Wormhole solutions with NUT charge in higher curvature theories

We present wormholes with a Newman–Unti–Tamburino (NUT) charge that arise in certain higher curvature theories, where a scalar field is coupled to a higher curvature invariant. For the invariants we employ (i) a Gauss–Bonnet term and (ii) a Chern–Simons term, which then act as source terms for the scalar field. We map out the domain of existence of wormhole solutions by varying the coupling parameter and the scalar charge for a set of fixed values of the NUT charge. The domain of existence for a given NUT charge is then delimited by the set of scalarized nutty black holes, a set of wormhole solutions with a degenerate throat and a set of singular solutions.

Scalarized Einstein–Maxwell-scalar black holes in a cavity

In this paper, we study the spontaneous scalarization of Reissner–Nordström (RN) black holes enclosed by a cavity in an Einstein–Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions are always thermodynamically preferred over RN black holes in a cavity. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge Q.

Scalarized Einstein–Maxwell-scalar black holes in anti-de Sitter spacetime

In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in an Einstein–Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner–Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a micro-canonical ensemble, scalarized solutions are always thermodynamically preferred over RNAdS black holes. However, the system has much richer phase structure and phase transitions in a canonical ensemble. In particular, we report a RNAdS BH/scalarized BH/RNAdS BH reentrant phase transition, which is composed of a zeroth-order phase transition and a second-order one.

Semilocal Convergence of the Extension of Chun’s Method

In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Fréchet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results.

Criminology: Some lines of flight

The 40th Anniversary Edition of Taylor, Walton and Young’s New Criminology, published in 2013, opened with these words: ‘The New Criminology was written at a particular time and place, it was a product of 1968 and its aftermath; a world turned upside down’. We are at a similar moment today. Several developments have been, and are turning, our 21st century world upside down. Among the most profound has been the emergence of a new earth, that the ‘Anthropocene’ references, and ‘cyberspace’, a term first used in the 1960s, which James Lovelock has recently termed a ‘Novacene’, a world that includes both human and artificial intelligences. We live today on an earth that is proving to be very different to the Holocene earth, our home for the past 12,000 years. To appreciate the Novacene one need only think of our ‘smart’ phones. This world constitutes a novel domain of existence that Castells has conceived of as a terrain of ‘material arrangements that allow for simultaneity of social practices without territorial contiguity’ – a world of sprawling material infrastructures, that has enabled a ‘space of flows’, through which massive amounts of information travel. Like the Anthropocene, the Novacene has brought with it novel ‘harmscapes’, for example, attacks on energy systems. In this paper, we consider how criminology has responded to these harmscapes brought on by these new worlds. We identify ‘lines of flight’ that are emerging, as these challenges are being met by criminological thinkers who are developing the conceptual trajectories that are shaping 21st century criminologies.

The domain of existence of solitary waves in fluid-filled thin elastic tubes

Under given prestress conditions, solitary waves in fluid-filled elastic tubes are confined to a rather narrow set of combinations of the background fluid velocity and the wave speed. This set, which we call the domain of existence, is bounded by several curves that represent various physical and mathematical restrictions. Remarkably, these restrictions can be cast as purely algebraic conditions to be imposed upon the governing system of differential equations. Paramount among the physical restrictions are the avoidance of wrinkles and the self-impenetrability of the wave profile. In particular, the existence of a critical wave speed of impending wrinkling, independent of the background fluid velocity, is established rigorously.

Scalarized Nutty Wormholes

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes is reached in the limit of vanishing NUT charge. In the Chern-Simons case, however, the limit is peculiar, since with vanishing NUT charge the coupling constant diverges. We focus on scalarized nutty wormholes with a single throat and study their properties. All these scalarized nutty wormholes feature a critical polar angle, beyond which closed timelike curves are present.

Critical Solutions of Scalarized Black Holes

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.

Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.

Stability with respect to coefficients of solution of difference schemes approximating initial boundary-value problems for semi-linear hyperbolic equations

The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.