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In this paper we propose a weaker version of Penrose's much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in Lp. Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W loc 1 , p , proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, (p > 4 to address uniform bounds, p > 2 without uniform bounds). [ABSTRACT FROM AUTHOR]

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

We establish the generalized second law (GSL) within the framework of higher curvature gravity theories, considering non-minimal couplings in the matter sector. Our proof pertains to the regime of linearized fluctuations around equilibrium black holes, aligning with previous works by Wall and Sarkar. Notably, while prior proofs addressed various gravity theories such as Lovelock theory and higher curvature gravity, they uniformly assumed minimally coupled matter sectors. In this work, we extend the proof of the linearized semi-classical GSL to encompass scenarios involving non-minimal couplings in the matter sector. Our approach involves a proposal for evaluation of the matter path integral in the expectation value of the stress tensor, adopting an effective field theory treatment for the higher derivative couplings. We leverage the recently established outcome regarding the linearized second law in such theories to substantiate our argument. [ABSTRACT FROM AUTHOR]

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson–Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers. [ABSTRACT FROM AUTHOR]

A sharp step on a chaotic potential can enhance primordial curvature fluctuations on smaller scales to the O (10 − 2) to form primordial black holes (PBHs). The present study discusses an inflationary potential with a sharp step that results in the formation of PBHs in four distinct mass ranges. Also this inflationary model allows the separate consideration of observable parameters ns and r on the CMB scale from the physics at small scales, where PBHs formation occur. In this work we computed the fractional abundance of PBHs ( f PBH ) using the GLMS approximation of peak theory and also the Press–Schechter (PS) formalism. In the two typical mass windows, 10 − 13 M ⊙ and 10 − 11 M ⊙ , f PBH calculated using the GLMS approximation is nearly equal to 1 and that calculated via PS is of 10−3. In the other two mass windows 1 M ⊙ and 6 M ⊙ , f PBH obtained using GLMS approximation is 0.01 and 0.001 respectively, while f PBH calculated via PS formalism yields 10−5 and 10−6. The results obtained via GLMS approximation are found to be consistent with observational constraints. A comparative analysis of f PBH obtained using the GLMS perspective and the PS formalism is also included. [ABSTRACT FROM AUTHOR]

Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology of waveguide cross section and scattering. Here, we study the polarization conversion mechanism in 1-THz-FSR X-cut lithium niobate microrings with multiple-resonance condition, that is the conversion can be implemented by birefringence of waveguides, which will also introduce an avoided-mode crossing. In the experiment, we find that this mode crossing results in severe suppression of one sideband in local nondegenerate four-wave mixing and disrupts the cascaded four-wave mixing on this side. Simultaneously, we propose one two-dimensional method to simulate the eigenmodes (TE and TM) in X-cut microrings, and the mode crossing point. This work will provide one approach to the design of polarization converters and simulation for monolithic photonics integrated circuits, and may be helpful to the studies of missed temporal dissipative soliton formation in X-cut lithium niobate rings. [ABSTRACT FROM AUTHOR]

In this paper, we construct an example of temperature patch solutions for the two-dimensional, incompressible Boussinesq system with kinematic viscosity such that both the curvature and perimeter grow to infinity over time. The presented example consists of two disjoint, simply connected patches. The rates of growth for both curvature and perimeter in this example are at least algebraic. [ABSTRACT FROM AUTHOR]

Medical image registration is an integral part of various clinical applications including image guidance, motion tracking, therapy assessment and diagnosis. We present a robust approach for mono-modal and multi-modal medical image registration. To this end, we propose the novel shape operator based local image distance (SOLID) which estimates the similarity of images by comparing their second-order curvature information. Our similarity metric is rigorously tailored to be suitable for comparing images from different medical imaging modalities or image contrasts. A critical element of our method is the extraction of local features using higher-order shape information, enabling the accurate identification and registration of smaller structures. In order to assess the efficacy of the proposed similarity metric, we have implemented a variational image registration algorithm that relies on the principle of matching the curvature information of the given images. The performance of the proposed algorithm has been evaluated against various alternative state-of-the-art variational registration algorithms. Our experiments involve mono-modal as well as multi-modal and cross-contrast co-registration tasks in a broad variety of anatomical regions. Compared to the evaluated alternative registration methods, the results indicate a very favorable accuracy, precision and robustness of the proposed SOLID method in various highly challenging registration tasks. [ABSTRACT FROM AUTHOR]

