Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

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Black Holes in Higher Dimensions

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.

/pdf/isolated-and-dynamical-horizons-and-their-applications-2ojdjee2p1.pdf

Isolated and dynamical horizons and their applications

The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM model, and a number of late time, model-independent determinations of $H_0$ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.[Abridged]

https://iopscience.iop.org/article/10.1088/1361-6382/ac086d/pdf

In the realm of the Hubble tension - a review of solutions

The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. S. 211-215

The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a specific subclass of discrete cosmologies, Black-Hole Lattice models. In particular, we illustrate the techniques used for the construction of these spacetimes, and examine their resulting physical properties. This includes their large-scale dynamics, the dressing of mass due to the interaction between individual black holes, along with features of direct observational interest such as the distance-to-redshift relation. This collection of results provides a novel perspective on the physical effects of averaging in General Relativity, as well as on the emergence of gravitational structures from solutions with isolated objects.

Black-Hole Lattices as Cosmological Models

https://pure.mpg.de/pubman/item/item_153886_3/component/file_2387747/.jtbi.2008.05.011.pdf

Short term synaptic depression model--analytical solution and analysis.

We present a numerical method for solving Weyl's embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on a construction introduced by Weingarten and was used in Nirenberg's proof of Weyl's conjecture. The target embedding results as the endpoint of an embedding flow in R^3 beginning at the unit sphere's embedding. We employ spectral methods to handle functions on the surface and to solve various (non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.

Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

Astronomical observations reveal hierarchical structures in the universe, from galaxies, groups of galaxies, clusters and superclusters, to filaments and voids. On the largest scales, it seems that some kind of statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous and isotropic solutions of the Einstein equations, and the evolution of the universe is approximated by the Friedmann equations. In parallel to standard homogeneous cosmology, the field of inhomogeneous cosmology and backreaction is being developed. This field investigates whether small scale inhomogeneities via nonlinear effects can backreact and alter the properties of the universe on its largest scales, leading to a non-Friedmannian evolution. This paper presents the current status of inhomogeneous cosmology and backreaction. It also discusses future prospects of the field of inhomogeneous cosmology, which is based on a survey of 50 academics working in the field of inhomogeneous cosmology.

Inhomogeneous cosmology and backreaction: Current status and future prospects

We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver developed for this purpose. We then apply the standard tools of numerical relativity to calculate the time development of this initial dataset and derive quantities of cosmological relevance, such as the scaling of proper lengths. Similarly to the case of S3 lattices, we find that the length scaling remains close to the analytical solution for Friedmann-Lemaitre-Robertson-Walker cosmologies throughout our simulations, which span a window of about one order of magnitude in the growth of the scale factor. We highlight, however, a number of important departures from the Friedmann-Lemaitre-Robertson-Walker class.

Mikołaj Korzyński

Papers

Black-Hole Lattices as Cosmological Models

Short term synaptic depression model--analytical solution and analysis.

Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

Inhomogeneous cosmology and backreaction: Current status and future prospects

Evolution of a family of expanding cubic black-hole lattices in numerical relativity