Abstract Addressing the general question whether Penrose-type singularities physically exist inside black holes, we investigate the problem in the context of an analogue system, a flowing laboratory liquid, for which the governing equations are at least in principle known to all relevant scales, and in all regions of the effective spacetime. We suggest to probe the physical phenomena taking place close to the singularity in the interior of a 2 + 1D analogue black hole arising from a polytropic, inviscid, irrotational, and axisymmetric steady flow. Showing also that previously studied analogue black holes were not proven to contain a Penrose-type singularity, we propose an experimental setup in a Bose-Einstein condensate that allows us for the first time to verify the occurrence of the Penrosetype singularity in a physical system. Our study, in addition, provides concrete evidence, for a well understood dynamical system, that the Einstein equations are not necessary for the singularity to form, demonstrating that Penrose-type spacetime singularities can potentially also exist in non-Einsteinian theories of gravity. Finally, we demonstrate how the singularity is physically avoided in our proposed laboratory setup.

The global demand for lithium-ion batteries (LIBs) has been increasing due to the transition toward low-carbon societies. However, concerns about the sustainability of lithium resources has been arisen due to their low crucial abundance and uneven regional distribution.¹ As a result, sodium-ion batteries (SIBs) have gained attention due to the abundance of sodium as a charge carrier. In this study, we focus on Na-based electrolytes, which play a crucial role in charge transport between electrodes. In aqueous solutions, Na⁺ is reported to diffuse faster than Li⁺.2 However, few studies have directly compared the diffusion behavior of Li⁺ and Na⁺ in organic solvents. Furthermore, due to the considerable nuclear quadrupole moment of Na⁺ and its extremely short relaxation time, measuring its self-diffusion coefficient (D) using pulsed-field gradient (PFG)-NMR is challenging.² The aim of this study is the systematic comparison of (Li, Na)-based electrolytes by measuring the D of various nuclei and evaluating their transport and physical properties, including viscosity (η) and density (ρ).All electrolyte preparations were conducted in an Ar-filled glovebox. LiN(SO₂F)₂ (LiFSA) and NaN(SO₂F)₂ (NaFSA) were used as electrolyte salts. Ethylene carbonate (EC) and ethyl methyl carbonate (EMC) were used as solvents. Electrolytes were prepared at concentrations ranging from 1.0 to 3.0 mol kg⁻¹ in EC and EMC with a 3:7 weight ratio. Additionally, mixed salt electrolytes (1.0 mol kg⁻¹) were prepared by dissolving equimolar ratios of (Li0.5Na0.5)FSA in EC and EC:EMC (3:7) to evaluate the transport properties of Li and Na in electrolytes under identical conditions. To evaluate their transport properties, η and ρ were measured from 283 to 323 K using a Stabinger viscometer/density measurement system. The D of each component (Li+, Na+, EC, EMC) was determined at 333 K using PFG-NMR, measuring 1H, 7Li, 19F, and 23Na nuclei. Addtionally, solvation structures and salt-solvent interactions were analyzed by Raman spectroscopy and excess density (E ρ ) analysis. To determine E ρ , the salt density (ρₛₐₗₜ) was obtained by melting (Li, Na)FSA in a volumetric flask at 150-200 ℃ and measuring its mass. The densities at 10-50 ℃ were estimated using calibration lines derived from these measurements.Fig. 1 shows the relationship between the inverse viscosity (η -1) and D for the electrolytes at 303 K. In electrolytes consisting only EC as a solvent, D Na was larger than D Li. According to the Stokes–Einstein equation, this behavior is attributed to differences in the Stokes radii of Na+ and Li+. In contrast, in electrolytes containing EC:EMC (3:7), D Na and D Li were nearly indentical. This behavior suggests that the Stokes radii of Li⁺ and Na⁺ become similar in the presence of EMC as duluent. To further explore this phenomenon, we conducted Raman spectroscopy and E ρ analysis. Fig. 2 shows the Raman spectra of the carbonyl-stretching vibrations of EC and EMC in the 1500-1800 cm⁻¹ region for (Li, Na)-based electrolytes with EC:EMC (3:7).3 The intensity of bound-state EC and EMC increased with salt concentration. To confirm the ratios of free and bound states of EC and EMC with cations, peak area ratios were calculated from Fig. 2 and are presented in Fig. 3. In Figure 3(a), Li⁺ exhibited a stronger coordination with EC than Na⁺, likely due to its higher charge density. Consequently, Li+ attracted more EC molecules in the electrolyte. In Fig. 3(b), no significant difference was observed in the peak area ratios of free and bound states of EMC between Li+ and Na+. This behavior is likely due to the low dielectric constant of EMC, which results in weak coordination with cations. To further investigate salt-solvent interactions, Fig. 4 shows the Eρ values for (Li, Na)-based electrolytes with EC:EMC (3:7). The equation used to calculated Eρ is also shown in Fig. 4. Eρ decreased with increasing salt concentration for both (Li, Na)-based electrolytes. Moreover, Na-based electrolytes exhibited more negative Eρ values than Li-based electrolytes. These differences are attributed to variations in the coordination numbers and coordination propensities of Li⁺ and Na⁺. We will also report the coordination numbers of Li⁺ and Na⁺ determined by Raman spectroscopy and discuss how EMC addition alters their solvation structures.(1) N. Yabuuchi, et.al., Chem. Rev., 114, 11636 (2014).(2) K. Hayamizu, et.al., RSC Adv., 33, 20252−20257 (2021).(3) Y. Zhang, et.al., Energy Environ. Sci., 13, 183–199 (2020). Figure 1

