True Singularity Research Articles

AdS3×S3$AdS_3 \times S^3$ Background From Poisson–Lie T‐Duality

AbstractThe author proceed to construct a dual pair for the background by applying non‐Abelian T‐duality (here as Poisson–Lie [PL] T‐duality on a semi‐Abelian double). By using a certain parametrization of the 4‐dimensional Lie group and by a suitable choice of spectator‐dependent matrices the original ‐model including the metric and a non‐trivial ‐field are constructed. The dual background constructed by means of the PL T‐duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non‐trivial ‐flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non‐Abelian T‐dual ‐models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two‐loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

Chromophore-assisted light inactivation of target proteins for singularity biology.

Singularity phenomena are rare events that occur only with a probability of one in tens of thousands and yet play an important role in the fate of the entire system. Recently, an ultra-wide-field microscopy imaging systems, AMATERAS, have been developed to reliably capture singularity phenomena. However, to determine whether a rare phenomenon captured by microscopy is a true singularity phenomenon-one with a significant impact on the entire system-, causal analysis is required. In this section, we introduce the CALI method, which uses light to inactivate molecules as one of the techniques enabling causal analysis. In addition, we discuss the technical innovations of the CALI method that are required to contribute to the future development of singularity biology.

(2+1)-dimensional black holes of Einstein\u2019s theory with Born\u2013Infeld type electrodynamic sources

A new family of (2+1)-dimensional black holes are investigated in the background of Born–Infeld type theories coupled to a Riemannian curved spacetime. We know that both the scale and dual invariances are violated for these nonlinear electromagnetic theories. In this set-up, first we consider a pure magnetic source in a model of exponential electrodynamics and find a magnetically charged (2+1)-dimensional black hole solution in terms of magnetic charge q and nonlinearity parameter beta . In the second case we consider a pure electric source of gravity in the framework of arcsin electrodynamics and derive the associated (2+1)-dimensional black hole solution in terms of electric charge Q and the parameter beta . The asymptotic behaviour of the solutions at infinity as well as at rrightarrow 0 in both the frameworks is discussed. The asymptotic expressions of curvature invariants in the case of exponential electrodynamics shows that there exists a finite value of curvature at the origin, while in arcsin electrodynamics, the corresponding asymptotic behaviour shows that there is a true curvature singularity at the centre of the charged object. Furthermore, thermodynamics of the resulting charged black holes within the context of both the models is studied. It is shown that the thermodynamic quantities corresponding to these objects satisfy the first law of black hole thermodynamics.

Can Naked Singularities Exist Without Violating The Laws of Black Hole Thermodynamics?

According to the cosmic censorship conjecture, it is impossible for nature to have a physical singularity without a horizon because if it were to arise in any formalism, for instance as an extremal black hole (Kerr or Reissner-Nordstrom) then the surface gravity κ = 0, which is a strict violation of the third law of black hole thermodynamics. In this paper we explore whether a true singularity can exist without defying this law.

New rotating black holes in nonlinear Maxwell f(R) gravity

We investigate static and rotating charged spherically symmetric solutions in the framework of $f(\mathcal{R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f(\mathcal{R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit, and one that arises purely from the gravitational modification with no general relativity limit. The novel black hole solution has a true central singularity which is hidden behind a horizon; however, for particular parameter regions the horizon disappears and the singularity becomes a naked one. Furthermore, we investigate the thermodynamical properties of the solutions, such as the temperature, energy, entropy, heat capacity, and Gibbs free energy. We extract the entropy and quasilocal energy positivity conditions, we show that negative-temperature, ultracold, black holes are possible, and we show that the obtained solutions are thermodynamically stable for suitable model parameter regions.

Control Issues of KKLT

AbstractWe analyze to which extent the KKLT proposal for the construction of de Sitter vacua in string theory is quantitatively controlled. Our focus is on the quality of the 10d supergravity approximation. As our main finding, we uncover and quantify an issue which one may want to call the “singular‐bulk problem”. In particular, we show that, requiring the curvature to be small in the conifold region, one is generically forced into a regime where the warp factor becomes negative in a significant part of the Calabi‐Yau orientifold. This implies true singularities, independent of the familiar, string‐theoretically controlled singularities of this type in the vicinity of O‐planes. We also discuss possible escape routes as well as other control issues, related to the need for a large tadpole and hence for a complicated topology.

