Non-extremal Solutions Research Articles

Time-dependent microstrata in AdS3

We use perturbation theory to construct a family of time-dependent microstrata: a set of non-extremal solutions of IIB supergravity asymptotic to AdS3 × S3 × T4. Our construction shows that the “special locus” constraints of [1] can be broken by allowing the solutions to depend on time. We study the secular terms appearing in the perturbation theory. Some of them can be resummed into frequency shifts, with the same interpretation as for the previously-studied microstrata solutions. Other secular terms appear harder to resum, questioning the long-term stability of the solutions.

Boosted rotating dyonic strings in Salam-Sezgin model

We show that the bosonic sector of the N = (1, 0), 6D Salam-Sezgin gauged supergravity model possesses a T-duality symmetry upon a circle reduction to D = 5. We then construct a simple magnetic rotating string solution with two equal angular momenta. Applying the T-duality transformation to this solution, we obtain the general boosted rotating dyonic black string solutions whose global structures and thermodynamic quantities are also analyzed. Owing to the fact that the solutions are not asymptotically flat, we find that there are two distinct globally-different non-extremal solutions with two different sets of thermal dynamic variables, with both satisfying the thermodynamic first law and the corresponding Small relations. However, their BPS limit becomes the same and we show that it preserves one quarter of supersymmetry by directly solving the corresponding Killing spinor equations.

Design and Multiobjective Optimization of Green Closed-Loop Manufacturing-Recycling Network Considering Raw Material Attribute

Regarding decision planning in the electronic manufacturing industry, this paper designs a green closed-loop manufacturing-recycling network for multiperiod production planning for multiple products. The network considers the tradeoff between production costs and environmental pollution induced by production scraps. Therefore, a mixed integer programming model with a dual objective is designed to achieve environmental protection and reduce production costs through resource recovery and utilization. At the same time, the recycled materials are considered to be treated, not entirely new, which could affect the manufacturing qualified rate. Thus, material attributes are proposed to distinguish new raw materials from recycled (second-hand) ones through the closed-loop manufacturing-recycling process to enhance the manufacturing qualified rate. In order to solve the dual-objective optimization model and realize optimal decisions, an epsilon constraint is designed to generate a nonextreme solution set by changing the original feasible region. The results show its ability to obtain a more balanced solution in terms of cost and environmental factors compared with the fuzzy-weighted method. Meanwhile, the analysis proves that the dual-objective optimization model with distinguishing material attributes can improve the efficiency of the manufacturing qualified rate and achieve a win-win situation for production and environmental protection during enterprise production.

\u03b1\u2032-corrections to near extremal dyonic strings and weak gravity conjecture

We construct non-extremal dyonic string solutions in 6D minimal supergravity where the leading higher derivative corrections arise from either the type IIA string theory compactified on K3 or the heterotic string theory compactified on 4-torus. The thermodynamical quantities and Euclidean actions of the strings are computed. In the near extremal regime, we calculate the force felt by a probe fundamental string in the background of the macroscopic dyonic string with leading α′ corrections. We find that in both the IIA and heterotic setups, away from extremality, the attractive force overwhelms the repulsive force. However, close to extremality, the α′ corrections can reduce the attractive force in the isoentropic process, where the charges are fixed. This feature may be used as a new constraint for supergravity models with consistent quantum gravity embedding, in cases where the extremal limit coincides with the BPS limit and the higher derivative corrections do not affect the mass-to-charge ratio. By contrast, the α′ corrections can enhance the attractive force in the isothermal or isoenergetic processes.

Thermodynamics of accelerating and supersymmetric AdS4 black holes

We study the thermodynamics of $AdS_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and non-extremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.

An evolutionary framework for estimating turning movements at road intersections

Turning movements are one of the key inputs required for several traffic studies. Several methods have been developed to measure them. However, present techniques have high operational or capital costs, which motivate researchers to develop new techniques to estimate turning movements. However, there is neither a flexible technique available to make best use of different available information types, nor a framework that supports deciding additional data to achieve a target accuracy. This paper proposes a new methodology using all available data to identify the subspace containing all solutions and determine its centroid; thus, providing the most realistic and non-extreme solution. In addition, a framework, including scenarios with different data combinations, is developed with capability to evaluate the proposed solution and then locate further measurements to achieve the target accuracy. The framework is validated using a considerable set of intersections at Edmonton city, Canada. The results show that the proposed framework can achieve the target accuracy with minimum field measurements saving time, effort and cost.