Abstract The gauge-theoretical method introduced in our previous paper is applied to solve the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of the non-Weyl class, where the gravitational and electric or magnetic potentials are not functionally related. In the electrostatic case, we show that the obtained solution coincides with the solution given by Bonnor in 1979. In the magnetostatic case, we present a solution describing the gravitational field created by two magnetically charged masses. In this solution, we present a case in which the Dirac string does not stretch to spatial infinity but lies between the magnetically charged masses.

Abstract We analyze the complexity factor in spherically symmetric stars undergoing dissipative collapse in the presence of shear. The interior spacetime is described by a general spherically symmetric metric, and the corresponding Einstein field equations are derived. Matching the interior spacetime to the exterior Vaidya geometry yields the boundary condition governing the temporal evolution of the collapsing body. The interior matter distribution obeys the Euclidean condition, i.e. the areal radius is identical to the proper radius as the star collapses. We present a complete model of a Euclidean star and investigate its physical viability. We further investigate the notion of complexity as defined by Herrera in terms of the pressure anisotropy, density inhomogeneity and heat flux. The novelty of our work is the demonstration of the interplay of these factors to the complexity in a shearing model which is absent in earlier treatments.

Abstract We present a new rotating black hole solution to the Einstein equations as an extension of the Kerr spacetime. Interestingly, the solution we find may not be uniquely characterized by asymptotic parameters such as mass, angular momentum, and charge, thereby it would be the additional hair. We also analyze in detail how this additional characteristics or this hair affects the thermodynamic properties of the black hole.

Abstract This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces (MOTS), within the framework of the Einstein-Maxwell equations. We show that, under appropriate energy and curvature conditions, saturation of the inequality Α≧4π(Q E 2 +Q M 2 ) imposes a rigid geometric structure in a neighborhood of the surface. In particular, the electric and magnetic fields must be normal to the foliation, and the local geometry is isometric to a Riemannian product. We establish two main rigidity theorems: one in the time-symmetric case and another for initial data sets that are not necessarily time-symmetric. In both cases, equality in the area-charge bound leads to a precise characterization of the intrinsic and extrinsic geometry of the initial data near the critical surface.

Abstract The known description of the universe near the cosmological
singularity in the framework of the Belinski-Khalatnikov-Lifshitz
(BKL) scenario is completed with a few exact results following
from the BKL asymptotic of the Einstein equations. The main
results: (1) The cosmological singularity is an inevitable
beginning or end of the universe. (2) Attaining the singularity
from shrinking initial conditions requires infinite time parameter
$\tau$; no singularity of any kind may occur for its finite
values. (3) The previously found exact solution [P.G. and W.
Piechocki, Eur. Phys. J. C 82:216 (2022)] is the only asymptotic
with well-defined proportions between the directional scale
factors appropriately compensated against indefinite growth of
anisotropy. In all other cases, the universe undergoes
oscillations of Kasner type, which reduce the length scales to
nearly zero in some directions, while largely extending it in the
others. Together with instability of the exact solution [op.
cit.], it makes the approach to the singularity inevitably
chaotic. (4) Reduced equations are proposed and explicitly solved
to describe these oscillations near their turning points. In
logarithmic variables, the oscillations are found to have sawtooth
shapes. A by-product is a quadric of kinetic energy, a simple
geometric tool for all this analysis.

Abstract We apply the perturbation methods of the post-Newtonian approximation to obtain equations for gravitation derived from the Rastall Theory, a modification of the Einstein Field Equations. This method allows us to get the components of the space-time metric in terms of the generalized potentials. Once obtained, we use the results to construct equations of gravitation in vector form, analogous to the Linear Jefimenko Gravitational Equations. In addition, we show the physical implications of the system of equations obtained, comparing the results with those obtained in General Relativity. As an application, we examine the gravitational potential of the Tolman-Oppenheimer-Volkoff (TOV) constant density solution.