In this paper, using the latest Pantheon+ sample of Type Ia supernovae, baryon acoustic oscillation measurements, and observational Hubble data, we carry out a joint constraint on the Hubble constant H 0, the spatial curvature ΩK, and the sound horizon at the end of the drag epoch r d. To be model-independent, four cosmography models—i.e., the Taylor series in terms of redshift y 1 = z /(1 + z), y 2 = arctan (z) , y 3 = ln (1 + z) , and the Padé approximants—are used without the assumption of a flat Universe. The results show that H 0 is anticorrelated with ΩK and r d, indicating that smaller ΩK or r d would be helpful in alleviating the Hubble tension. The values of H 0 and r d are consistent with the estimate derived from the Planck cosmic microwave background data based on the flat ΛCDM model, but H 0 is in 2.3 ∼ 3.0 σ tension with that obtained by Riess et al. in all these cosmographic approaches. Meanwhile, a flat Universe is preferred by the present observations under all approximations except the third order of y 1 and y 2 of the Taylor series. Furthermore, according to the values of the Bayesian evidence, we found that the flat ΛCDM remains to be the most favored model by the joint data sets, and the Padé approximant of order (2,2), the third order of y 3 and y 1 are the top three cosmographic expansions that fit the data sets best, while the Taylor series in terms of y 2 are essentially ruled out. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic spacetimes. We also obtain results regarding the geometry of submanifolds by ensuring, under some mild hypothesis, the non-existence of local minima or maxima of certain distinguished function. Furthermore, in this last case the submanifold does not need to be parabolic or even complete. As an application in General Relativity, we obtain several nice results regarding (non-necessarily closed) trapped surfaces in a huge family of spacetimes. In fact, we show how our technique allows us to recover some relevant previous results for trapped surfaces in both, standard static spacetimes and generalized Robertson–Walker spacetimes. [ABSTRACT FROM AUTHOR]

Spectro-astrometry is applied to echelle spectra of the young intermediate-mass star T CrA. The aim is to better understand the origin of the [O i ] and [S ii ] emission from T CrA and further explore the usefulness of spectro-astrometry in the search for a reliable tracer of MHD disk winds. The analysis reveals a small-scale curved jet in an east–west direction and inclined parallel to the plane of the sky. It is the inclination of this jet that led to the classification of the forbidden emission lines as a low-velocity component. Thus, spectro-astrometry highlights here that for close to edge-on disks spatial information is necessary. The position angle of the jet is not perpendicular to the position angle of the accretion disk nor does it agree with older observations of outflows likely driven by T CrA. The mass outflow rate of 5–10 × 10−8 M ⊙ yr−1 is within the range for intermediate-mass stars. We conclude that more than one outflow is driven by the T CrA system and that the curvature seen in the first detection of an outflow from T CrA and in the data presented here is likely due to the multiplicity of the system. [ABSTRACT FROM AUTHOR]

Filaments are ubiquitous in the interstellar medium, yet their formation and evolution remain the topic of intense debate. In order to obtain a more comprehensive view of the 3D morphology and evolution of the Musca filament, we model the C18O(2-1) emission along the filament crest with several large-scale velocity field structures. This indicates that Musca is well described by a 3D curved cylindrical filament with longitudinal mass inflow to its center unless the filament is a transient structure with a lifetime ≲0.1 Myr. Gravitational longitudinal collapse models of filaments appear unable to explain the observed velocity field. To better understand these kinematics, we further analyze a map of the C18O(2-1) velocity field at the location of SOFIA HAWC+ dust polarization observations that trace the magnetic field in the filament. This unveils an organized magnetic field that is oriented roughly perpendicular to the filament crest. Although the velocity field is also organized, it progressively changes its orientation by more than 90° when laterally crossing the filament crest and thus appears disconnected from the magnetic field in the filament. This strong lateral change of the velocity field over the filament remains unexplained and might be associated with important longitudinal motion that can be associated to the large-scale kinematics along the filament. [ABSTRACT FROM AUTHOR]

In this work we study the long-lived post-merger gravitational wave signature of a boson-star binary coalescence. We use full numerical relativity to simulate the post-merger and track the gravitational afterglow over an extended period of time. We implement recent innovations for the binary initial data, which significantly reduce spurious initial excitations of the scalar field profiles, as well as a measure for the angular momentum that allows us to track the total momentum of the spatial volume, including the curvature contribution. Crucially, we find the afterglow to last much longer than the spin-down timescale. This prolonged gravitational wave afterglow provides a characteristic signal that may distinguish it from other astrophysical sources. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-dimensional numerical study on a helium atmospheric pressure plasma jet interacting with a wavy substrate surface, focusing on the effects of the substrate relative dielectric constant and substrate morphologies on the plasma jet behavior near the wavy surface. The results show that when the dielectric constant is small, the jet can form separate discharge channels near the wavy substrate surface and can penetrate the cavity of the wavy substrate surface. With increasing dielectric constant, the penetration distance of the discharge channels decreases. When the substrate dielectric constant exceeds a certain value, the plasma jet only propagates above the wavy substrate surface and there are no prominent separated channels near the surface. Meanwhile, the radial propagation distance along the substrate surface decreases. For a certain dielectric constant, the penetration depth of the separated channel depends on the curvature radius of the wavy substrate surface and there exists a minimum curvature radius that allows the separated channel to enter the cavity. This minimum curvature radius varies with the substrate dielectric constant. If the dielectric constant becomes larger, the minimum curvature radius increases. [ABSTRACT FROM AUTHOR]

