Static Vacuum Research Articles

Revisiting Buchdahl transformations: new static and rotating black holes in vacuum, double copy, and hairy extensions

This paper investigates Buchdahl transformations within the framework of Einstein and Einstein-Scalar theories. Specifically, we establish that the recently proposed Schwarzschild–Levi-Civita spacetime can be obtained by means of a Buchdahl transformation of the Schwarschild metric along the spacelike Killing vector. The study extends Buchdahl’s original theorem by combining it with the Kerr–Schild representation. In doing so, we construct new vacuum-rotating black holes in higher dimensions which can be viewed as the Levi-Civita extensions of the Myers–Perry geometries. Furthermore, it demonstrates that the double copy scheme within these new generated geometries still holds, providing an example of an algebraically general double copy framework. In the context of the Einstein-Scalar system, the paper extends the corresponding Buchdahl theorem to scenarios where a static vacuum seed configuration, transformed with respect to a spacelike Killing vector, generates a hairy black hole spacetime. We analyze the geometrical features of these spacetimes and investigate how a change of frame, via conformal transformations, leads to a new family of black hole spacetimes within the Einstein-Conformal-Scalar system.

Effect of temperature and heat input on helium isotope separation driven by an entropy filter

To understand the effect of temperature and heat input on helium isotope separation driven by an entropy filter, the thermomechanical flow of superfluid helium through an entropy filter for obtaining high purity 4He is experimentally investigated. For this method, there are two important indicators: separation flow (flow rate) and separation effect (3He concentration). The separation flow rate is examined at various temperatures ranging from 1.6 K to 1.9 K of feed helium. Different heat inputs (Q) are applied to the entropy filter outlet to drive superfluid 4He flowing through the porous element. The results demonstrate that the flow rate increases as the feed helium temperature decreases and heat input increases. Simultaneously, 3He diffusion is detected as the superfluid helium passes through the entropy filter. The concentration of 3He, filtered at different temperature ranging from 1.6 K to 1.9 K, are analyzed using HELIX SFT Static Vacuum Mass Spectrometer. The findings reveal that the 3He concentration decreases with an increase in the temperature of the feed helium bath. 3He concentration of feed helium is around 3.3×10-8. Specifically, the 3He concentration in the filtered helium at 1.6 K is approximately 3.2×10-10, while at 1.9 K, it reduced to 2.2×10-10. This suggests that 3He diffusion in He II is inversely proportional to the He II temperature from 1.6 K to 1.9 K, resulting in a lower 3He concentration at higher temperatures.

Uniqueness of the static vacuum asymptotically flat spacetimes with massive particle spheres

In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for static vacuum asymptotically flat spacetimes, which focus on scenarios featuring event horizons or photon spheres. Similarly to the uniqueness theorems concerning photon spheres or event horizons, only a single massive particle sphere is sufficient to obtain a unique solution. However, in contrast to previous theorems, our result leads to the existence of an entire spacetime foliation sliced by a set of massive particle spheres spanning various energies. Published by the American Physical Society 2024

Spherically symmetric electrovac spacetimes in conformal Killing gravity

Recently Harada proposed a third-order gravitational theory for the derivatives of the metric. Mantica and Molinari showed that Harada’s theory may be recast into the form of Einstein’s field equations (EFEs) with an additional source term which is a second-order conformal Killing tensor. Accordingly they named the theory conformal Killing gravity. However, they overlooked the fact that all solutions of the new theory (except those satisfying EFEs) admit a non-trivial second-order Killing tensor. Harada derived an analog of the Schwarzschild solution. Recently Tarciso et al obtained a generalization of Harada’s vacuum solution analogous to the Reissner–Nordström solution. However, like Harada they assumed a restricted form for a static spherically symmetric metric. In this study the most general spherically symmetric static vacuum solution of Harada’s theory and its generalization with a Maxwell electromagnetic field as source were obtained. The validity of Birkhoff’s theorem for static spherically symmetric electrovac fields in conformal Killing gravity is investigated.

