Numerical investigation of black hole interiors

Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole's (quasi-local) mass function along the inner horizon. The region near the inner horizon is described to great accuracy by a plane wave spacetime. While Einstein's equations for this metric are still too complicated to be solved in closed form it is relatively simple to integrate them numerically. We find for generic regular initial data the predicted mass inflation type null singularity, rather than a spacelike singularity. It thus seems that mass inflation indeed represents a generic self-consistent picture of the black hole interior.Comment: 6 pages LaTeX, 3 eps figure

Cosmic Censorship: As Strong As Ever

Spacetimes which have been considered counter-examples to strong cosmic censorship are revisited. We demonstrate the classical instability of the Cauchy horizon inside charged black holes embedded in de Sitter spacetime for all values of the physical parameters. The relevant modes which maintain the instability, in the regime which was previously considered stable, originate as outgoing modes near to the black hole event horizon. This same mechanism is also relevant for the instability of Cauchy horizons in other proposed counter-examples of strong cosmic censorship.Comment: 4 pages RevTeX style, 1 figure included using epsfi

The late-time singularity inside non-spherical black holes

It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geometry of black holes indicate a more complicated structure is typical. While it seems likely that an observer falling into a black hole with the collapsing star encounters a crushing spacelike singularity, an observer falling in at late times generally reaches a null singularity which is vastly different in character to the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity. In the spirit of the classic work of BKL we present an asymptotic analysis of the null singularity inside a realistic black hole. Motivated by current understanding of spherical models, we argue that the Einstein equations reduce to a simple form in the neighborhood of the null singularity. The main results arising from this approach are demonstrated using an almost plane symmetric model. The analysis shows that the null singularity results from the blueshift of the late-time gravitational wave tail; the amplitude of these gravitational waves is taken to decay as an inverse power of advanced time as suggested by perturbation theory. The divergence of the Weyl curvature at the null singularity is dominated by the propagating modes of the gravitational field. The null singularity is weak in the sense that tidal distortion remains bounded along timelike geodesics crossing the Cauchy horizon. These results are in agreement with previous analyses of black hole interiors. We briefly discuss some outstanding problems which must be resolved before the picture of the generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi

Homothetic Wyman Spacetimes

The time-dependent, spherically symmetric, Wyman sector of the Unified Field Theory is shown to be equivalent to a self-gravitating scalar field with a positive-definite, repulsive self-interaction potential. A homothetic symmetry is imposed on the fundamental tensor, and the resulting autonomous system is numerically integrated. Near the critical point (between the collapsing and non-collapsing spacetimes) the system displays an approximately periodic alternation between collapsing and dispersive epochs.Comment: 15 pages with 6 figures; requires amsart, amssymb, amsmath, graphicx; formatted for publication in Int. J. Mod. Phys.

LISA data analysis: The monochromatic binary detection and initial guess problems

We consider the detection and initial guess problems for the LISA gravitational wave detector. The detection problem is the problem of how to determine if there is a signal present in instrumental data and how to identify it. Because of the Doppler and plane-precession spreading of the spectral power of the LISA signal, the usual power spectrum approach to detection will have difficulty identifying sources. A better method must be found. The initial guess problem involves how to generate {\it a priori} values for the parameters of a parameter-estimation problem that are close enough to the final values for a linear least-squares estimator to converge to the correct result. A useful approach to simultaneously solving the detection and initial guess problems for LISA is to divide the sky into many pixels and to demodulate the Doppler spreading for each set of pixel coordinates. The demodulated power spectra may then be searched for spectral features. We demonstrate that the procedure works well as a first step in the search for gravitational waves from monochromatic binaries.Comment: 8 pages, 8 figure

Spacetime structure of static solutions in Gauss-Bonnet gravity: neutral case

We study the spacetime structures of the static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-$\Lambda$ system systematically. We assume the Gauss-Bonnet coefficient $\alpha$ is non-negative. The solutions have the $(n-2)$-dimensional Euclidean sub-manifold, which is the Einstein manifold with the curvature $k=1,~0$ and -1. We also assume $4{\tilde \alpha}/\ell^2\leq 1$, where $\ell$ is the curvature radius, in order for the sourceless solution (M=0) to be defined. The general solutions are classified into plus and minus branches. The structures of the center, horizons, infinity and the singular point depend on the parameters $\alpha$, $\ell^2$, $k$, $M$ and branches complicatedly so that a variety of global structures for the solutions are found. In the plus branch, all the solutions have the same asymptotic structure at infinity as that in general relativity with a negative cosmological constant. For the negative mass parameter, a new type of singularity called the branch singularity appears at non-zero finite radius $r=r_b>0$. The divergent behavior around the singularity in Gauss-Bonnet gravity is milder than that around the central singularity in general relativity. In the $k=1,~0$ cases the plus-branch solutions do not have any horizon. In the $k=-1$ case, the radius of the horizon is restricted as $r_h\sqrt{2\tilde{\alpha}}$) in the plus (minus) branch. There is also the extreme black hole solution with positive mass in spite of the lack of electromagnetic charge. We briefly discuss the effect of the Gauss-Bonnet corrections on black hole formation in a collider and the possibility of the violation of third law of the black hole thermodynamics.Comment: 19 pages, 11 figure

Billions in Misspent EU Agricultural Subsidies Could Support the Sustainable Development Goals

The Common Agricultural Policy (CAP) is the guiding policy for agriculture and the largest single budget item in the European Union (EU). Agriculture is essential to meet the Sustainable Development Goals (SDGs), but the CAP's contribution to do so is uncertain. We analyzed the distribution of (sic)59.4 billion of 2015 CAP payments and show that current CAP spending exacerbates income inequality within agriculture, while little funding supports climate-friendly and biodiverse farming regions. More than (sic)24 billion of 2015 CAP direct payments went to regions where average farm incomes are already above the EU median income. A further (sic)2.5 billion in rural development payments went to primarily urban areas. Effective monitoring indicators are also missing. We recommend redirecting and better monitoring CAP payments toward achieving the environmental, sustainability, and rural development goals stated in the CAP's new objectives, which would support the SDGs, the European Green Deal, and green COVID-19 recovery

'Are we losing touch?' Mainstream parties' failure to represent their voters on immigration and its electoral consequences

In many advanced democracies, mainstream political parties have been disrupted either by the rise of new (populist) parties or by hostile takeovers. In this article we argue that immigration attitudes have had a powerful impact on the strategic environment of political parties and leaders. We show, based on evidence from a comparative study conducted by YouGov in spring of 2015, that immigration attitudes had, by that time, driven a wedge between mainstream parties - those that regularly play a role in government - and their partisans. This ‘immigration gap' opened up enormous space for new political movements to form, either inside existing parties or outside. Furthermore, we show that the representation gap on immigration issues is a relevant predictor of vote choice, so that parties are particularly likely to lose votes when they are more distant from their supporters on immigration