We present new determinations of the rest-UV luminosity functions (LFs) at z = 2â€"9 to extremely low luminosities (>âˆ'14 mag) from a sample of >2500 lensed galaxies found behind the Hubble Frontier Fields (HFF) clusters. For the first time, we present faint-end slope results from lensed samples that are fully consistent with blank-field results over the redshift range z = 2â€"9, while reaching to much lower luminosities than possible from the blank-field studies. Combining the deep lensed sample with the large blank-field samples allows us to set tight constraints on the faint-end slope α of the z = 2â€"9 UV LFs and its evolution. We find a smooth flattening in α from âˆ'2.28 ± 0.10 (z = 9) to âˆ'1.53 ± 0.03 (z = 2) with cosmic time (dα / dz = âˆ'0.11 ± 0.01), fully consistent with dark matter halo buildup. We utilize these new results to present new measurements of the evolution in the UV luminosity density ρ UV brighter than âˆ'13 mag from z ∼ 9 to z ∼ 2. Accounting for the star formation rate (SFR) densities to faint luminosities implied by our LF results, we find that unobscured star formation dominates the SFR density at z ≳ 4, with obscured star formation dominant thereafter. Having shown we can quantify the faint-end slope α of the LF accurately with our lensed HFF samples, we also quantify the apparent curvature in the shape of the UV LF through a curvature parameter δ. The constraints on the curvature δ strongly rule out the presence of a turn-over brighter than âˆ'13.1 mag at z ∼ 3, âˆ'14.3 mag at z ∼ 6, and âˆ'15.5 mag at all other redshifts between z ∼ 9 and z ∼ 2. [ABSTRACT FROM AUTHOR]

Alkylation of the cylindrical part of single-walled carbon nanotubes can improve solubility and oriented aggregation. In this study, the activation energy of the monomethylation of carbon belt surfaces was investigated using density functional theory to clarify the effect of curvature on nucleophilic radical addition. The activation energy decreases with increasing curvature, and at Îş = 0.290 Ă...âˆ'1, it is approximately half (7.1 kcal·molâˆ'1) of that of the monomethylation of flat graphene flakes. The curvature significantly affects the repulsive energy between the CH3 and carbon belt portions, as well as local deformation around the bonding site. [ABSTRACT FROM AUTHOR]

Is the Universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the Universe is assumed to be homogeneous and isotropic. Here we address the above questions in highly general cosmological models, with the only assumption being that the average flow of matter is irrotational. Using techniques from differential geometry, specifically extensions of the Bonnetâ€"Myers theorem, we derive a condition which implies a finite Universe and yields a bound for its diameter. Furthermore, under a weaker condition involving the interplay between curvature and diameter, together with the assumption that the Universe is finite (i.e. has closed spatial slices), we provide a concise list of possible topologies. Namely, the spatial sections then would be either the ring topologies S 1 Ă— S 2, S 1 Ă— ~ S 2 , S 1 Ă— R P 2 , R P 3 # R P 3 , or covered by the sphere S 3 or torus T 3. In particular, under this condition the basic construction of connected sums would be ruled out (save for one), along with the plethora of topologies associated with negative curvature. These results are obtained from consequences of the geometrization of three-manifolds, by applying a generalization of the almost splitting theorem together with a curvature formula of Ehlers and Ellis. [ABSTRACT FROM AUTHOR]

We investigate the occurrence of naked singularities, local and global, in the incoming Vaidya spacetimes with zero initial mass. While it is well-known that these spacetimes admit locally and globally naked singularities, we demonstrate that globally naked singularities are significantly more common than is stressed in the literature, being generic in a natural topology on this collection of spacetimes. A heuristic consequence of the results is that the slow accumulation of mass is both necessary and sufficient for both types of naked singularity in these spacetimes. We demonstrate that the naked singularity, as long as it exists, always has divergent curvature (Kretschmann scalar) associated to it along emerging null curves, regardless of the form of the mass function. In particular, a consequence is that the curvature strength of the singularity cannot be smoothed away. [ABSTRACT FROM AUTHOR]

In type IIB fibre inflation models the inflation is a Kähler modulus which is kinetically coupled to the corresponding axion. In this setup the curvature of the field space induces tachyonic isocurvature perturbations normal to the background inflationary trajectory. However we argue that the associated instability is unphysical since it is due to the use of ill-defined entropy variables. In fact, upon using the correct relative entropy perturbation, we show that in fibre inflation axionic isocurvature perturbations decay during inflation and the dynamics is essentially single-field. [ABSTRACT FROM AUTHOR]

It is shown that the Bornâ€"Infeld nonlinear electrodynamics with a polynomial type nonlinearity accommodates finite-energy electric point charges but rejects finite-energy magnetic point charges, or monopoles, thereby spelling out an electromagnetic asymmetry. Moreover, it is demonstrated, in a systematic way, that the curvature singularities of finite-energy charged black holes in the context of the Bornâ€"Infeld theory may effectively be relegated or in some cases removed under a critical massâ€"energy condition, which has been employed successfully in earlier concrete studies. Furthermore, it is illustrated through numerous examples considered here that, when adapted to describe scalar-wave matters known as k-essences, the Bornâ€"Infeld formalism provides a fertile ground for cosmological applications, including achieving accelerated dark-energy expansions and acquiring adequate field-theoretical realizations of the equations of state of various cosmic fluid models. [ABSTRACT FROM AUTHOR]

