Real Valued Functions for the BFKL Eigenvalue

We consider known expressions for the eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation in N=4 super Yang-Mills theory as a real valued function of two variables. We define new real valued functions of two complex conjugate variables that have a definite complexity analogous to the weight of the nested harmonic sums. We argue that those functions span a general space of functions for the BFKL eigenvalue at any order of the perturbation theory.

Axially symmetric Petrov type II general space–time and closed timelike curves

We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

Toward error estimates for general space-time discretizations of the advection equation

We develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these new estimates. Our analysis also shows the existence of synergistic space-time discretization methods that permit to gain one order of accuracy at a given CFL number. Our new error estimates can be used to analyze the choice of space-time discretizations considered when testing Parallel-in-Time methods.

Continued Gravitational Collapse for Newtonian Stars

The classical model of an isolated selfgravitating gaseous star is given by the Euler–Poisson system with a polytropic pressure law $$P(\rho )=\rho ^\gamma $$ P ( ρ ) = ρ γ , $$\gamma >1$$ γ > 1 . For any $$1<\gamma <\frac{4}{3}$$ 1 < γ < 4 3 , we construct an infinite-dimensional family of collapsing solutions to the Euler–Poisson system whose density is in general space inhomogeneous and undergoes gravitational blowup along a prescribed space-time surface, with continuous mass absorption at the origin. The leading order singular behavior is described by an explicit collapsing solution of the pressureless Euler–Poisson system.

Observations in statistically homogeneous, locally inhomogeneous cosmological toy models without FLRW backgrounds

ABSTRACT We study observations in toy models that constitute exact cosmological solutions to the Einstein equation. These models are statistically homogeneous but locally inhomogeneous, without an a priori introduced Friedmann–Lemaître–Roberston–Walker (FLRW) background and with ‘structures’ evolving fairly slowly. The mean redshift–distance relation and redshift drift along 500 light rays in each of two models are compared with relations based on spatial averages. The relations based on spatial averages give a good reproduction of the mean redshift–distance relation, although most convincingly in the model where the kinematical backreaction and average spatial curvature cancel each other to a subpercentage precision. In both models, the mean redshift drift clearly differs from the drift of the mean redshift. This indicates that redshift drift could be an important tool for testing the backreaction conjecture as redshift drift appears to distinguish between local and global effects. The method presented for computing the redshift drift is straightforward to generalize and can thus be utilized to fairly easily compute this quantity in a general space–time.

The Symbolic Value of Ethnic Spaces

In four experiments, students read that their university was creating either an ethnic space (a space geared to people of particular ethnic groups) or a general space for students. In an internal meta-analysis, underrepresented students of color ( N = 205), but not White students ( N = 760), who read about the ethnic space reported greater belonging, value of underrepresented students by the university, support, and academic engagement compared to those who read about a general space. Ethnic spaces may hold broader psychological significance than that of mere gathering places, improving outcomes even for those who do not frequently use them. Creating ethnic spaces may be one strategy for making university environments more welcoming for underrepresented students of color.