Warped Solutions Research Articles

Warped AdS3black holes

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant ???2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass ?. These are all known to be perturbatively unstable except at the recently explored chiral point ?? = 1. However we show herein that for every value of ?? ? 3 there are two other (potentially stable) vacuum solutions given by SL(2,) ? U(1)-invariant warped AdS3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at ?? = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For 3$>?? > 3, there are known warped black hole solutions which are asymptotic to warped AdS3. We show that these black holes are discrete quotients of warped AdS3 just as BTZ black holes are discrete quotients of ordinary AdS3. Moreover new solutions of this type, relevant to any theory with warped AdS3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for 3$>?? > 3, the warped AdS3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges and .

GRAVITATIONAL FIELD OF SPHERICAL BRANES

The warped solution of Einstein's equations corresponding to the spherical brane in five-dimensional AdS is considered. This metric represents interiors of black holes on both sides of the brane and can provide gravitational trapping of physical fields on the shell. It is found that the analytic form of the coordinate transformations from the Schwarzschild to co-moving frame that exists only in five dimensions. It is shown that in the static coordinates active gravitational mass of the spherical brane, in agreement with Tolman's formula, is negative, i.e. such objects are gravitationally repulsive.

Strain measurement in the left ventricle during systole with deformable image registration

The objective of this study was to validate a deformable image registration technique, termed Hyperelastic Warping, for left ventricular strain measurement during systole using cine-gated, non-tagged MR images with strains measured from tagged MRI. The technique combines deformation from high resolution, non-tagged MR image data with a detailed computational model, including estimated myocardial material properties, fiber direction, and active fiber contraction, to provide a comprehensive description of myocardial contractile function. A normal volunteer (male, age 30) with no history of cardiac pathology was imaged with a 1.5 T Siemens Avanto clinical scanner using a TrueFISP imaging sequence and a 32-channel cardiac coil. Both tagged and non-tagged cine MR images were obtained. The Hyperelastic Warping solution was evolved using a series of non-tagged images in ten intermediate phases from end-diastole to end-systole. The solution may be considered as ten separate warping problems with multiple templates and targets. At each stage, an active contraction was initially applied to a finite element model, and then image-based warping penalty forces were utilized to generate the final registration. Warping results for circumferential strain (R(2)=0.75) and radial strain (R(2)=0.78) were strongly correlated with results obtained from tagged MR images analyzed with a Harmonic Phase (HARP) algorithm. Results for fiber stretch, LV twist, and transmural strain distributions were in good agreement with experimental values in the literature. In conclusion, Hyperelastic Warping provides a unique alternative for quantifying regional LV deformation during systole without the need for tags.

An asymptotic analysis of composite beams with kinematically corrected end effects

A finite element-based beam analysis for anisotropic beams with arbitrary-shaped cross-sections is developed with the aid of a formal asymptotic expansion method. From the equilibrium equations of the linear three-dimensional (3D) elasticity, a set of the microscopic 2D and macroscopic 1D equations are systematically derived by introducing the virtual work concept. Displacements at each order are split into two parts, such as fundamental and warping solutions. First we seek the warping solutions via the microscopic 2D cross-sectional analyses that will be smeared into the macroscopic 1D beam equations. The variations of fundamental solutions enable us to formulate the macroscopic 1D beam problems. By introducing the orthogonality of asymptotic displacements to six beam fundamental solutions, the end effects of a clamped boundary are kinematically corrected without applying the sophisticated decay analysis method. The boundary conditions obtained herein are applied to composite beams with solid and thin-walled cross-sections in order to demonstrate the efficiency and accuracy of the formal asymptotic method-based beam analysis (FAMBA) presented in this paper. The numerical results are compared to those reported in literature as well as 3D FEM solutions.