Anomalous Thermodynamic Response in the Vicinity of a Pseudo-Transition of a Spin-1/2 Ising Diamond Chain

The spin-1/2 Ising diamond chain in a magnetic field displays a remarkable pseudo-transition whenever it is driven sufficiently close to a ground-state phase boundary between a classical ferrimagnetic phase and a highly degenerate frustrated phase. The pseudo-transition of the spin-1/2 Ising diamond chain relates to intense thermal excitations from a nondegenerate ferrimagnetic ground state to a highly degenerate manifold of excited states with a frustrated character, which are responsible for an anomalous behavior of thermodynamic quantities. Temperature dependences of entropy and specific heat are indeed reminiscent of a temperature-driven phase transition of a discontinuous (entropy) or continuous (specific heat) nature though there are no true singularities of these thermodynamic quantities at a pseudo-critical temperature.

Dynamics of general barotropic stellar fluid in the framework of R + 2αT gravity

Gravitational collapse of a spherically symmetric homogeneous perfect barotropic fluid with linear as well as polytropic-type Equation of State (EoS) has been investigated in the framework of a linear model of [Formula: see text] gravity. This modified gravity has the potential to explain the observed cosmic acceleration. The calculations have been done taking the transformed time coordinate [Formula: see text], where [Formula: see text] is the initial density of the fluid. For linear EoS [Formula: see text], the condition for being a true singularity, along with sufficient condition for the formation of apparent horizon covering the singularity has been derived. For a polytrope having the EoS [Formula: see text], the scale factor [Formula: see text] as a function of fluid density [Formula: see text] has been obtained which is then used to study the dynamics of the fluid. Role of the polytropic index [Formula: see text] and the constant of proportionality [Formula: see text] in the dynamics of the fluid is also studied. A new type of exotic matter field having varied dependence of scale factor on the density, and having the potential to give rise to bouncing cosmology, provided it is the dominating fluid in the universe, is obtained in this domain and is investigated. Energy conditions are discussed.

New black-string solutions for an anti–de Sitter brane in scalar-tensor gravity

We consider a five-dimensional theory with a scalar field non-minimally-coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-Anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely-long string singularity in the bulk, the four-dimensional effective theory on the brane is robust with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.

Crack paths in soft thin sheets

Highly deformable materials (elastomers, gels, biological tissues, etc.) are ubiquitous in nature as well as in technology. The understanding of their flaw sensitivity is crucial to ensure a desired safety level. Fracture failure in soft materials usually occurs after the development of an uncommon crack path because of the non-classical near-tip stress field and the viscous effects. In a neo-Hookean material, the true opening stress singularity along the crack profile is of the order of , while it is of the order of ahead of the crack tip, promoting the appearance of a crack tip splitting leading to a tortuous crack. In the present paper, experimental tests concerning the fracture behavior of highly deformable thin sheets under tension are discussed, and the observed crack paths are interpreted according to the crack tip stress field arising for large deformations. The study reveals that higher strain rates facilitate the development of a simple Mode-I crack path, while lower strain rates induce a mixed Mode in the first crack propagation stage, leading to the formation of new crack tips. The above described behavior seems to not be affected by the initial crack size.

Rigidity of square-tiled interval exchange transformations

We look at interval exchange transformations defined as first return maps on the set of diagonals of a flow of direction \begin{document}$ \theta $\end{document} on a square-tiled surface: using a combinatorial approach, we show that, when the surface has at least one true singularity both the flow and the interval exchange are rigid if and only if \begin{document}$ \tan\theta $\end{document} has bounded partial quotients. Moreover, if all vertices of the squares are singularities of the flat metric, and \begin{document}$ \tan\theta $\end{document} has bounded partial quotients, the square-tiled interval exchange transformation \begin{document}$ T $\end{document} is not of rank one. Finally, for another class of surfaces, those defined by the unfolding of billiards in Veech triangles, we build an uncountable set of rigid directional flows and an uncountable set of rigid interval exchange transformations.

Classifying (almost)-Belyi maps with five exceptional points

We classify all rational functions f:P1→P1 whose branching pattern above 0,1,∞ satisfy a certain regularity condition with precisely d=5 exceptions. This work is motivated by solving second order linear differential equations, with d=5 true singularities, in terms of hypergeometric functions. A similar problem was solved for d=4 in Vidunas and Filipuk (2013).

Estimating Quadrature Errors in the EFIE-Based MoM Matrix, Due to Inner Integrals

The method of moments based on the electric-field integral equation is widely used for numerically solving induced surface currents on conducting structures. To set up the impedance matrix, weakly singular and near-singular inner-surface integrals must be evaluated. A leading numerical integration scheme for this purpose is Radial-Angular- ${\rm R}^{1}$ -Sqrt (RA- ${\rm R}^{1}$ -Sqrt), near and true singularity cancellation transformation quadrature. For outer integrals, standard Gauss–Legendre quadrature is used. A new and improved, closed-form, RA- ${\rm R}^{1}$ -Sqrt quadrature error estimate is derived. It is then used for a priori matrix entry error estimation due to inner integral, near-singularity quadrature. Standard, Rao–Wilton–Glisson basis functions on flat triangle elements are considered.