The coupling between the spin and momentum degrees of freedom due to spinâ€"orbit interactions (SOI) suggests that the strength of the latter can be modified by controlling the motion of the charge carriers. In this paper, we investigate how the effective SOI can be modulated by constraining the motion of charge carriers to curved waveguides thereby introducing real-space geometric curvature in their motion. The change in the SOI can in turn induce topological phase transitions in the system. Specifically, we study how the introduction of periodic sinusoidal curvature in nanowires with intrinsic SOC can induce the onset of mid-gap topologically protected edge states, which can be characterized by a topological invariant or Chern number. The Chern number corresponds to the number of discrete charges that would be pumped across the length of the nanowire when the phase of a sliding gate potential relative to that of the sinusoidal curvature is varied adiabatically over a complete period. In addition, coupling to an external magnetization can be utilized as an experimental knob to modify the Chern number by displacing the energies of the curvature-induced bands relative to one another. The magnetization can be tuned to achieve large discrete jumps in the number of pump charges per phase period. [ABSTRACT FROM AUTHOR]

There is a growing interest in making stimuli-responsive polymer systems, particularly ones that are bio-inspired/biomimetic and could perform mechanical work. Here, a biological device made from gelatin is described that can mechanically cycle back and forth in response to solution pH and ionic strength (IS) changes. The gelatin bilayer has one layer of Type A gelatin and the other of Type B gelatin, which have two different isoelectric points and therefore ionization states at a given solution pH. The bilayer mechanically cycles back and forth when one layer swells more than the other layer, which occurs because of solution pH or IS change. Maximum bilayer bending occurs at pH 10, when the Type B gelatin layer swells significantly more than the Type A layer. The results show the ability to use the unique properties of different sources of gelatin to design a simple purely biological machine. [ABSTRACT FROM AUTHOR]

The curvature scalar invariants of the Riemann tensor are important in general relativity because they allow a manifestly coordinate invariant characterisation of certain geometrical properties of spacetimes such as, among others, curvature singularities, gravitomagnetism. We calculate explicit analytic expressions for the set of Zakharyâ€"McIntosh curvature invariants for accelerating Kerrâ€"Newman black holes in (anti-)de Sitter spacetime as well as for the Kerrâ€"Newmanâ€"(anti-)de Sitter black hole. These black hole metrics belong to the most general type D solution of the Einsteinâ€"Maxwell equations with a cosmological constant. Explicit analytic expressions for the Eulerâ€"Poincare density invariant, which is relevant for the computation of the Eulerâ€"Poincare characteristic χ (M), and the Kretschmann scalar are also provided for both cases. We perform a detailed plotting of the curvature invariants that reveal a rich structure of the spacetime geometry surrounding the singularity of a rotating, electrically charged and accelerating black hole. These graphs also help us in an exact mathematical way to explore the interior of these black holes. Our explicit closed form expressions show that the above gravitational backgrounds possess a non-trivial Hirzebruch signature density. Possible physical applications of this property for the electromagnetic duality anomaly in curved spacetimes that can spoil helicity conservation are briefly discussed. [ABSTRACT FROM AUTHOR]

We present new results involving general higher-curvature gravities in three dimensions. The most general Lagrangian of that kind can be written as a function of R , S 2 , S 3 , where R is the Ricci scalar, S 2 ≡ R ~ a b R ~ b a , S 3 ≡ R ~ a b R ~ b c R ~ c a , and R ~ a b is the traceless part of the Ricci tensor. First, we provide a general formula for the exact number of independent order- n densities, #(n). This satisfies the identity #(n âˆ' 6) = #(n) âˆ' n. Then, we show that, linearized around a general Einstein solution, a generic order- n â©ľ 2 density can be written as a linear combination of R n , which by itself would not propagate the generic massive graviton, plus a density which by itself would not propagate the generic scalar mode, R n âˆ' 12 n (n âˆ' 1) R n âˆ' 2 S 2 , plus #(n) âˆ' 2 densities which contribute trivially to the linearized equations. Next, we obtain an analytic formula for the quasinormal modes and frequencies of the BTZ black hole as a function of the masses of the graviton and scalar modes for a general theory. Then, we provide a recursive formula as well as a general closed expression for order- n densities which non-trivially satisfy an holographic c-theorem, clarify their relation with Bornâ€"Infeld gravities and prove that the scalar mode is always absent from their spectrum. We show that, at each order n â©ľ 6, there exist #(n âˆ' 6) densities which satisfy the holographic c-theorem in a trivial way and that all of them are proportional to a single sextic density Ω (6) ≡ 6 S 3 2 âˆ' S 2 3 . Next, we show that there are also #(n âˆ' 6) order- n generalized quasi-topological densities in three dimensions, all of which are ‘trivial’ in the sense of making no contribution to the metric function equation. Remarkably, the set of such densities turns out to coincide exactly with the one of theories trivially satisfying the holographic c-theorem. We comment on the meaning of Ω(6) and its relation to the Segre classification of three-dimensional metrics. [ABSTRACT FROM AUTHOR]