Visualisation of counter-rotating dust disks using ray tracing methods

Physical aspects of stationary axisymmetric vacuum spacetimes given by exact solutions of the Einstein equations are discussed via ray tracing. A detailed study of the spacetime generated by a disk of counter-rotating dust is presented. The spacetime is given in explicit form in terms of hyperelliptic theta functions. The numerical approach to ray tracing is set up for general stationary axisymmetric spacetimes and tested at the well-studied example of the Kerr solution. Similar features as in the case of a rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the ultrarelativistic disk, where the exterior of the disk can be interpreted as the extreme Kerr solution, and the transition from a single component disk to a static disk is explored. Frame dragging, as well as photon spheres, are discussed.

An exact stationary axisymmetric vacuum solution within a metric-affine bumblebee gravity

Within the framework of the spontaneous Lorentz symmetry breaking (LSB), we consider a metric-affine generalization of the gravitational sector of the Standard Model Extension (SME), including the Lorentz-violating (LV) coefficients u and sμν . In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of LSB through the LV dimensionless parameter X = ξb 2, with ξ is the nonminimal coupling constant, and b 2 = bμbμ , with bμ is the vacuum expectation value of the bumblebee field; as the LSB is turned off, X = 0, we recover the well-established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for X by using astrophysical data of the advance of Mercury's perihelion.

Multiscale experimental insights into vacuum drying of sludge for enhanced energy efficiency and emission control

This study provides a comprehensive analysis of the vacuum drying process for sludge drying, with a focus on optimizing energy efficiency and emission control. The study used both lab-scale static and pilot-scale vacuum drying systems to test various parameters like vacuum levels, heat source temperatures, and sludge thicknesses. The results indicated that optimal drying conditions were achieved at a vacuum level of −0.06 MPa, a heat temperature of 140 °C, and a sludge thickness of 3.4 mm, where the drying rate reaches 0.13278 g·g−1·min−1. The study underscores the significant influence of vacuum level, temperature, and sludge thickness on drying rates. The Page model was used to analyze drying kinetics, elucidating how changes in these parameters affect drying characteristics. Furthermore, the study also examined the pollutant emissions and energy efficiency at the pilot scale. It found that high vacuum environments could efficiently dry sludge using low-temperature heat source, leading to average energy consumption per unit evaporation of 3020.29 kJ/kg, which is lower compared to traditional methods. By harnessing low-grade industrial waste heat, this can be further reduced to 875.76 kJ/kg. This study offers valuable insights for sustainable sludge management systems, highlighting the environmental and economic benefits of vacuum drying technology. The detailed experimental approach and thorough analysis make a significant contribution to the field of the sludge drying.

A new gravitational theory and dark matter problem

We propose a new gravitational theory with torsion based on Riemann–Cartan geometry, in which all physical quantities are dynamical. In addition to the spacetime metric, the gravitational degrees of freedom in this theory also include the torsion and two scalar fields. The energy-momentum tensor of the matter fields in this theory is also proposed. A spherically symmetric static vacuum solution of the theory is obtained. It turns out that this solution can fit the observational data of the rotation curve outside the stellar disk in the Milky Way. Therefore, the galactic dark matter may just be the gravitational effect of the theory with torsion.

Observational tests of 4D double field theory

Although General Relativity (GR) is a very successful theory of gravity, it cannot explain every observational phenomenon. People have tried many kinds of modified gravity theory to explain these phenomena which GR cannot explain very well, such as string theory. In recent years Double Field Theory (DFT) has been an exciting research area in string theory. The most general, spherically symmetric, asymptotically flat, static vacuum solution to D=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=4$$\\end{document} double field theory has been derived by S.M. Ko, J.H. Park and M. Suh. In this article, we calculate the minor corrections to the three predictions in GR: optical deflation, planet precession and gravitational redshift. These three predictions should be able to tested by observations and find the discrepancies between GR and DFT in the future.