A point mass and continuous collapse to a point mass in general relativity

An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A maximally generalized description restricted by physically reasonable requirements is developed. A so-called field-theoretical formulation of general relativity, being equivalent to the standard geometrical presentation of general relativity, is used. All of the dynamical fields, including the gravitational field, are considered as propagating in a background (curved or flat) spacetime. Namely these properties allow us to present a non-contradictive picture of the point mass description. The results can be useful for studying the structure of the black hole true singularities and could be developed for practical calculations in models with black holes.

Cosmological perturbations in an effective and genuinely phantom dark energy Universe

We carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the Universe. These three set-ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely accepted $\Lambda$CDM model. In addition, each of the models under study induce different future singularities or abrupt events known as (i) Big Rip, (ii) Little Rip and (iii) Little Sibling of the Big Rip. Only the first one is regarded as a true singularity since it occurs at a finite cosmic time. For this reason, we refer to the others as abrupt events. With the aim to find possible footprints of this scenario in the Universe matter distribution, we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model. We have carried the perturbations in the absence of any anisotropic stress and within a phenomenological approach for the speed of sound. We constrain observationally these models using several measurements of the growth rate function, more precisely $f\sigma_8$, and compare our results with the observational ones.

Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

A Comment on Background Independence in Quantum Theory

AbstractIn this communication we take up the significance and purpose of selecting the proper coordinate system from the flat space‐time of non‐relativistic theories to the quantum theoretic formulation of general relativity. The universal background problem is straight forwardly framed as a momentum‐energy portrait in nexus with its space‐time conjugates. The description is based on operator matrix algebra, where the related analogue of the secular equation yields a Klein‐Gordon type equation and the associated Minkowski eigentime element. The energy‐momentum and their conjugate partners are represented by spaces that have (+,−) signatures. The general theory implicates both non‐zero‐ and zero rest‐mass entities, and it is proved that the conjugate relationship between energy and time provide a simple derivation of the Schwarzschild line element for the case of a gravitational field outside a spherical non‐rotational uncharged mass. This result, indicating the appearance of a black hole as a true singularity in the energy‐time formulation, and obtained as a direct consequence of their conjugate relationship, manifests background independence in concert with Einstein’s equivalence principle. Inducing a reformulation of the Lorentz Transformation respecting the indefinite Minkowski metric, displays an interesting relation between complex dilations and indefinite metric spaces, validating the complex symmetric ansatz.

Black holes and gravitational waves in three-dimensionalf(R)gravity

In the three-dimensional pure Einstein gravity, the geometries of the vacuum space-times are always trivial, and gravitational waves (gravitons) are strictly forbidden. For the first time, we find a vacuum circularly symmetric black hole with nontrivial geometries in $f(R)$ gravity theory, in which a true singularity appears. In this frame with nontrivial geometry, a perturbative gravitational wave does exist. Beyond the perturbative level, we make a constructive proof of the existence of a gravitational wave in $f(R)$ gravity, where the Birkhoff-like theorem becomes invalid. We find two classes of exact solutions of circularly symmetric pure gravitational wave radiation and absorption.

The thermodynamics and thermodynamic geometry of the Park black hole

We study the thermodynamics and thermodynamic geometry of the Park black hole in Hořava gravity. By incorporating the ideas of differential geometry, we investigate the thermodynamics by using the Weinhold and the Ruppeiner geometry. We have also analyzed it in the context of the newly developed geometrothermodynamics (GTD). The divergence of the specific heat is associated with a second-order phase transition. Here in the context of the Park black hole, both Weinhold’s metric and Ruppeiner’s metric well explain this phase transition. But these explanations depend on the choice of the potential. Hence the Legendre invariant GTD is used, and with the true singularities in the curvature scalar, they well explain the second-order phase transition. All these methods together give an exact idea of all the behaviors of the Park black hole thermodynamics.

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency (RF) spectroscopy probes OC in the frequency domain. The OC in such systems is universal for all times and is determined by the impurity scattering length and Fermi wave vector of itinerant fermions. We calculate the universal Ramsey response and RF absorption spectra. In addition to the standard power-law contribution, which corresponds to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel contribution to OC that comes from exciting one extra particle from the bottom of the itinerant band. This gives rise to a non-analytic feature in the RF absorption spectra, which evolves into a true power-law singularity with universal exponent 1/4 at the unitarity. Furthermore, we discuss the manifestations of OC in spin-echo experiments, as well as in the energy counting statistic of the Fermi gas following a sudden quench of the impurity state. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying non-equilibrium impurity physics, allowing one to explore non-equilibrium OC and to simulate quantum transport through nano-structures. This provides a useful connection between cold atomic systems and mesoscopic quantum transport.