Gravitino in six-dimensional warped supergravity

We consider the gravitino spectrum for the general warped solution in a specific six-dimensional gauged supergravity. We find that although the brane tensions introduced at the conical singularities break the bulk supersymmetry explicitly, massless modes of the gravitino can exist with a nontrivial wave function profile, due to a nonzero U ( 1 ) R gauge flux. We also compute the wave function and the mass spectrum of Kaluza–Klein massive modes of the gravitino explicitly. We show that the introduction of a gravitino mass term on a regularized brane can give a suppressed effective gravitino mass compared to the compactification scale, due to the delocalization of the wave function of the zero-mode gravitino.

Scalar mode analysis of the warped Salam–Sezgin model

We study the scalar perturbations (which mix with the dilaton) of the general axisymmetric warped Salam–Sezgin model with codimension-2 branes. We show that the scalar fluctuation analysis can be reduced to studying two scalar modes of constant wavefunction, plus modes of non-constant wavefunction which obey a single Schrödinger equation. From the obtained explicit solution of the scalar modes, we point out the importance of the non-constant modes in describing the four dimensional effective theory. Furthermore, we show that due to these modes, the warped solutions can be unstable for a certain region of the parameter space.

Gauge/gravity duality and warped resolved conifold

We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) \times SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A_1, A_2, B_1, B_2. For the resolved conifold, we find a non-singular SU(2)\times U(1)\times U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS_5 \times T^{1,1} in the UV to AdS_5 \times S^5 in the IR, produced by giving a VEV to just one field, e.g. B_2. The presence of a condensate of baryonic operator det B_2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Green's functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.

Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS5 braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact 5-dimensional warped solutions which are associated with conformal bulk fields of weight -4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.

Scalar mode analysis of the warped Salam–Sezgin model

We study the scalar perturbation sector of the general axisymmetric warped Salam–Sezgin model with codimension-2 branes. We focus on the perturbations which mix with the dilaton. We show that the scalar fluctuation analysis can be reduced to studying two scalar modes of constant wavefunction, plus modes of non-constant wavefunction which obey a single Schrödinger equation. From the obtained explicit solution of the scalar modes, we point out the importance of the non-constant modes in describing the four-dimensional effective theory. This observation remains true for the unwarped case and was neglected in the relevant literature. Furthermore, we show that due to these modes, the warped solutions can be unstable for a certain region of the parameter space.

The general warped solution with conical branes in six-dimensional supergravity

We present the general regular warped solution with 4D Minkowski spacetime in six-dimensional gauged supergravity. In this framework, we can easily embed multiple conical branes into the warped geometry by choosing an undetermined holomorphic function. As an example, for the holomorphic function with many zeroes, we find warped solutions with multi-branes and discuss the generalized flux quantization in this case.

(BPS) Fayet–Iliopoulos terms in 5D orbifold SUGRA

We discuss Fayet–Iliopoulos terms in the context of five-dimensional supergravity compactified on an orbifold. For this purpose we use our superfield formulation of the off-shell 5D SUGRA. In the case of tuned FI terms, contrary to other claims, we find BPS solutions which ensure that N=1 supersymmetry is unbroken also in warped geometries. As in the rigid case, the FI terms induce odd masses for charged hypermultiplets, leading to the (de)localisation of the KK wave-functions near the fix-point branes. In the case of ungauged U(1)R symmetry, we present also supersymmetric warped solutions in the presence of non-trivial profiles of charged hyperscalars.

Superfield approach to 5D conformal SUGRA and the radion

We propose that the radion chiral supermultiplet of five-dimensional compactified supergravity is obtained by reduction of the graviphoton gauge multiplet to N = 1 superfields in the off shell 5D superconformal gravity formalism of Fujita, Kugo and Ohashi. We present a superfield Lagrangian of Chern–Simons type (similar to global SUSY), which reproduces all component couplings of gauge fields and the radion. A hypermultiplet superspace action is also proposed which correctly accounts for the coupling of matter multiplets with gauge and radion superfields. 4D supergravity enters by the coupling to the 4D Weyl multiplet, an even orbifold parity multiplet embedded in the 5D Weyl multiplet. We apply this formalism to a discussion of Fayet–Iliopolous terms, and the gauging of orbifold SUGRA to obtain warped solutions.

