Planckian physics comes into play at Planckian distance from horizon

In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow exponentially with time and become of order 1 when the collapsing matter is about a Planck length outside the horizon. As a result, the effective theory breaks down at the scrambling time, invalidating its prediction of Hawking radiation. Planckian physics comes into play to decide the fate of black-hole evaporation.

A quantum bound on the compactness

We present a simple quantum description of the gravitational collapse of a ball of dust which excludes those states whose width is arbitrarily smaller than the gravitational radius of the matter source and supports the conclusion that black holes are macroscopic extended objects. We also comment briefly on the relevance of this result for the ultraviolet self-completion of gravity and the connection with the corpuscular picture of black holes.

Complexity of scalar collapse in anti-de Sitter spacetime

We calculate the volume and action forms of holographic complexity for the gravitational collapse of scalar field matter in asymptotically anti-de Sitter spacetime, using numerical methods to reproduce the geometry responding to the oscillating field over multiple crossing times. Like the scalar field pulse, the volume complexity oscillates quasiperiodically before horizon formation. It also shows a scaling symmetry with the amplitude of the scalar field. The action complexity is also quasiperiodic with spikes of increasing amplitude.

Gravitational collapse of compact stars in f(R) = ξR4 gravity

In this paper, model of gravitational collapse of anisotropic compact stars in a new theory of [Formula: see text] gravity has been developed. The author considers the modified gravity model of [Formula: see text] to investigate a physically acceptable model of gravitational collapse of anisotropic compact stars. First, the author presents a brief review of the development of field equations of gravitational collapse in [Formula: see text] gravity for a particular interior metric for compact stars. Then analytical solutions for various physical quantities of collapsing anisotropic compact stars in [Formula: see text] gravity have been developed. By analyzing plots of various physical parameters and conditions, it is shown that the model is physically acceptable for describing the gravitational collapse of anisotropic compact stars in [Formula: see text] gravity.

The growth of structure

The growth of structure by gravitational collapse from initially small perturbations is described. The Jeans instability is calculated. The structure equations are obtained and solved in various cases (radiation-dominated, matter-dominated and others) via a linearized treatment. Hence the main features of the growth of density perturbations are obtained. The observed spectrum in the present is used to infer the primordial spectrum. The scale-invariant (Harrison-Zol’dovich) spectrum is described. The process of baryon acoustic oscillations is outlined and the sound horizon is defined. The chapter concludes with brief notes on galaxy formatiom.

Black holes

We discuss event horizons and black holes. First Birkhoff’s theorem is derived, and we consider the general nature of spherically symmetric spaces. Then the concepts of null surface, Killing horizon and event horizon are defined and related to one another. Cosmic censorship is briefly discussed. The Schwarzshild horizon is discussed in detail. The divergence or otherwise of redshift, acceleration, speed and proper time is obtained for infalling observers and for Schwarzschild observers. Eddington-Finkelstein coordinates are introduced and used to discuss gravitational collapse. The growth of the horizon is noted, and the causality structure is briefly considered via an introduction to the conformal (Penrose-Carter) diagram. The maximal extension is then presented, with the Kruskal-Szekeres coordinates and associated diagram. Wormholes are briefly discussed. The chapter finishes with a survey of astronomical evidence for black holes.

Palatini approach and large-scale magnetogenesis

Large-scale magnetogenesis is analyzed within the Palatini approach when the gravitational action is supplemented by a contribution that is nonlinear in the Einstein-Hilbert term. While the addition of the nonlinear terms does not affect the scalar modes of the geometry during the inflationary phase, the tensor-to-scalar ratio is nonetheless suppressed. In this context it is plausible to have a stiff phase following the standard inflationary stage provided the potential has a quintessential form. The large-scale magnetic fields can even be a fraction of the nG over typical length scales of the order of the Mpc prior to the gravitational collapse of the protogalaxy.