Vacuum Solutions Research Articles

Einstein-Maxwell theory and the Weyl double copy

The Weyl double copy relates vacuum solutions in general relativity to Abelian gauge fields in Minkowski spacetime. In a previous work, we showed how the Weyl double copy can be extended to provide a treatment of external gravitational sources consistent with the classical Kerr-Schild double copy. Using this generalization, here we provide a complete double copy analysis of electrovacuum Petrov type D spacetimes. This includes the first analysis of the charged C-metric, whose single copy interpretation invokes the two-potential formalism of electrodynamics. We also present the first double copy prescription for the Ricci spinor, which for non-accelerating spacetimes, takes a form similar to the original double copy relation for the Weyl spinor.

Combined Vacuum Evaporation and Solution Process for High-Efficiency Large-Area Perovskite Solar Cells with Exceptional Reproducibility.

Organic-inorganic hybrid perovskites exhibit outstanding performances in perovskite solar cells (PSCs). However, the complex solution chemistry of perovskites precursors renders it difficult to prepare large-area devices in a reproducible way, which is a prerequisite for the technology to make an impact beyond lab scale. Vacuum processing, instead, is an established technology for large-scale coating of thin films. However, with respect to the hybrid perovskites it is highly challenging due to the high vapor pressure of the organic ammonium halide. In this work, vacuum evaporation of lead iodide and solution processing of organic ammonium halide is combined to produce large-area homogeneous perovskite films with large grains in a highly reproducible way. The resulting PSCs achieve a power conversion efficiency (PCE) of 24.3% (certified 23.9%) on small area (0.10cm2 ), 24.0% (certified 23.7%) on large area (1cm2 ) and 20.0% for minimodule (16cm2 ), and maintain 90% of its initial efficiency after 1000h 1-sun operation. The vacuum evaporation prevents advert environmental effects on lead halide formation and guarantees a reproducible fabrication of high-quality large-area perovskite films, which opens a promising way for large-scale fabrication of perovskite optoelectronics.

Nöther currents, black hole entropy universality and CFT duality in conformal Weyl gravity

In this paper, we study black hole entropy universality within the conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in conformal Weyl gravity via both the Nöther current method and Wald’s entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case, we couple the conformal Weyl gravity field equations to a near horizon (linear) [Formula: see text] gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However, despite non-universality, the respective black hole entropies are in congruence with Wald’s entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call [Formula: see text] and relating to the Weyl anomaly coefficient. The construction follows an [Formula: see text] correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work.

Exact analytical vacuum solutions of [formula omitted]-gravity model depending on two variables

In this paper we consider the metric power-law f(R)∼Rn-gravity model for the four-dimensional metric tensor depending on two coordinates. We obtain exact analytical vacuum solutions for different values of n. These solutions contain both non-stationary configurations of the travelling wave type and stationary ones, in particular, depending on one radial variable.

4D dS vacua from AdS vacua of type IIB string theory and the AdS distance conjecture

In order for string theory to be made compatible with the low-energy observations of a positive cosmological constant, there have been attempts to construct dS vacua in string theory which are particularly difficult to realize. Instead of attempting to find de Sitter (dS) vacuum solutions, we point to a new way to make string theory consistent with low-energy dS cosmology. In this way, string theory lives in an anti-de Sitter (AdS) vacuum (which is simple to construct) that exists only in the high-energy regime; however, as going to the low-energy scales where the heavy string excitations and Kaluza-Klein modes are integrated out, we show that the effective picture of string theory in lower dimensions would exhibit a 4D dS vacuum without needing to add additional structures such as anti-D3 branes. Additionally, we point to evidence from bottom-up physics for the strong version of the AdS distance conjecture realized from AdS vacua in string theory. This evidence hence supports the sharpening of the AdS distance conjecture as one of the universal features of quantum gravity.

Black holes surrounded by Einstein clusters as models of dark matter fluid

We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form P_t=omega rho . We assume that dark matter is made of weakly interacting particles orbiting around the supermassive black hole in the galactic center and the dark matter halo is formed by means of Einstein clusters having only tangential pressure. In the large distance from the black hole we obtain the constant flat curve with the upper bound for the dark matter state parameter omega lesssim 10^{-7}. To this end, we also check the energy conditions of the dark matter fluid outside the black hole/naked singularity, the deflection of light by the galaxy, and the shadow images of the Sgr A^star black hole using the rotating and radiating particles. For the black hole case, we find that the effect of dark matter fluid on the shadow radius is small, in particular the angular radius of the black hole is shown to increase by the order 10^{-4}, upmu arcsec compared to the vacuum solution. For the naked singularity we obtain significantly smaller shadow radius compared to the black hole case. Finally, we study the stability of the S2 star orbit around Sgr A^star black hole under dark matter effects. It is argued that the motion of S2 star orbit is stable for values omega lesssim 10^{-7}, however further increase of omega leads to unstable orbits. Using the observational result for the shadow images of the Sgr A^star reported by the EHT along with the tightest constraint for omega found from the constant flat curve, we show that the black hole model is consistent with the data while the naked singularity in our model can be ruled out.

