Related papers: Quantum Singularities
General relativity predicts its own demise at singularities, but also appears to conveniently shield itself from the catastrophic consequences of such singularities, making them safe. For instance, if strong cosmic censorship were…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…
The focusing theorem fails for evaporating black holes because the null energy condition is violated by quantum effects. The quantum focusing conjecture is proposed so that it is satisfied even if the null energy condition is violated. The…
We consider the radial Schroedinger equation with an attractive potential singular in the origin. The additional continuum of states caused by the singularity, that usually remain nontreatable, are shown to correspond to particles,…
We propose a universal inequality that unifies the Bousso bound with the classical focussing theorem. Given a surface $\sigma$ that need not lie on a horizon, we define a finite generalized entropy $S_\text{gen}$ as the area of $\sigma$ in…
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by…
Classical critical collapse yields naked singularities from smooth initial data, challenging cosmic censorship, and shaping the spectrum of primordial black holes. We show that one-loop vacuum polarization near the threshold qualitatively…
General Relativity predicts that the spacetime near a cosmological singularity undergoes an infinite number of chaotic oscillations between different Kasner epochs with rapid transitions between them. This so-called BKL behaviour persists…
Some long standing issues concerning the quantum nature of the big bang are resolved in the context of homogeneous isotropic models with a scalar field. Specifically, the known results on the resolution of the big bang singularity in loop…
We review recent work on the existence and nature of cosmological singularities that can be formed during the evolution of generic as well as specific cosmological spacetimes in general relativity. We first discuss necessary and sufficient…
We conjecture that space-like singularities are simply regions in which all available degrees of freedom are excited, and the system cycles randomly through generic quantum states in its Hilbert space. There is no simple geometric…
Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of…
By applying Rosen's quantization approach to the historical Oppenheimer and Snyder gravitational collapse and by setting the constraints for the formation of the Schwarzschild black hole (SBH), in a previous paper [1] two of the Authors (CC…
Quantum effects are expected to modify the cosmological dynamics of the early universe while maintaining some (potentially discrete) notion of space-time structure. In one approach, loop quantum cosmology, current models are shown here to…
Spherically symmetric space-times provide many examples for interesting black hole solutions, which classically are all singular. Following a general program, space-like singularities in spherically symmetric quantum geometry, as well as…
There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star,…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
We examine the conjecture for the complete monotonicity of certain curvature invariants for quantum black holes. In this note, we study a class of quantum regular black holes that are static, spherically symmetric, and characterized only by…
The tunneling approach for entropy generation in quantum gravity is applied to black holes. The area entropy is recovered and shown to count only a tiny fraction of the black hole degeneracy. The latter stems from the extension of the wave…