Weyl type N solutions with null electromagnetic fields in the Einstein–Maxwell <Emphasis Type="Italic">p</Emphasis>-form theory

We consider d-dimensional solutions to the electrovacuum Einstein–Maxwell equations with the Weyl tensor of type N and a null Maxwell \((p+1)\)-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the corresponding spacetime and the electromagnetic field share the same aligned null direction (AND). Moreover, this AND is geodetic, shear-free, non-expanding and non-twisting and hence Einstein–Maxwell equations imply that Weyl type N spacetimes with a null Maxwell \((p+1)\)-form field belong to the Kundt class. Moreover, these Kundt spacetimes are necessarily \({ CSI}\) and the \((p+1)\)-form is \({ VSI}\). Finally, a general coordinate form of solutions and a reduction of the field equations are discussed.     

$$$$-Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

In \((2+1)\)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter \(k=1\) and \(k\ne 1\)), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with \(k\ne 1\), we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.     

Covariant holographic entanglement negativity

We propose a covariant holographic conjecture for the entanglement negativity of bipartite mixed states in \((1+1)\)-dimensional conformal field theories dual to bulk non static \(AdS_{3}\) configurations. Application of our conjecture to \((1+1)\)-dimensional conformal field theories dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduce the corresponding entanglement negativity obtained through the replica technique, in the large central charge limit. We briefly discuss the issue of the generalization of our conjecture to higher dimensions.     

All static and electrically charged solutions with Einstein base manifold in the arbitrary-dimensional Einstein–Maxwell system with a massless scalar field

We present a simple and complete classification of static solutions in the Einstein–Maxwell system with a massless scalar field in arbitrary \(n(\ge 3)\) dimensions. We consider spacetimes which correspond to a warped product \(M^2 \times K^{n-2}\), where \(K^{n-2}\) is a \((n-2)\)-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant real scalar field consists of nine solutions for \(n\ge 4\) and three solutions for \(n=3\). A complete geometric analysis of the solutions is presented and the global mass and electric charge are determined for asymptotically flat configurations. There are two remarkable features for the solutions with \(n\ge 4\): (i) Unlike the case with a vanishing electromagnetic field or constant scalar field, asymptotically flat solution is not unique, and (ii) The solutions can asymptotically approach the Bertotti–Robinson spacetime depending on the integrations constants. In accordance with the no-hair theorem, none of the solutions are endowed of a Killing horizon.     

Black holes in the generalized Proca theory

We investigate static and spherically symmetric black hole solutions in the generalized Proca theory which corresponds to the generalization of the shift-symmetric scalar–tensor Horndeski theory to the vector–tensor theory. Any solution obtained in this paper possesses a constant spacetime norm of the vector field, \(X:=-\frac{1}{2}g^{\mu \nu }A_\mu A_\nu =X_0=\mathrm{constant}\). The solutions in the theory with generalized quartic coupling \(G_4(X)\) generalize the stealth Schwarzschild and the Schwarzschild- (anti-) de Sitter solutions obtained in the theory with the nonminimal coupling to the Einstein tensor \(G^{\mu \nu } A_\mu A_\nu \). While in the vector–tensor theory with the coupling \(G^{\mu \nu }A_\mu A_\nu \) the electric charge does not explicitly affect the spacetime geometry, in more general cases with nonzero \(G_{4XX}(X_0)\ne 0\) this property does not hold in general. The solutions in the theory with generalized cubic coupling \(G_3(X)\) are given by the Schwarzschild- (anti-) de Sitter spacetime, where the dependence on \(G_3(X)\) does not appear in the metric function.     

Light deflection and Gauss–Bonnet theorem: definition of total deflection angle and its applications