Ultra high vacuum beam pipe of the Einstein Telescope project: Challenges and perspectives

The Einstein Telescope (ET) is a project aiming to realize a facility to host a gravitational wave (GW) detector of the third generation. The new instrument will change our vision of the Universe by observing millions of GW signals emitted during the coalescence of stellar and intermediate-mass black hole binary systems. It will permit to shed light on the first phase of the Universe formation and it will contribute to solving the dark matter enigma. The new GW detector is conceived as a series of six nested Michelson interferometers forming a triangle of 10 km side. The laser light biasing the interferometers must propagate in large ultra-high vacuum (UHV) tubes in order to reduce the noise induced by the residual gas pressure fluctuations, setting a requirement on the residual pressure in the 10−10 mbar range. The vacuum system will be made of a pipe with a 1 m diameter and an overall length of 120 km, making ET one of the largest UHV systems ever made. The giant UHV project asks for attentive optimization of material choice, manufacturing processes, post-processing treatments of the tubes, and pumping systems in order to find a cost-effective solution. In this article, we shortly review the vacuum solution adopted in the case of the second generation of GW detectors. After a general description of the main elements that constitute the ET vacuum system, the detailed design being the subject of the next 3 years of work, we will present a refined calculation of the noise due to residual-gas pressure fluctuations in the ET beam pipe.

General relativity versus dark matter for rotating galaxies

A very general class of axially symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally supported galaxies. The exact vacuum solutions of the Einstein equations for this extended Weyl class of metrics allow us to rigorously deduce the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz’s law in GR). (ii) A non-vanishing intrinsic angular momentum (J) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter (a)—a behaviour identical to that found for the Kerr metric. (iii) Asymptotic constancy of the same parameter a also demands a plateau in the rotational velocity. Unlike the Kerr metric, the extended Weyl metric can and has been continued within the galaxy, and it has been shown under what conditions Gauß and Ampére laws emerge along with Ludwig’s extended gravito-electromagnetism (GEM) theory with its attendant non-linear rate equations for the velocity field. Better estimates (than that from the Newtonian theory) for the escape velocity of the Sun have been presented.

Particles of a de Sitter Universe

The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of a zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding of particle physics. The isometry group of d+1-dimensional de Sitter is the group SO(d+1,1), whose representations are well known. Given this insight, what can we learn about the elementary degrees of freedom in a four dimensional de Sitter universe by exploring how the unitary irreducible representations of SO(4,1) present themselves in cosmological setups? This article aims to summarize recent advances along this line that benefit towards a broader understanding of quantum field theory and holography at different signs of the cosmological constant. Particular focus is given to the manifestation of SO(4,1) representations at the late-time boundary of de Sitter. The discussion is concluded by pointing towards future questions at the late-time boundary and the static patch with a focus on the representations.

Static spherical vacuum solutions in the bumblebee gravity model

The bumblebee gravity model is a vector-tensor theory of gravitation where the vector field nonminimally couples to the Ricci tensor. By investigating the vacuum field equations with spherical symmetry, we find two families of black-hole (BH) solutions in this model: one has a vanishing radial component of the vector field and the other has a vanishing radial component of the Ricci tensor. When the coupling between the vector field and the Ricci tensor is set to zero, the first family becomes the Reissner-Nordstr\"om solution while the second family degenerates to the Schwarzschild solution with the vector field being zero. General numerical solutions in both families are obtained for nonzero coupling between the vector field and the Ricci tensor. Besides BH solutions, we also reveal the existence of solutions that have a nonvanishing $tt$-component of the metric on the supposed event horizon where the $rr$-component of the metric diverges while the curvature scalars are finite. These solutions are not supported by existing observations but present certain properties that are of academic interests. We conclude the study by putting the BH solutions into tests against the Solar-System observations and the images of supermassive BHs.