Rapid altitude displacement induce zebrafish appearing acute high altitude illness symptoms

Rapid ascent to high-altitude areas above 2500 m often leads to acute high altitude illness (AHAI), posing significant health risks. Current models for AHAI research are limited in their ability to accurately simulate the high-altitude environment for drug screening. Addressing this gap, a novel static self-assembled water vacuum transparent chamber was developed to induce AHAI in zebrafish. This study identified 6000 m for 2 h as the optimal condition for AHAI induction in zebrafish. Under these conditions, notable behavioral changes including slow movement, abnormal exploration behavior and static behavior in the Novel tank test. Furthermore, this model demonstrated changes in oxidative stress-related markers included increased levels of malondialdehyde, decreased levels of glutathione, decreased activities of superoxide dismutase and catalase, and increased levels of inflammatory markers IL-6, IL-1β and TNF-α, and inflammatory cell infiltration and mild edema in the gill tissue, mirroring the clinical pathophysiology observed in AHAI patients. This innovative zebrafish model not only offers a more accurate representation of the high-altitude environment but also provides a high-throughput platform for AHAI drug discovery and pathogenesis research.

Static Vacuum Extensions With Prescribed Bartnik Boundary Data Near a General Static Vacuum Metric

Static Vacuum Extensions With Prescribed Bartnik Boundary Data Near a General Static Vacuum Metric

Determination of ultra-trace level krypton concentration in high-purity nitrogen by a static vacuum mass spectrometer

Uncovering the nature of dark matter microscopic particles is one of the most important disciplinary goals of physics and astronomy in the 21st century, and how to reduce background signals...

Research on longitudinal dynamics and design of RF parameters of synchrotron for XiPAF-upgrading project

Xi ’an 200 MeV Proton Application Facility (XiPAF) will be upgraded to proton and heavy ion synchrotron recently. In order to ensure the enough life of heavy ion beam, the synchrotron requires ultra-high vacuum, and the designed static vacuum is better than 5×10-10 Pa. In order to place enough vacuum pumps in the synchrotron, the circumference of the synchrotron was increased from 30.9 m to 39.96 m. The revolution frequency range of heavy ions is 0.49∼1.03 MHz. In order to reduce the engineering difficulty and improve the lower limit of frequency bandwidth requirement of the RF system, the harmonic of h=2 is used to capture and accelerate the heavy ions, and the frequency bandwidth range of the RF system is adjusted from 1∼6 MHz to 0.8∼5.0 MHz. In this paper, the longitudinal dynamics parameters of the upgraded synchrotron are designed, and the simulation calculation is carried out. Finally, the parameter requirements of the RF system are proposed.

A stationary axisymmetric vacuum solution for pure 2 gravity

The closed-form expression for pure vacuum solution obtained in Phys. Rev. D 107, 104 008 (2023) lends itself to a generalization to axisymmetric setup via the modified Newman–Janis algorithm. We adopt the procedure put forth in Phys. Rev. D 90, 064 041 (2014) bypassing the complexification of the radial coordinate. The procedure presumes the existence of Boyer-Lindquist coordinates. Using the Event Horizon Telescope Collaboration results, we model the central black hole M87* by the thus obtained exact rotating metric, depending on the mass, rotation parameter and a third dimensionless parameter. The latter is constrained upon investigating the shadow angular size assuming mass and rotation parameters are those of M87*. Stability is investigated.

Geometry of Twisted Products and Applications on Static Perfect Fluid Spacetimes

In this paper, first we study the harmonicity of the functions and forms on the twisted products, and then we determine its sectional curvature. We explore some characteristics of static perfect fluid and static vacuum spacetimes on twisted product manifolds by proving the existence and obstructions on Ricci curvature. Finally, we study the problem of the existence static perfect fluid spacetime associated with the twisted generalized Robertson-Walker and standard static spacetime metrics.

Gravitational multipoles in general stationary spacetimes

The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that these formalisms can be generalized to non-vacuum stationary solutions, except in a few special cases. This paper shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes for metrics that are sufficiently smooth at infinity. The key is the construction of an improved twist vector, which is well-defined under a mild topological condition on the spacetime (which is automatically satisfied for black holes). Ambiguities in the construction of this improved twist vector are discussed and fixed by imposing natural “gauge fixing” conditions, which also immediately lead to the equivalence between the Geroch-Hansen and Thorne formalisms for such arbitrary stationary spacetimes.