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild–de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle \(\alpha \) of the light ray by constructing a quadrilateral \(\varSigma ^4\) on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) determined by the optical metric \(\bar{g}_{ij}\). On the basis of the definition of the total deflection angle \(\alpha \) and the Gauss–Bonnet theorem, we derive two formulas to calculate the total deflection angle \(\alpha \); (1) the angular formula that uses four angles determined on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) or the curved \((r, \phi )\) subspace \({\mathscr {M}}^\mathrm{sub}\) being a slice of constant time t and (2) the integral formula on the optical reference geometry \({\mathscr {M}}^\mathrm{opt}\) which is the areal integral of the Gaussian curvature K in the area of a quadrilateral \(\varSigma ^4\) and the line integral of the geodesic curvature \(\kappa _g\) along the curve \(C_{\varGamma }\). As the curve \(C_{\varGamma }\), we introduce the unperturbed reference line that is the null geodesic \(\varGamma \) on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting \(\varGamma \) vertically onto the curved \((r, \phi )\) subspace \({\mathscr {M}}^\mathrm{sub}\). We demonstrate that the two formulas give the same total deflection angle \(\alpha \) for the Schwarzschild and the Schwarzschild–de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein–Shapiro’s formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild–de Sitter case, there appear order \({\mathscr {O}}(\varLambda m)\) terms in addition to the Schwarzschild-like part, while order \({\mathscr {O}}(\varLambda )\) terms disappear.     

Implementation of three reliable methods for finding the exact solutions of (2 + 1) dimensional generalized fractional evolution equations

In this study, we have implemented the three methods namely extended \((G^{\prime}/G)\)-expansion, extended \((1/G^{\prime})\)-expansion and \((G^{\prime}/G,\,\,1/G)\)-expansion methods to determine exact solutions for the (2 + 1) dimensional generalized time–space fractional differential equations. We use Conformable fractional derivative and its properties in this research to convert fractional differential equations to ordinary differential equations with integer order. By using above mentioned methods, three types of traveling wave solutions are successfully obtained which have been expressed by the hyperbolic, trigonometric, and rational function solutions. The considered methods and transformation techniques are efficient and consistent for solving nonlinear time and space-fractional differential equations.     

General relativistic effects in the structure of massive white dwarfs

In this work we investigate the structure of white dwarfs using the Tolman–Oppenheimer–Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of general relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs (\(M>1.3M_{\odot }\)) are overestimated in comparison with GR outcomes. For a mass of \(1.415M_{\odot }\) the white dwarf radius predicted by GR is about 33% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65%. We depict the general relativistic mass–radius diagrams as \(M/M_{\odot }=R/(a+bR+cR^2+dR^3+kR^4)\), where a, b, c and d are parameters obtained from a fitting procedure of the numerical results and \(k=(2.08\times 10^{-6}R_{\odot })^{-1}\), being \(R_{\odot }\) the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.     

Curved Space-Times by Crystallization of Liquid Fiber Bundles

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifolds. The fields are pairs of \(((\alpha ,\omega ),\varpi )\), where \((\alpha ,\omega )\) is a 1-form with coefficients in the Lie algebra of the Poincaré group and \(\varpi \) is an 8-form with coefficients in the dual of this Lie algebra. The dynamical equations derive from a simple variational principle and imply that the 10-dimensional manifold looks locally like the total space of a fiber bundle over a 4-dimensional base manifold. Moreover this base manifold inherits a metric and a connection which are solutions of a system of Einstein–Cartan equations.     

On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson–Walker spacetime

A characterization of the foliation by spacelike slices of an \((n+1)\)-dimensional spatially closed Generalized Robertson–Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some natural assumptions, of physical or geometric nature, all the entire solutions of such an equation are obtained. In particular, the case of entire spacelike graphs in de Sitter spacetime is faced and completely solved by means of a new application of a known integral formula.     

A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy

We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions \(M(0)>0\) and \(s^{2}<\frac{1}{3}c^{2}\), which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729–755, 2006).     

Buchdahl–Vaidya–Tikekar model for stellar interior in pure Lovelock gravity

In the paper (Khugaev et al. in Phys Rev D94:064065. arXiv: 1603.07118, 2016), we have shown that for perfect fluid spheres the pressure isotropy equation for Buchdahl–Vaidya–Tikekar metric ansatz continues to have the same Gauss form in higher dimensions, and hence higher dimensional solutions could be obtained by redefining the space geometry characterizing Vaidya–Tikekar parameter K. In this paper we extend this analysis to pure Lovelock gravity; i.e. a \((2N+2)\)-dimensional solution with a given \(K_{2N+2}\) can be taken over to higher n-dimensional pure Lovelock solution with \(K_n=(K_{2N+2}-n+2N+2)/(n-2N-1)\) where N is degree of Lovelock action. This ansatz includes the uniform density Schwarzshild and the Finch–Skea models, and it is interesting that the two define the two ends of compactness, the former being the densest and while the latter rarest. All other models with this ansatz lie in between these two limiting distributions.     