Complete Evaporation of Black Holes and Page Curves

The problem of complete evaporation of a Schwarzschild black hole, the simplest spherically symmetric vacuum solution of the Einstein field equation, posed by Hawking, is that when the black hole mass M disappears, an explosion of temperature T=1/8πM takes place. We consider the Reissner–Nordstrom black hole, a static spherically symmetric solution to the Einstein–Maxwell field equations, and show that if mass M and charge Q<M satisfy the bound Q>M−CM3, C>0 for small M, then the complete evaporation of black holes without blow-up of temperature is possible. We describe curves on the surface of state equations such that the motion along them provides complete evaporation without temperature explosion. In this case, the radiation entropy follows the Page curve and vanishes at the end of evaporation. Similar results for rotating Kerr, Schwarzschild–de Sitter and Reissner–Nordstrom-(Anti)-de Sitter black holes are discussed.

Stability of vacuum for the Landau equation with hard potentials

We consider the spatially inhomogeneous Landau equation with Maxwellian and hard potentials (i.e with $\gamma\in[0,1)$) on the whole space $\mathbb{R}^3$. We prove that if the initial data $f_{\text{in}}$ are close to the vacuum solution $f_{\text{vac}}=0$ in an appropriate weighted norm then the solution $f$ exists globally in time. This work builds up on the author's earlier work on local existence of solutions to Landau equation with hard potentials. Our proof uses $L^2$ estimates and exploits the null-structure established by Luk [Stability of vacuum for the Landau equation with moderately soft potentials, Annals of PDE (2019) 5:11]. To be able to close our estimates, we have to couple the weighted energy estimates, which were established by the author in a previous paper [Local existence for the Landau equation with hard potentials, arXiv:1910.11866], with the null-structure and devise new weighted norms that take this into account.

Riemann problems for the 2-D pressureless gas dynamics with external forces

Abstract This paper is concerned with the pressureless gas dynamics with a space-dependent gravity or a time-dependent friction in two dimensions. The basic Riemann problems with two pieces of constant initial data are considered. By the characteristic analysis, the Riemann problems are constructively solved by two kinds of solutions: vacuum solution and delta-shock solution, which describe the phenomena of cavitation and concentration, respectively. Especially, the generalized Rankine–Hugoniot relations for delta-shock waves are clarified and applied to the Riemann problems.

Twisted Affine Integrable Hierarchies and Soliton Solutions

A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine \(A_{2r}^{(2)}\) Lie algebra. The zero curvature representation of the time evolution equations is shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non-zero) vacuum solutions. Another consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting only zero vacuum and another of constant strictly non-zero vacuum solutions. The two-dimensional gauge potentials in the vacuum play a crucial ingredient and are shown to be expanded in powers of the vacuum parameter \(v_0\). Soliton solutions are constructed from vertex operators, which for the non-zero vacuum solutions correspond to deformations characterized by \(v_0\).

PATHFINDING THE “FIELD OF TRUTH”: GEDANKENEXPERIMENT, MACH'S PRINCIPLE AND THE PHENOMENOLOGICAL METHOD OF VARIATIONS

The article contributes to the development of an a priori methodology adequate to the legitimate claims of fundamental physics as a mathematical philosophy of nature. Husserl’s phenomenological method of variations - the most important part of this methodology - is seen as a means of bringing to clarity and achieving apodictic evidence, highly relevant in the current conditions of erosion of the empirical criterion of truth, when the invention of hypotheses for the needs of deductive theorization has become the norm of so-called fundamental research. As an example for express testing of the method, a problematic principle is taken that needs to be clarified: the “Mach principle” formulated in many ways since the time of A. Einstein. The result of a clarifying reflection of one of the transitions between versions of the principle is the conclusion that the conceptual development of the general theory of relativity on methodologically clarified grounds, one of which would be a correctly formulated Mach principle, should proceed from a relational understanding of space-time consistent with this principle. Mach’s principle, since it determines the structure of the equations of the theory themselves, the solutions of which are conceived in the modus of the possible, is in no way affected in its truth value by the fact of the existence of vacuum solutions of these equations. In conclusion, the article examines the question of the influence of the Mach theory of thought experiment on the genesis of the phenomenological method of variations.