Abstract Naked singularities (NkSs) are solutions to the Einstein field equations that violate the cosmic censorship conjecture. Recent studies indicate that these objects may serve as compelling mimickers of black hole (BH) shadows. In this work, we investigate the accretion dynamics of selected time-like NkSs using general relativistic magnetohydrodynamic simulations. Our objective is to determine whether NkSs exhibit distinct signatures compared to BHs. We find that, unlike BHs, NkSs exhibit a centrifugal barrier that prevents direct accretion of rotating matter onto the NkSs. Despite reduced magnetization in the funnel region, these objects are capable of generating jet powers comparable to those observed in BHs. Additionally, we observe that accreting matter releases gravitational energy as it is driven toward the NkSs, powering the strong outflow via local fluid pressure gradient or magnetic pressure forces.

Abstract In this work, we model static spherically symmetric compact stars within the framework of classical general relativity. In order to obtain exact solutions of the Einstein field equations with non-singular density profile we adopt the generalised Mak–Harko ansatz (Mak and Harko in Chin. J. Astron. Astrophys. 2:248, 2002) and demand that the complexity factor as defined by Herrera for static relativistic spheres (Herrera, Phys. Rev. D 97:044010, 2018) vanishes everywhere inside the self-gravitating object. Exact solutions of the Einstein field equations describing anisotropic fluid spheres are obtained via the gravitational decoupling method. We show that the decoupling constant, central and surface density values play a crucial role in dictating the stability of the stellar structure. The interplay between these factors accounts for mass–radius profiles associated with gravitational wave events such as GW190814 and further predicts stellar masses in the range 2.9 $$M_\odot $$ M ⊙ and 3.4 $$M_\odot $$ M ⊙ . Our models are excellent candidates for predicting compact objects such as neutron stars residing in the so-called mass gap associated with binary mergers without invoking exotic matter and modified gravity theories.

Abstract We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the Einstein equations, we use a n+1 splitting of the manifold and compute the evolution and constraint equations for the Einstein-Cartan system. In the process, we derive the Gauss-Codazzi-Ricci equations including torsion. We prove that the constraint equations are preserved during evolution. Imposing a generalized harmonic gauge, it is shown that the evolution equations can be cast as a quasilinear system in a Cauchy regular form with a characteristic determinant having a non-trivial multiplicity of characteristics. Using the Leray-Ohya theory for non-strictly hyperbolic systems we then establish the local geometric well-posedness of the Cauchy problem, for sufficiently regular initial data. For vanishing torsion we recover the classical results for the Einstein equations.

Abstract In this study, we investigate the electromagnetic field properties of a rotating charged black hole (BH) within the Kalb–Ramond gravity, as well as the circular motion and collisions of test charged particles in the spacetime of the BH. First, the static solutions of the Kalb–Ramond BH are derived using modified Einstein field equations and Maxwell’s equations to obtain the anisotropic solutions of the charged Kalb–Ramond BH. Then, using the Janis–Newman formalism, the exact solutions of the rotating Kalb–Ramond BH are obtained from the static metric. Subsequently, we investigate the horizon properties of the resulting rotating BH. It is shown that all the BH parameters charge and rotation, together with the Kalb–Ramond field, cause the horizon to extend, thereby providing additional gravitational mass. Then, we derive expressions for non-zero components of electromagnetic field configurations with respect to a zero angular momentum observer around the BHs. We also explore the circular motion of charged test particles, determining their effective potential and innermost stable circular orbits (ISCOs), which are influenced by the interplay of gravitational, rotational, and electromagnetic forces. Furthermore, we examine high-energy collisions of charged particles near the event horizon, computing the center-of-mass energy and demonstrating its enhancement by the Kalb–Ramond parameter and BH charge. Our results highlight the potential of charged rotating Kalb–Ramond BHs as natural particle accelerators, offering insights into extreme gravitational and electromagnetic phenomena with implications for astrophysics and theoretical physics.

In this paper, the uniqueness of steady Schwarzschild gradient Ricci solitons is studied. The role of the weight functions is analyzed. The generalized steady Schwarzschild gradient Ricci solitons are investigated; the implications of the rotational ansatz of Bryant are developed; and the new Generalized Schwarzschildsteady gradient solitons are defined. The aspects of the weight functions of the latter type of solitons are researched as well. The new most-accurate curvature bound of the steady Ricci gradient solitons is provided. The uniqueness of the Schwarzschild solitons is discussed. The Ricci flow is reconciled with the Einstein Field Equations such that the weight functions are utilized to spell out the determinant of the metric tensor, the procedure for which is commented on following the use of the appropriate geometrical objects. The mean curvature is discussed. The configurations of the observer are issued from the geodesics spheres of the solitonic structures.