The surface functionalization of single-walled carbon nanotubes (SWCNTs) by direct radical addition has received considerable attention. The introduction of substituents is useful for tuning the Ď€ -character, enhancing the substrate anchoring, and improving the solubility. In this study, we investigated the binding energies of mono-methylated carbon belts (short SWCNTs) using density functional theory to elucidate the effect of curvature. The binding energy decreased as the curvature Îş decreased and was approximately 25 kcal molâˆ'1 less for Îş = 0.166 Ă...âˆ'1 than for Îş = 0.364 Ă...âˆ'1. This is because a change in curvature significantly impacts the interaction energy between the CH3 moiety and the carbon belt portion but not the deformation energy of the system. These results suggest that curvature can control the grafting onto the SWCNT surface. [ABSTRACT FROM AUTHOR]

We show assuming small data that massless solutions to the reflection symmetric Einsteinâ€"Vlasov system with Bianchi VII0 symmetry which are not locally rotational symmetric, can be arbitrarily close to and will remain close to isotropy as regards to the shear. However in general the shear will not tend to zero and the Hubble normalised Weyl curvature will blow up. This generalises the work (Nilsson et al 2000 Class. Quantum Grav. 17 3119â€"34; Wainwright et al 1999 Class. Quantum Grav. 16 2577â€"98), which considered a non-tilted radiation fluid to the massless Vlasov case. This represents another example of the fact that almost Ehlersâ€"Gerenâ€"Sachs theorems do not hold in general and that collisionless matter behaves differently than a perfect fluid. [ABSTRACT FROM AUTHOR]

We consider the most general quadratic metric-affine gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all 17 quadratic invariants (both parity even and odd) in torsion and non-metricity as well as their mixings, along with the terms that are linear in the curvature namely the Ricci scalar and the totally antisymmetric Riemann piece. Adding also a matter sector to the latter we first obtain the field equations for the generalized quadratic theory. Then, using a recent theorem, we successfully find the exact form of the affine connection under some quite general non-degeneracy conditions. Having obtained the exact and unique solution of the affine connection we subsequently derive the closed forms of spacetime torsion and non-metricity and also recast the metric field equations into a GR form with modified source terms that are quadratic in the hypermomentum and linear in its derivatives. We also study the vacuum quadratic theory and prove that in this instance, or more generally for vanishing hypermomentum, the connection becomes the Levi-Civita one. Therefore, we also find exactly to what does the quadratic vacuum theory correspond to. Finally, we generalize our result even further and also discuss the physical consequences and applications of our study. [ABSTRACT FROM AUTHOR]

We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range 0 ≲ z ≲ 8 to explore the Hubble tension. The age of the universe at any z is inversely proportional to the Hubble constant, H 0, so requiring the universe to be older than the OAO it contains at any z will lead to an upper limit on H 0. Assuming flat ΛCDM and setting a Gaussian prior on the matter density parameter Ωm = 0.315 ± 0.007 informed by Planck, we obtain a 95% confidence level upper limit of H 0 < 70.6 km sâˆ'1 Mpcâˆ'1, representing a 2 σ tension with the measurement using the local distance ladder. We find, however, that the inferred upper limit on H 0 depends quite sensitively on the prior for Ωm, and the Hubble tension between early-time and local measurements of H 0 may be due in part to the inference of both Ωm and H 0 in Planck, while the local measurement uses only H 0. The age-redshift data may also be used for cosmological model comparisons. We find that the R h = ct universe accounts well for the data, with a reasonable upper limit on H 0, while Einsteinâ€"de Sitter fails to pass the cosmic-age test. Finally, we present a model-independent estimate of the spatial curvature using the ages of 61 galaxies and the luminosity distances of 1048 Pantheon Type Ia supernovae. This analysis suggests that the geometry of the universe is marginally consistent with spatial flatness at a confidence level of 1.6 σ, characterized as Ω k = 0.43 âˆ' 0.27 + 0.27 . [ABSTRACT FROM AUTHOR]

In this paper, we aim to use the DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), a future Japanese space gravitational-wave antenna sensitive to the frequency range between LISA and ground-based detectors, to provide gravitational-wave constraints on the cosmic curvature at z ∼ 5. In the framework of the well-known distance sum rule, the perfect redshift coverage of the standard sirens observed by DECIGO, compared with lensing observations including the source and lens from LSST, makes such cosmological-model-independent tests more natural and general. Focusing on three kinds of spherically symmetric mass distributions for the lensing galaxies, we find that the cosmic curvature is expected to be constrained with the precision of ΔΩK ∼ 10−2 in the early universe (z ∼ 5.0), improving the sensitivity of ET constraints by about a factor of 10. However, in order to investigate this further, the mass-density profiles of early-type galaxies should be properly taken into account. Specifically, our analysis demonstrates the strong degeneracy between the spatial curvature and the lens parameters, especially the redshift evolution of the power-law lens index parameter. When the extended power-law mass-density profile is assumed, the weakest constraint on the cosmic curvature can be obtained, whereas the addition of DECIGO to the combination of LSST+DECIGO does improve significantly the constraint on the luminosity–density slope and the anisotropy of the stellar velocity dispersion. Therefore, our paper highlights the benefits of synergies between DECIGO and LSST in constraining new physics beyond the standard model, which could manifest themselves through accurate determination of the cosmic curvature. [ABSTRACT FROM AUTHOR]