Exactly solvable gravitating perfect fluid solitons in (2 + 1) dimensions

The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity is considered. We show that in an asymptotically flat space-time the model still possesses the BPS property, i.e., admits a BPS reduction to first order Bogomolnyi equations, which guarantees that the corresponding proper energy is a linear function of the topological charge. We also find the mass-radius relation as well as the maximal mass and radius. All these results are obtained in an analytical manner, which implies the complete solvability of this selfgravitating matter system.If a cosmological constant is added, then the BPS property is lost. In de Sitter (dS ) space-time both extremal and non-extremal solutions are found, where the former correspond to finite positive pressure solutions of the flat space-time model. For the asymptotic anti-de Sitter (AdS ) case, extremal solutions do not exist as there are no negative pressure BPS baby Skyrmions in flat space-time. Non-extremal solutions with AdS asymptotics do exist and may be constructed numerically. The impact of the negative cosmological constant on the mass-radius relation is studied. We also found two potentials for which exact multi-soliton solutions in the external AdS space can be obtained. Finally, we elaborate on the implications of these findings for certain three-dimensional models of holographic QCD.

New black holes in D=5 minimal gauged supergravity: Deformed boundaries and frozen horizons

A new class of black hole solutions of the five dimensional minimal gauged supergravity is presented. They are characterized by the mass, the electric charge, two equal magnitude angular momenta and the magnitude of the magnetic potential at infinity. These black holes possess a horizon of spherical topology; however, both the horizon and the sphere at infinity can be arbitrarily squashed, with nonextremal solutions interpolating between black strings and black branes. A particular set of extremal configurations corresponds to a new one-parameter family of supersymmetric black holes. While their conserved charges are determined by the squashing of the sphere at infinity, these supersymmetric solutions possess the same horizon geometry.

Inside black holes with synchronized hair

Recently, various examples of asymptotically flat, rotating black holes (BHs) with synchronized hair have been explicitly constructed, including Kerr BHs with scalar or Proca hair, and Myers-Perry BHs with scalar hair and a mass gap, showing there is a general mechanism at work. All these solutions have been found numerically, integrating the fully non-linear field equations of motion from the event horizon outwards. Here, we address the spacetime geometry of these solutions inside the event horizon. Firstly, we provide arguments, within linear theory, that there is no regular inner horizon for these solutions. Then, we address this question fully non-linearly, using as a tractable model five dimensional, equal spinning, Myers-Perry hairy BHs. We find that, for non-extremal solutions: $(1)$ the inside spacetime geometry in the vicinity of the event horizon is smooth and the equations of motion can be integrated inwards; $(2)$ before an inner horizon is reached, the spacetime curvature grows (apparently) without bound. In all cases, our results suggest the absence of a smooth Cauchy horizon, beyond which the metric can be extended, for hairy BHs with synchronized hair.

Heating up branes in gauged supergravity

In this note, we explore the solution space of non-extremal black objects in $4D$ and $5D$ ${\cal N}=2$ gauged supergravity in the presence of fluxes. We present first order rewritings of the $4D$ action for a classes of non-extremal dyonic and electric solutions with electric flux backgrounds. Additionally, we obtain the non-extremal version of the Nernst brane in $AdS_5$ using a simple deformation. Finally, we develop a new technique to deform extremal black solutions in $4D$ to non-extremal solutions by an analysis of the symmetries of the equations of motion.

Multidimensional gravity, flux and black brane solutions governed by polynomials

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions $\mathcal{H}_s $ (for fluxbranes) and H s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for $\mathcal{H}_s $ and H s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H s and $\mathcal{H}_s $ , as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials $\mathcal{H}_s $ were shown to be used for the construction of black brane polynomials H s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A 2, C 2, and G 2.

A bubbling bolt

We present a new solvable system, solving the equations of five-dimensional ungauged N=1 supergravity coupled to vector multiplets, that allows for non-extremal solutions and reduces to a known system when restricted to the floating brane Ansatz. A two-centre globally hyperbolic smooth geometry is obtained as a solution to this system, describing a bubble linking a Gibbons--Hawking centre to a charged bolt. However this solution turns out to violate the BPS bound, and we show that its generalisation to an arbitrary number of Gibbons--Hawking centres never admits a spin structure.

On extremal limits and duality orbits of stationary black holes

With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting global symmetry orbits (duality orbits) of non-extremal solutions to those of extremal black holes. We focus our attention on a generic representative of these orbits, providing its explicit description in terms of D=4 fields. As a byproduct, using a new characterization of the angular momentum in terms of quantities intrinsic to the geometry of the D=3 effective model, we are able to prove on general grounds its invariance, as a function of the boundary data, under the D=4 global symmetry. In the extremal under-rotating limit it becomes moduli-independent. We also discuss the issue of the fifth parameter characterizing the four-dimensional seed solution, showing that it can be generated by a transformation in the global symmetry group which is manifest in the D=3 effective description.