We present a quantum response approach to momentum-space gravity in dissipative multiband systems, which dresses both the quantum geometry-through an interband Weyl transformation-and the equations of motion. In addition to clarifying the roles of the contorsion and symplectic terms, we introduce the three-state quantum geometric tensor as a necessary element in the geometric classification of nonlinear responses and discuss the significance of the emergent terms from a gravitational point of view. We also identify a dual quantum geometric drag force in momentum space that provides an entropic source term for the multiband matrix of Einstein field equations.

Abstract We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the future boundary of de Sitter. Hence our result allows a non-zero gravitational flux across the boundary of the de Sitter. We present an explicit gauge-free computation to show that the Gibbons-Hawking boundary term, counterterm in the action, and fall-off condition of gravitational field in conformal Einstein equation are crucial to reproduce the finite symplectic flux.

We study local properties of solutions to 3+1-dimensional Einstein equations which are close to a Schwarzschild metric. Roughly speaking, assume that [Formula: see text] is a local solution to [Formula: see text] in [Formula: see text] and close to a Schwarzschild metric, if its curvature tensor [Formula: see text] is close to a Type D tensor [Formula: see text], then we can find a Kerr metric [Formula: see text] satisfying the interior bound [Formula: see text]

Abstract Double Field Theory (DFT) has emerged as a comprehensive framework for gravity, presenting a testable and robust alternative to General Relativity (GR), rooted in the $$\textbf{O}(D,D)$$ O ( D , D ) symmetry principle of string theory. These lecture notes aim to provide an accessible introduction to DFT, structured in a manner similar to traditional GR courses. Key topics include doubled-yet-gauged coordinates, Riemannian versus non-Riemannian parametrisations of fundamental fields, covariant derivatives, curvatures, and the $$\textbf{O}(D,D)$$ O ( D , D ) -symmetric augmentation of the Einstein field equation, identified as the unified field equation for the closed string massless sector. By offering a novel perspective, DFT addresses unresolved questions in GR and enables the exploration of diverse physical phenomena, paving the way for significant future research.

Abstract On a manifold we term a hypersurface foliation a slicing if it is the level set foliation of a slice function—meaning some real valued function f satisfying that df is nowhere zero. On Riemannian manifolds we give a non-linear PDE on functions whose solutions are generic constant-mean-curvature (CMC) slice functions. Conversely, to any generic transversely-oriented constant-mean-curvature foliation the equation uniquely associates such a function. In one sense the equation is a scalar analogue of the Einstein equations. Given any slicing we show that, locally, one can conformally prescribe any smooth mean curvature function. We use this to show that, locally on a Riemannian manifold, a slicing is CMC for a conformally related metric. These results admit global versions assuming certain restrictions. Finally, given a conformally compact manifold we study the problem of normalising the defining function so that it is a CMC slice function for a compactifying metric. We show that two cases of this problem are formally solvable to all orders.

This work explores the shadow of a black hole within the framework of F(R)-ModMax gravity coupled with a cloud of strings. The Einstein field equations are solved for a nonlinear ModMax electromagnetic source in the context of F(R) gravity and a string cloud. From this solution, we obtain analytical expressions for the photon sphere and shadow radii. Our findings reveal that the interplay between nonlinear electrodynamics, F(R) gravity, and the string cloud significantly alters spacetime geometry, leading to distinct dynamical behaviors for test particles while also amplifying the shadow radius. These results underscore the critical role of cosmic strings effects and modified gravity parameters in shaping black hole shadows.

We investigate the gravitational field of a kinetic gas beyond its standard derivation from the second moment of the one-particle distribution function (1PDF), which typically serves as the energy-momentum tensor in the Einstein equations. This standard procedure raises an important question: why do the other moments of the 1PDF (which are needed to fully characterize the kinematical properties of the gas) not contribute to the gravitational field? Moreover, could these moments be relevant in addressing the dark energy problem? Using the canonical coupling of the full 1PDF to Finsler spacetime geometry via the Finsler gravity equation, we show that in general all moments contribute non-trivially. We derive the Finsler gravity equation in homogeneous and isotropic symmetry in conformal time — dubbed the Finsler-Friedmann equation — which determines both the scale factor and the causal structure dynamically. Remarkably, this equation naturally admits a vacuum solution describing an exponentially expanding spacetime, without requiring a cosmological constant or any additional quantities. The resulting causal structure is a mild deformation of the one of Friedmann-Lemaître-Robertson-Walker (FLRW) geometry; close to the rest frame defined by cosmological time (i.e. for slowly moving objects), the causal structures of the two geometries are nearly indistinguishable.