In this paper, we define Jacobi fields for nonholonomic mechanics using a similar characterization than in Riemannian geometry. We give explicit conditions to find Jacobi fields and finally we find the nonholonomic Jacobi fields in two equivalent ways: the first one, using an appropriate complete lift of the nonholonomic system and, in the second one, using the curvature and torsion of the associated nonholonomic connection. [ABSTRACT FROM AUTHOR]

Misfit strain in coreâ€"shell nanowires can be elastically released by nanowire bending in case of asymmetric shell growth around the nanowire core. In this work, we investigate the bending of GaAs nanowires during the asymmetric overgrowth by an In x Ga1âˆ' x As shell caused by avoiding substrate rotation. We observe that the nanowire bending direction depends on the nature of the substrate’s oxide layer, demonstrated by Si substrates covered by native and thermal oxide layers. Further, we follow the bending evolution by time-resolved in situ x-ray diffraction measurements during the deposition of the asymmetric shell. The XRD measurements give insight into the temporal development of the strain as well as the bending evolution in the coreâ€"shell nanowire. [ABSTRACT FROM AUTHOR]

In this experiment we have first determined the focal length of an equiconvex lens. We have observed that a real image can be formed by the lens on the same side of the source if the source is sufficiently strong. This is due to the reflection from the concave surface of the lens. We have measured these image distances for different object distances. From these measurements, we have determined the refractive index of the lens as well as its radii of curvature. The relationship between the object and image distances in the reflection from the concave surface of a lens as formulated here, is similar to the ordinary reflection from a concave mirror. However, the focal length, in this case, turns out to be smaller than that of a regular concave mirror of the same radius of curvature by a factor of two, for a lens of refractive index of 1.5. [ABSTRACT FROM AUTHOR]

The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known sl (2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miura-gauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of A n . The construction of generalized gauge-Bäcklund transformation for the A n -KdV hierarchy is obtained as a composition of Miura and Bäcklund-gauge transformations for A n -mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy. [ABSTRACT FROM AUTHOR]

This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the contribution of operators quadratic in curvature. This we do both in the usual second order approach (in which the independent variable is the spacetime metric) and in the first order one (where the independent variables are the spacetime metric and the connection field). In second order, it is claimed that the generic solution in the asymptotic regime (large radius) can be matched not only with the usual solutions with horizons (like Schwarzschildâ€"de Sitter) but also with a more generic (in the sense that it depends on more arbitrary parameters) horizonless family of solutions. It is however remarkable that these horizonless solutions are absent in the restricted (that is, when the background connection is the metric one) first order approach. [ABSTRACT FROM AUTHOR]

We analytically derive the covariant form of the Riemann (curvature) tensor for homogeneous metric-affine cosmologies. That is, we present, in a cosmological setting, the most general covariant form of the full Riemann tensor including also its non-Riemannian pieces which are associated to spacetime torsion and non-metricity. Having done so we also compute a list of the curvature tensor by-products such as Ricci tensor, homothetic curvature, Ricci scalar, Einstein tensor etc. Finally we derive the generalized metric-affine version of the usual Gauss–Bonnet density in this background and demonstrate how under certain circumstances the latter represents a total derivative term. [ABSTRACT FROM AUTHOR]

We study the evaporation of a four-dimensional spherically symmetric black hole formed in a gravitational collapse. We analyze the back-reaction of a massless quantum scalar field conformally coupled to the scalar curvature by means of the semiclassical Einstein equations. We show that the evaporation is linked to an ingoing negative energy flux at the dynamical horizon and that this flux is induced by the quantum matter trace anomaly outside the black hole horizon whenever a suitable averaged energy condition is satisfied. For illustrative purposes, we evaluate the negative ingoing flux and the corresponding rate of evaporation in the case of a null radiating star described by the Vaidya spacetime. [ABSTRACT FROM AUTHOR]

Several geometric properties of complete spacelike submanifolds, with codimension at least two, in a Brinkmann spacetime are shown from natural assumptions involving the mean curvature vector field H of the spacelike submanifold. Especially, we get sufficient conditions that assure that a spacelike submanifold is contained in a leaf of the foliation of the Brinkmann spacetime defined by the orthogonal vectors to the parallel lightlike vector field. When this vector field is the gradient of a smooth function, a characterization of arbitrary codimension spacelike submanifolds contained in a leaf of this foliation is given. In the case of plane fronted wave spacetimes, relevant examples of Brinkmann spacetimes that generalize pp-waves spacetimes, several uniqueness results for codimension two spacelike submanifolds are obtained. In particular, it is proven that any compact codimension two spacelike submanifold with H = 0 in a plane fronted spacetime wave must be a (totally geodesic) front of wave. [ABSTRACT FROM AUTHOR]