Compound Poisson Law for Hitting Times to Periodic Orbits in Two-Dimensional Hyperbolic Systems

We show that a compound Poisson distribution holds for scaled exceedances of observables \(\phi \) uniquely maximized at a periodic point \(\zeta \) in a variety of two-dimensional hyperbolic dynamical systems with singularities \((M,T,\mu )\), including the billiard maps of Sinai dispersing billiards in both the finite and infinite horizon case. The observable we consider is of form \(\phi (z)=-\ln d(z,\zeta )\) where d is a metric defined in terms of the stable and unstable foliation. The compound Poisson process we obtain is a Pólya-Aeppli distibution of index \(\theta \). We calculate \(\theta \) in terms of the derivative of the map T. Furthermore if we define \(M_n=\max \{\phi ,\ldots ,\phi \circ T^n\}\) and \(u_n (\tau )\) by \(\lim _{n\rightarrow \infty } n\mu (\phi >u_n (\tau ) )=\tau \) the maximal process satisfies an extreme value law of form \(\mu (M_n \le u_n)=e^{-\theta \tau }\). These results generalize to a broader class of functions maximized at \(\zeta \), though the formulas regarding the parameters in the distribution need to be modified.     

Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model

We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \(\overline{\hbox {v}}\) of the walk. Namely, there exists some critical value \(\lambda _{\hbox {c}}>0\) such that \(\overline{\hbox {v}}>0\) if \(\lambda \in (0,\lambda _{\hbox {c}})\) and \(\overline{\hbox {v}}=0\) if \(\lambda \ge \lambda _{\hbox {c}}\). We show that the speed \(\overline{\hbox {v}}\) is continuous in \(\lambda \) on \((0,\infty )\) and differentiable on \((0,\lambda _{\hbox {c}}/2)\). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \(\overline{\hbox {v}}\) on \((0,\lambda _{\hbox {c}}/2)\), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for \(\lambda \ge \lambda _{\hbox {c}}/2\).     

Scale-dependent three-dimensional charged black holes in linear and non-linear electrodynamics

In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein–Maxwell as well as in Einstein–power-Maxwell theories in \((2+1)\)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the null energy condition. Certain properties, such as horizon structure and thermodynamics, are discussed in detail.     

Dispersive bright,dark and singular optical soliton solutions in conformable fractional optical fiber Schrödinger models and its applications

In this paper, we study three different space-time fractional models of the Schrödinger equation. By using the properties of conformable derivative and fractional complex transform, the bright, dark and singular optical solitons for conformable space–time fractional nonlinear \((1+1)\)-dimensional Schrödinger models are determined.     

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

Comparison of the DeWitt metric in general relativity with the fourth-rank constitutive tensors in electrodynamics and in elasticity theory

We perform a short comparison between the local and linear constitutive tensor \(\chi ^{\lambda \nu \sigma \kappa }\) in four-dimensional electrodynamics, the elasticity tensor \(c^{ijkl}\) in three-dimensional elasticity theory, and the DeWitt metric \(G^{abcd}\) in general relativity, with \({a,b,\ldots =1,2,3}\). We find that the DeWitt metric has only six independent components.     

Antihydrogen formation via antiproton scattering on positronium between the $e^{-} +\bar {H}(n = 2)$ and e−+H̄(n=3)$e^{-}+\bar {H}(n = 3)$ thresholds

The charge exchange reaction \(\bar {\mathrm {p}} + \text {Ps} \rightarrow \mathrm {e}^{-} + \bar {\mathrm {H}} \), of interest for the future experiments (GBAR, AEGIS, ATRAP, ...) aiming to produce antihydrogen atoms, is investigated in the energy range between the \(\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 2)\) and \(\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 3)\) thresholds. An ab-initio method based on the solution of the Faddeev-Merkuriev equations is used. Special focus is put on the impact of the Feshbach resonances and the Gailitis-Damburg oscillations, appearing in the vicinity of the \(\bar {\mathrm {p}} +\text {Ps}(n = 2)\) threshold, on the \(\bar {\mathrm {H}}\) production cross section.