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Cosmic censorship is known to fail in some well-controlled phenomena, calling into question the predictive power of General Relativity and opening up the possibility of observing Planck-scale physics. We propose that the cosmic censorship conjecture can be amended so that its spirit prevails. Naked singularities that, classically, have zero mass are allowed. Physically, these are Planck-sized "black holes", which evaporate in a few Planck times. General Relativity fails only for a tiny interval in time, to then quickly regain control in a Miltonian evolution that returns us to the predictive paradise of Einstein's equations. If this refinement of the conjecture is correct, then, even though Nature does allow to expose breakdowns in the smooth fabric of spacetime, it limits them to a mostly harmless minimum. [ABSTRACT FROM AUTHOR]

In this paper, we present a model for the late-time evolution of the universe where a dark energy-dark matter interaction is invoked. Dark energy is modeled through an holographic Ricci dark energy component. The model is embedded within an induced gravity braneworld model. For suitable choices of the interaction coupling, the big rip and little rip induced by the holographic Ricci dark energy, in a relativistic model and in an induced gravity braneworld model, are removed. In this scenario, the holographic dark energy will have a phantom like behavior even though the brane is asymptotically de Sitter. [ABSTRACT FROM AUTHOR]

We report on recent developments toward a relativistic quantum-mechanical theory of motion for a fixed, finite number of electrons, photons and their anti-particles, as well as its possible generalizations to other particles and interactions. [ABSTRACT FROM AUTHOR]

We derive set of solutions with flat transverse sections in the framework of a teleparallel equivalent of general relativity which describes rotating black holes. The singularities supported from the invariants of torsion and curvature are explained. We investigate that there appear more singularities in the torsion scalars than in the curvature ones. The conserved quantities are discussed using Einstein-Cartan geometry. The physics of the constants of integration is explained through the calculations of conserved quantities. These calculations show that there is a unique solution that may describe true physical black hole. [ABSTRACT FROM AUTHOR]

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe. [ABSTRACT FROM AUTHOR]

In this paper, we review some general aspects of modified gravity theories, investigating mathematical and physical properties and, more specifically, the feature of viable and realistic models able to reproduce the dark energy (DE) epoch and the early-time inflation. We will discuss the black hole (BH) solutions in generalized theories of gravity: it is of fundamental interest to understand how properties and laws of BHs in General Relativity (GR) can be addressed in the framework of modified theories. In particular, we will discuss the energy issue and the possibility to derive the First Law of thermodynamics from the field equations. Then, in the analysis of cosmological solutions, we will pay particular attention to the occurrence of finite-time future singularities and to the possibility to avoid them in -gravity. Furthermore, realistic models of F(R)-gravity will be analyzed in detail. A general feature occurring in matter era will be shown, namely, the high derivatives of Hubble parameter may be influenced by the high frequency oscillation of the DE and some correction term may be required in order to stabilize the theory at high redshift. The inflationary scenario is also carefully analyzed and a unified description of the universe is evolved. In the final part of the work, we will look at the last developments in modified gravity, namely, we will investigate cosmological and BH solutions in a covariant field theory of gravity and we will introduce the extended "teleparallel" F(T)-gravity theories. A nice application to the dark matter (DM) problem will be presented. [ABSTRACT FROM AUTHOR]

We apply the Dirac's square root idea to constraints for embedded four-geometries swept by a three-dimensional membrane. The resulting Dirac-like equation is then analyzed for general coordinates as well as for the case of a Friedmann-Robertson-Walker (FRW) metric for spatially closed geometries. The problem of the singularity formation at the quantum level is addressed. [ABSTRACT FROM AUTHOR]

We discuss recent developments related to certain blow-up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research about universes with various kinds of extreme states, higher-order gravity and certain models of braneworlds. [ABSTRACT FROM AUTHOR]

Recent work has revealed intriguing connections between a Belinsky–Khalatnikov–Lifshitz-type analysis of spacelike singularities in general relativity and certain infinite-dimensional Lie algebras, particularly the "maximally extended" hyperbolic Kac–Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(–time) at the Planck scale, and hence — via an effective "de-emergence" of space near the singularity — to a novel mechanism for achieving background independence in quantum gravity. [ABSTRACT FROM AUTHOR]

We study Einstein gravity minimally coupled to a scalar field in a static, spherically symmetric space–time in four dimensions. Black hole solutions are shown to exist for a phantom scalar field whose kinetic energy is negative. These "scalar black holes" have an infinite horizon area and zero Hawking temperature and are termed "cold black holes" (CBHs). The relevant explicit solutions are well known in the massless case (the so-called anti-Fisher solution), and we have found a particular example of a CBH with a nonzero potential V(ϕ). All CBHs with V(ϕ) ≢ 0 are shown to behave near the horizon, quite similarly to those with a massless field. The above solutions can be converted by a conformal transformation to Jordan frames of a general class of scalar–tensor theories of gravity, but CBH horizons in one frame are in many cases converted to singularities in the other, which gives rise to a new type of conformal continuation. [ABSTRACT FROM AUTHOR]

In singularity-generating space–times both the outgoing and the ingoing expansions of null geodesic congruences θ+ and θ- should become increasingly negative without bound, inside the horizon. This behavior leads to geodetic incompleteness, which in turn predicts the existence of a singularity. In this work we inquire whether, in gravitational collapse, space–time can sustain singularity-free trapped surfaces, in the sense that such a space–time remains geodetically complete. As a test case, we consider a type D space–time of Dymnikova which is Schwarzschild-like at large distances and consists of a fluid with a p = -ρ equation of state near r = 0. By following both the expansion parameters θ+ and θ- across the horizon and into the black hole, we find that both θ+ and θ+θ- have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region, 0 ≤ r < r0 (which includes the black hole center), which is not trapped. Thus the trapped region is bounded from both outside and inside. The space–time is geodetically complete, a result which violates a condition for singularity formation. It is inferred that, in general, if gravitational collapse were to proceed with a p =-ρ fluid formation, the resulting black hole might be singularity-free. [ABSTRACT FROM AUTHOR]

General relativity successfully describes space–times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time, there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essentially close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings, one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another. [ABSTRACT FROM AUTHOR]

The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and the singularity behaves locally like a homogeneous oscillatory spacetime. [ABSTRACT FROM AUTHOR]