The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian and solves Einstein's equations with an (in this case inevitably smooth) energy–momentum–stress tensor of a 'matter field' as the source of spacetime curvature, this identity implies the physical laws of energy and momentum conservation for the 'matter field'. The present work inquires into whether such a Bianchi identity can still hold in a weak sense for spacetimes with curvature singularities associated with timelike singularities in the 'matter field'. Sufficient conditions that establish a distributional version of the twice-contracted second Bianchi identity are found. In our main theorem, a large class of spherically symmetric static Lorentzian metrics with timelike one-dimensional singularities is identified, for which this identity holds. As an important first application we show that the well-known Reissner–Weyl–Nordström spacetime of a point charge does not belong to this class, but that Hoffmann's spacetime of a point charge with negative bare mass in the Born–Infeld electromagnetic vacuum does. [ABSTRACT FROM AUTHOR]

We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and curvature around the center of mass of the system, generalizing the results of Parker (1980 Phys. Rev. Lett. 44 1559), Parker (1980 Phys. Rev. D 22 1922–1934). Under a non-relativistic approximation, one obtains a quantum description in a Hilbert space of complex wavefunctions defined in the rest space of the system. The wavefunction of the particle then evolves according to a modified Schrödinger equation associated with a symmetric Hamiltonian. When compared to the standard Schrödinger equation for a wavefunction, we obtain corrections in terms of the acceleration of the system's center of mass and curvature of spacetime along its trajectory. In summary, we provide a formalism for the use of a complex wavefunction to describe a localized quantum particle in curved spacetimes. [ABSTRACT FROM AUTHOR]

We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa–Holm equation. New proofs of asymptotic behavior of the solutions are given. In particular we recover well-known collision conditions. Additionally the Gauss curvature (in the twopeakon case) and the sectional curvature (in the threepeakon case) of corresponding manifolds are computed. [ABSTRACT FROM AUTHOR]

We present a numerical study of the local stability of mean curvature flow (MCF) of rotationally symmetric, complete noncompact hypersurfaces with type-II curvature blowup. Our numerical analysis employs a novel overlap method that constructs 'numerically global' (i.e., with spatial domain arbitrarily large but finite) flow solutions with initial data covering analytically distinct regions. Our numerical results show that for certain prescribed families of perturbations, there are two classes of initial data that lead to distinct behaviours under MCF. Firstly, there is a 'near' class of initial data which lead to the same singular behaviour as an unperturbed solution; in particular, the curvature at the tip of the hypersurface blows up at a type-II rate no slower than (T − t)−1. Secondly, there is a 'far' class of initial data which lead to solutions developing a local type-I nondegenerate neckpinch under MCF. These numerical findings further suggest the existence of a 'critical' class of initial data which conjecturally lead to MCF of noncompact hypersurfaces forming local type-II degenerate neckpinches with the highest curvature blowup rate strictly slower than (T − t)−1. [ABSTRACT FROM AUTHOR]

An MHD-RE hybrid model is developed and implemented into the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), where the runaway electrons (REs) are treated as a fluid species. The model is utilized to study the tearing mode (TM) stability in a tokamak plasma, with the numerical results compared to that of the analytic theory. The RE effect on the n = 1 TM is systematically investigated in the absence or presence of the favorable average curvature stabilization (the GGJ-effect). Without the GGJ-effect, for a force-free toroidal plasma equilibrium, REs are found to destabilize the TM and induce a finite real frequency to the mode (in a plasma with vanishing equilibrium flow). The RE contribution is found to significantly enhance the toroidal mode coupling. In the presence of the GGJ-effect, for a plasma with finite equilibrium pressure, the MARS-F hybrid model finds that REs destroy the symmetry in the TM spectrum and introduce extra branch of the TM solution due to the eigenvalue bifurcation. This happens because REs lead to coupling to a stable fluid TM mode and destabilize this mode. Despite complicated mode spectrum introduced by REs, we find that the latter play an overall destabilizing role for the TM also in the presence of the GGJ-effect. The MARS-F computed eigenvalues are well fitted with the analytic dispersion relation derived by Liu et al (2020 Phys. Plasmas 27 092507) for the force-free equilibrium. Less satisfactory is the fitting result with a TM dispersion relation that includes both the GGJ-effect and the RE contribution, suggesting further improvement of the proposed dispersion relation. [ABSTRACT FROM AUTHOR]

The parallelization of algorithms is an essential step towards the optimization of large-scale computations. The modeling of evolving multi-domain problems is not an exception to this rule, specifically when it is applied to the context of microstructural evolutions. A new method for the simulation of evolving microstructures has been introduced in a previous work, consisting on a modified front-tracking approach where the main originality is that not only interfaces between domains are discretized but also their bulks. This new model has obtained promising results in terms of accuracy and numerical performance, however, it has been implemented in a sequential environment and is not readily usable in modern HPC units for parallel computations. This article proposes a parallel implementation for the new model using a distributed-memory approach developed with the standard protocol 'message passing interface'. The new parallel methodology has been tested in an HCP station with up to 140 cores for problems involving motion by curvature flow in polycrystals, i.e. by considering pure grain growth. Good results were obtained in terms of CPU-time and speed-up for large polycrystals (with up to 560 000 initial grains), showing that this model can lead to fast and/or large computations of microstructural evolutions in a full-field context. [ABSTRACT FROM AUTHOR]