Born–Infeld strings in brane worlds

We study Born–Infeld strings in a six-dimensional brane world scenario recently suggested by Giovannini, Meyer and Shaposhnikov (GMS). In the limit of the Einstein–Abelian–Higgs model, we classify the solutions found by GMS. Especially, we point out that the warped solutions, which lead to localisation of gravity, are the—by the presence of the cosmological constant—deformed inverted string solutions. Further, we construct the Born–Infeld analogues of the anti-warped solutions and determine the domain of existence of these solutions, while a analytic argument leads us to a “no-go” hypothesis: solutions which localise gravity do not exist in a six-dimensional Einstein–Born–Infeld–Abelian–Higgs (EBIAH) brane world scenario. This latter hypothesis is confirmed by our numerical results.

Born?Infeld strings in brane worlds

We study Born–Infeld strings in a six-dimensional brane world scenario recently suggested by Giovannini, Meyer and Shaposhnikov (GMS). In the limit of the Einstein–Abelian–Higgs model, we classify the solutions found by GMS. Especially, we point out that the warped solutions, which lead to localisation of gravity, are the—by the presence of the cosmological constant—deformed inverted string solutions. Further, we construct the Born–Infeld analogues of the anti-warped solutions and determine the domain of existence of these solutions, while a analytic argument leads us to a “no-go” hypothesis: solutions which localise gravity do not exist in a six-dimensional Einstein–Born–Infeld–Abelian–Higgs (EBIAH) brane world scenario. This latter hypothesis is confirmed by our numerical results.

General warped solutions in 5D dilaton gravity

We present an explicit analytic form of the general warped solutions of the string-inspired dilaton gravity system with bulk cosmological constant in five dimensions. The general solution allows for either a non-vanishing effective four-dimensional cosmological constant or the non-trivial four-dimensional dilaton but not both.

Dilaton tadpoles, warped geometries and large extra dimensions for non-supersymmetric strings

We analyze the backreaction of dilaton tadpoles on the geometry of non-supersymmetric strings. After finding explicit warped solutions for a T-dual version of the Sugimoto model, we examine the possibility of realizing large extra dimension scenarios within the context of non-supersymmetric string models. Our analysis reveals an appealing mechanism to dynamically reduce the number of flat, non-compact directions in non-supersymmetric string theories.

Global Properties of Warped Solutions in General Relativity

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly constructed and analysed. The classification of the solutions includes the Schwarzschild, the (anti-)de Sitter, and other well-known solutions but also many exact ones whose detailed global properties to our knowledge have not been discussed before. They have a natural physical interpretation describing single or several wormholes, domain walls of curvature singularities, cosmic strings, cosmic strings surrounded by domain walls, solutions with closed timelike curves, etc.

Warping Solution for Shear Lag in Thin-Walled Orthotropic Composite Beams

A warping solution for prismatic thin-walled orthotropic composite beams is presented. For beam-wall macroelements, the macro approach solution is applied to obtain the displacements as a sum of polynomial plus Fourier functions. The kinematics of a beam-wall are obtained from a generalized plane stress solution. Constitutive equations that account for both slender and stiffened FRP sections are proposed. A fast converging continuous closed-form solution is obtained for the macroelement. The wall displacement field is evaluated in terms of nodal line parameters. Elastic coefficients that account for warping effects are introduced to provide a mechanics interpretation of the formulation. The macroelement assembling technique is illustrated by presenting an explicit warping solution for bending of box beams. The warping solution is correlated with existing analytical solutions. An expression for both the effective width and the effective longitudinal modulus variation in flanges of box beams is presented. A...

Unified nonlinear analysis for nonhomogeneous anisotropic beams withclosed cross sections

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.