Nonlocal Static and Dynamical Vacuum Field Correlations and Casimir-Polder Interactions.

In this review, we investigate several aspects and features of spatial field correlations for the massless scalar field and the electromagnetic field, both in stationary and nonstationary conditions, and show how they manifest in two- and many-body static and dynamic dispersion interactions (van der Waals and Casimir-Polder). We initially analyze the spatial field correlations for noninteracting fields, stressing their nonlocal behavior, and their relation to two-body dispersion interactions. We then consider how field correlations are modified by the presence of a field source, such as an atom or in general a polarizable body, firstly in a stationary condition and then in a dynamical condition, starting from a nonstationary state. We first evaluate the spatial field correlation for the electric field in the stationary case, in the presence of a ground-state or excited-state atom, and then we consider its time evolution in the case of an initially nonstationary state. We discuss in detail their nonlocal features, in both stationary and nonstationary conditions. We then explicitly show how the nonlocality of field correlations can manifest itself in van der Waals and Casimir-Polder interactions between atoms, both in static and dynamic situations. We discuss how this can allow us to indirectly probe the existence and the properties of nonlocal vacuum field correlations of the electromagnetic field, a research subject of strong actual interest, also in consequence of recent measurements of spatial field correlations exploiting electro-optical sampling techniques. The subtle and intriguing relation between nonlocality and causality is also discussed.

An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

Geometrical and physical interpretation of the Levi-Civita spacetime in terms of the Komar mass density

We revisit the interpretation of the cylindrically symmetric, static vacuum Levi-Civita metric, known in either Weyl, Einstein–Rosen, or Kasner-like coordinates. The Komar mass density of the infinite axis source arises through a suitable compactification procedure. The Komar mass density mu _{K} calculated in Einstein–Rosen coordinates, when employed as the metric parameter, leads to a number of advantages. It eliminates double coverages of the parameter space, vanishes in flat spacetime and when small, it corresponds to the mass density of an infinite string. After a comprehensive analysis of the local and global geometry, we proceed with the physical interpretation of the Levi-Civita spacetime. First we show that the Newtonian gravitational force is attractive and its magnitude increases monotonically with all positive mu _{K}, asymptoting to the inverse of the proper distance in the radial direction. Second, we reveal that the tidal force between nearby geodesics (hence gravity in the Einsteinian sense) attains a maximum at mu _{K}=1/2 and then decreases asymptotically to zero. Hence, from a physical point of view the Komar mass density of the Levi-Civita spacetime encompasses two contributions: Newtonian gravity and acceleration effects. An increase in mu _{K} strengthens Newtonian gravity but also drags the field lines increasingly parallel, eventually transforming Newtonian gravity through the equivalence principle into a pure acceleration field and the Levi-Civita spacetime into a flat Rindler-like spacetime. In a geometric picture the increase of mu _{K} from zero to infty deforms the planar sections of the spacetime into ever deepening funnels, eventually degenerating into cylindrical topology in an appropriately chosen embedding.

Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates

Using a quasispherical approximation of an affine-null metric adapted to an asymptotic Bondi inertial frame, we present high order approximations of the metric functions in terms of the specific angular momentum for a slowly rotating stationary and axisymmetric vacuum spacetime. The metric is obtained by following the procedure of integrating the hierarchy of Einstein equations in a characteristic formulation utilizing master functions for the perturbations. It further verified its equivalence with the Kerr metric in the slowly rotating approximation by carrying out an explicit transformation between the Boyer-Lindquist coordinates to the employed affine-null coordinates. A peculiar feature of the derivation is that in the solution of the perturbation equations for every order a new integration constant appears which cannot be set to zero using asymptotical flatness or regularity arguments. However, these additional integration constants can be absorbed into the overall Komar mass and Komar angular momentum of a slowly rotating black hole.