Conics are relevant in many undergraduate course on classical physics, from free fall to Rutherford scattering. A pedagogical derivation of the intrinsic expressions of the curvature radius of different types of conic sections is presented. Our proof is carried out without resorting to any coordinate systems, but rather on using only elementary kinematic concepts together with basics of vector calculus and the very definition of conics. As a byproduct application of the present analysis, a simple and compact deduction of the Newton 'inverse square law' for gravitation from the three Kepler laws is also presented. [ABSTRACT FROM AUTHOR]

To realize high-precision machining of free-form blade surfaces, it is necessary to measure and reconstruct the blade morphology several times. Sampling measurements and data compression through free-curve approximation technology are of great benefit in shortening the processing time. A novel B-spline approximation method is proposed in this paper, which can determine a few dominant points based on curvature characteristics to approximate dense and noisy measured points with high precision. We adopt a unique adaptive knot placement strategy combined with a curvature dependent evaluation parameter and a conformal transformation method. This strategy is error-bounded in the initial knot placement, which greatly reduces the time consumed by subsequent iterative insertions. The proposed method shows advantages in approximation accuracy, compression rate, and especially in computational efficiency, in comparison with four traditional knot placement methods. Experiments were carried out and the results show that the dominant point selected by this method can replace the fine measurement results, and the compression rate of the measurement points can reach more than 90%. This method is suitable for the sampling measurement and compression of the data of blades, aircraft wings, and other similar free-form surfaces, and is especially suitable for solving the inefficiency problem caused by repeated measurements made in the process of iterative machining of aero-engine blades. [ABSTRACT FROM AUTHOR]

One of the most appealing results of metric–affine gauge theory of gravity is a close parallel between the Riemann curvature two-form and the Cartan torsion two-form: while the former is the field strength of the Lorentz-group connection one-form, the latter can be understood as the field strength of the coframe one-form. This parallel, unfortunately, is not fully established until one adopts Trautman's idea of introducing an affine–vector-valued zero-from, the meaning of which has not been satisfactorily clarified. This paper aims to derive this parallel from first principles without any ad hoc prescriptions. We propose a new mathematical framework of an associated affine–vector bundle as a more suitable arena for the affine group than a conventional vector bundle, and rigorously derive the covariant derivative of a local section on the affine–vector bundle in the formal Ehresmann-connection approach. The parallel between the Riemann curvature and the Cartan torsion arises naturally on the affine–vector bundle, and their geometric and physical meanings become transparent. The clear picture also leads to a conjecture about a kinematical effect of the Cartan torsion that in principle can be measured ŕ la the Aharonov–Bohm effect. [ABSTRACT FROM AUTHOR]

The results on the initial boundary value problem for Einstein's vacuum field equation obtained in Friedrich and Nagy Commun. Math. Phys. 201 619–655 rely on an unusual gauge. One of the defining gauge source functions represents the mean extrinsic curvature of the time-like leaves of a foliation that includes the boundary and covers a neighbourhood of it. The others steer the development of a frame field and coordinates on the leaves. In general their combined action is needed to control in the context of the reduced field equations the evolution of the leaves. In this article are derived the hyperbolic equations implicit in that gauge. It is shown that the latter are independent of the Einstein equations and well defined on arbitrary space-times. The analysis simplifies if boundary conditions with constant mean extrinsic curvature are stipulated. It simplifies further if the boundary is required to be totally geodesic. [ABSTRACT FROM AUTHOR]

We adapt Sklyanin's K-matrix formalism to the sinh–Gordon equation, and prove that all free boundary constant mean curvature annuli in the unit ball in are of finite type. [ABSTRACT FROM AUTHOR]

It is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of Einstein spaces with negative scalar curvature. This class of spacetimes admits a smooth conformal extension with a spacelike conformal boundary. Central to the analysis is the use of conformal Gaussian systems to obtain a hyperbolic reduction of the conformal Einstein field equations for which standard Cauchy stability results for symmetric hyperbolic systems can be employed. The use of conformal methods allows to rephrase the question of global existence of solutions to the Einstein field equations into considerations of finite existence time for the conformal evolution system. [ABSTRACT FROM AUTHOR]

In general, geometries of Petrov type II do not admit symmetries in terms of Killing vectors or spinors. We introduce a weaker form of Killing equations which do admit solutions. In particular, there is an analog of the Penrose–Walker Killing spinor. Some of its properties, including associated conservation laws, are discussed. Perturbations of Petrov type II Einstein geometries in terms of a complex scalar Debye potential yield complex solutions to the linearized Einstein equations. The complex linearized Weyl tensor is shown to be half Petrov type N. The remaining curvature component on the algebraically special side is reduced to a first order differential operator acting on the potential. [ABSTRACT FROM AUTHOR]