Extremal limits of rotating black holes

We consider non-extremal, stationary, axion-dilaton solutions to ungauged symmetric supergravity models, obtained by Harrison transformations of the non-extremal Kerr solution. We define a general algebraic procedure, which can be viewed as an Inonu-Wigner contraction of the Noether charge matrix associated with the effective D=3 sigma-model description of the solution, yielding, through different singular limits, the known BPS and non-BPS extremal black holes (which include the under-rotating non-BPS one). The non-extremal black hole can thus be thought of as "interpolating" among these limit-solutions. The algebraic procedure that we define generalizes the known Rasheed-Larsen limit which yielded, in the Kaluza-Klein theory, the first instance of under-rotating extremal solution. As an example of our general result, we discuss in detail the non-extremal solution in the T^3-model, with either (q_0, p^1) or (p^0, q_1) charges switched on, and its singular limits. Such solutions, computed in D=3 through the solution-generating technique, is completely described in terms of D=4 fields, which include the fully integrated vector fields.

Black-hole solutions of N = 2, d = 4 supergravity with a quantum correction, in the H-FGK formalism

We apply the H-FGK formalism to the study of some properties of the general class of black holes in N=2 supergravity in four dimensions that correspond to the harmonic and hyperbolic ansatze and obtain explicit extremal and non-extremal solutions for the t^3 model with and without a quantum correction. Not all solutions of the corrected model (quantum black holes), including in particular a solution with a single q_1 charge, have a regular classical limit.

Charged black holes in string theory with Gauss-Bonnet correction in various dimensions

We study charged black hole solutions in Einstein-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$-dimensional and assumed to be static and spherically symmetric with the ($D\ensuremath{-}2$)-dimensional constant curvature space and asymptotically flat. The system of the basic equations is complex and the solutions are obtained numerically. We identify the allowed parameter region where the black hole solutions exist, and show configurations of the field functions in $D=4--6$ and 10. We also show the relations of the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on, and find several results. The forms of the allowed parameter regions are different depending on the dimension. There is no extreme black hole solution with $T=0$ that can be obtained by taking the limit of the nonextreme solutions within the parameter range we chose. Entropy of the black holes in the dilatonic theory is always larger than that in the nondilatonic theory. Our analysis includes the higher order term of the dilaton field which is not in our previous works. Its effect remarkably appears in five dimensions and is given in the Appendix. By our analysis it is found that the properties of the black hole solutions strongly depend on the dimension, charge, existence of the dilaton field. Hence both the detailed analyses of the individual systems and the investigations from the systematic point of view are important.

Nonextremality, chemical potential, and the infrared limit of largeNthermal QCD

Nonextremal solution with warped resolved-deformed conifold background is important to study the infrared limit of large $N$ thermal QCD. Earlier works in this direction have not taken into account all the backreactions on the geometry, namely from the branes, fluxes, and black-hole carefully. In the present work we make some progress in this direction by solving explicitly the supergravity equations of motions in the presence of the backreaction from the black hole. The backreactions from the branes and the fluxes on the other hand and to the order that we study, are comparatively suppressed. Our analysis reveal, among other things, how the resolution parameter would depend on the horizon radius and how the renormalization group flows of the coupling constants should be understood in these scenarios, including their effects on the background three-form fluxes. We also study the effect of switching on a chemical potential in the background and, in a particularly simplified scenario, compute the actual value of the chemical potential for our case.

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

We study general classes and properties of extremal and non-extremal static black-hole solutions of N = 2, d = 5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine the integration constants and physical parameters of the blackhole and black-string solutions. We derive some model-independent statements, including the transformation of non-extremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K 3 × S 1). In the cases where we have calculated it explicitly, the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges.

Imaginary soaring branes: a hidden feature of non-extremal solutions

Abstract A key property of many BPS solutions of supergravity is the fact that certain probe branes placed in these solutions feel no force, essentially because electric repulsion and gravitational attraction balance one another. In this letter we show that the existence of brane probes that feel no force is also a property of many non-supersymmetric, non-extremal solutions of supergravity. This observation requires a new class of brane probes that move with constant velocity along one or several internal directions of the solution but the zero-force condition that makes the branes “float along” at constant speed, or soar, requires the velocity to be purely imaginary. While these probes are not physical, their no-force condition implies the existence of hidden relations between the warp factors and electric potentials of non-extremal solutions in certain duality frames, and this provides insight into the structure of such solutions and can greatly simplify the search for them.

Geometry and stability of spinning branes in AdS gravity

The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed points. The discussion focuses on the cases where the parameters of spinning states can be related to the velocity of a boosted static codimension-two brane. The resulting configuration describes a single spinning brane, or a set of intersecting branes, each one produced by an independent identification. The nature of the singularity is also examined, establishing that the AdS curvature acquires one in the form of a Dirac delta distribution. The stability of the branes is studied in the framework of Chern-Simons AdS supergravity. A class of branes, characterized by one free parameter, are shown to be stable when the BPS conditions are satisfied. In 3D, these stable branes are extremal, while in higher dimensions, the BPS branes are not the extremal ones.