Friction for flexible pressure sensors and arrays on polymers

The rapid development of internet technology and artificial intelligence drives the demands of flexible sensors. Compared with vacuum technology and solution method, the fabrication of flexible sensor by pencil writing directly has advantages such as low cost, simple operation, low temperature and no pollution. However, they are based on paper and rely on rigid fibers on the surface of it. The polymer is comfortable, portable and has excellent tensile properties, making it more suitable than paper as flexible substrates for wearable devices. In this paper, flexible pressure sensors and arrays are prepared by friction on polymers (Eco-flex、PDMS and bionic skin). The sensitivity of the prepared pressure sensor was 0.78 kPa -1 in the range of 20 kPa, and the response time was 400 ms, while the pressure detection ranges up to 160 kPa, finally it can be reused for 1000 cycles. As a wearable device, it can be applied to object grasping, muscle movement and respiratory monitoring. Furthermore, by combining the friction process with the transfer printing process, the stretchable flexible pressure sensor can be prepared on 3D cylindrical and hemispherical curved surfaces. Moreover, patterned sensors can also be prepared. It should be noted that the sensor can be cleaned after being discarded and has no pollution to the environment due to the mild type of materials, which is of certain significance for the development of flexible sensors towards green and low-cost development trend.

Gauss-Bonnet black holes in a special anisotropic scaling spacetime

Inspired by the Lifshitz gravity as a theory with anisotropic scaling behavior, we suggest a new (n + 1)-dimensional metric in which the time and spatial coordinates scale anisotropically as (t, r, θi) → (λzt, λ−1r, λxiθi). Due to the anisotropic scaling dimension of the spatial coordinates, this spacetime does not support the full Schrödinger symmetry group. We look for the analytical solution of Gauss-Bonnet gravity in the context of the mentioned geometry. We show that Gauss-Bonnet gravity admits an analytical solution provided that the constants of the theory are properly adjusted. We obtain an exact vacuum solution, independent of the value of the dynamical exponent z, which is a black hole solution for the pseudo-hyperbolic horizon structure and a naked singularity for the pseudo-spherical boundary. We also obtain another exact solution of Gauss-Bonnet gravity under certain conditions. After investigating some geometrical properties of the obtained solutions, we consider the thermodynamic properties of these topological black holes and study the stability of the obtained solutions for each geometrical structure.

Yang–Mills solutions on Minkowski space via non-compact coset spaces

We find a two-parameter family of solutions of the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H3≅SO(1,3)/SO(3), while the exterior of the lightcone employs de Sitter space dS≅3SO(1,3)/SO(1,2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang–Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang–Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy-momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.

Shadow of black hole surrounded by magnetized plasma: Axion-plasmon cloud

By exploiting the extreme environment of the black hole (BH) as a potential place for axion-photon interaction, we use an axion-producing model of the magnetized plasma to study the shadow of an asymptotically flat rotating BH immersed into an axion-plasmon cloud. By aiming to reveal footprints of axion in the dark shadow of BH, we in this paper explore the influence of the fixed axion-plasmon background on the motion of incident photons around the rotating BH. Under some free parameter settings, we find that axion-plasmon cloud around rotating BH affects the shape and size of the shadow in such a way that its role is distinguishable from non-magnetized plasma and standard vacuum solutions. By being limited to high rotation BH, we show that the size of the BH shadow increases as the axion-plasmon coupling gets strong. Interestingly, our analysis indicates that as the mass of axion gets heavier, it can leave a subtle imprint of itself on the shadow. Conversely, in the non-rotating limit (Schwarzschild), by recovering the spherical symmetry of the shadow shape of BH, its size decreases. In coordination with the trend of change in shadow size, the investigation of the energy emission from the BH surrounded by the magnetized plasma shows that the maximal energy emission rate from the rotating BH in the presence of axion-plasmon cloud increases compared to the non-magnetized plasma and the vacuum solutions. Subsequently, by relaxing the rotation, the axion-plasmon cloud causes a decrease in the energy emission rate from the BH.

Static-fluid black hole and wormhole in three-dimensions

We introduce the so-called static-fluid solutions in 2+1-dimensional spacetime. We assume the spacetime to be static and circular symmetric and for the perfect fluid we consider an equation of state (EoS) of the form where r is the radial coordinate. Since, unlike the 3+1-dimensions, in 2+1-dimensions there is no vacuum solution other than the flat spacetime, our approach is not exactly the same as the 3+1-dimensions such that the static-fluid is accompanied by a cosmological constant. In addition to that, at first, we present a static solution supported by a static-fluid of constant energy-momentum tensor with a general EoS. Then, in the nonconstant energy-momentum tensor case, we introduce a large class of solutions. Depending on the values of the integration constants it implies black holes, wormholes, or cosmological solutions. Some of these solutions are closed in two-space which are considered for the first time in 2+1-dimensions. In both cases i.e. the constant and nonconstant energy-momentum tensor we imposed the satisfaction of conservation of the energy-momentum i.e. .