition on f(R) gravities that admit Killing spinor equations and construct explicit such examples. The Killing spinor equations can be used to reduce the fourth-order differential equations of motion to the first order for both the domain wall and FLRW cosmological solutions. We obtain exact "BPS" domain walls that describe the smooth Randall-Sundrum II, AdS wormholes and the RG flow from IR to UV. We also obtain exact smooth cosmological solutions that describe the evolution from an inflationary starting point with a larger cosmological constant to an ever-expanding universe with a smaller cosmological constant. In addition, We find exact smooth solutions of pre-big bang models, bouncing or crunching universes. An important feature is that the scalar curvature R of all these metrics is varying rather than a constant. Another intriguing feature is that there are two different f(R) gravities that give rise to the same "BPS" solution. We also study linearized f(R) gravities in (A)dS vacua.Comment: 37 pages, discussion on gravity trapping in RSII modified, typos corrected, further comments and references added; version to appear in JHE