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The prevalent opinion that infalling objects can freely cross a black hole horizon is based on the assumptions that the horizon region is governed by classical General Relativity and by specific singular coordinate transformations it is possible to remove divergences in the geodesic equations. However, the coordinate transformations usually used to demonstrate the geodesic completeness are of class C0, while the standard causality theory requires that the metric tensor to be at least C1. Introduction of C0-class functions leads to the appearance of the additional delta-like sources in the Einstein equations and in the equations for quantum particles. Therefore, to explore the horizon region, in addition to the classical geodesic equations, one needs to use equation of quantum particles. Applying physical boundary conditions at the Schwarzschild and Kerr event horizons, we show existence of the exponentially decay/enhanced solutions (with the complex phases) to the Klein-Gordon equation. This means that in semi-classical approximation particles probably do not enter the black hole horizon, but are absorbed/reflected by it. Then it follows that the minimal classical size of any isolated body is its horizon radius, what potentially can solve main black hole mysteries. [ABSTRACT FROM AUTHOR]

In Stoica (Int. J. Theor. Phys. 55, 71-80, ) a regularization procedure is suggested for regularizing Big Bang singularities in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities. [ABSTRACT FROM AUTHOR]

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by Loop quantum cosmology. Dark energy in the form of Generalized Cosmic Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is taken into account in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy model. Graphs and phase diagrams are drawn to study the variations of these parameters. It is seen that the background dynamics of Generalized Cosmic Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. From the graphs, generalized cosmic Chaplygin gas is identified as a dark fluid with a lesser negative pressure compared to Modified Chaplygin gas, thus supporting a 'No Big Rip' cosmology. It has also been shown that in this model the universe follows the power law form of expansion around the critical point, which is consistent with the known results. Future singularities that may be formed in this model as an ultimate fate of the universe has been studied in detail. It was found that the model is completely free from any types of future singularities. [ABSTRACT FROM AUTHOR]

We study the exact solution of Einstein's field equations consisting of a ( n+2)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density ρ and thickness d, surrounded by two different vacua. We explicitly write down the pressure and the external gravitational fields in terms of ρ and d, the pressure is positive and bounded, presenting a maximum at an asymmetrical position. And if $\sqrt{\rho} d$ is small enough, the dominant energy condition is satisfied all over the spacetime. We find that this solution presents many interesting features. In particular, it has an empty singular boundary in one of the vacua. [ABSTRACT FROM AUTHOR]

Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles: Δ=2 π(1−1/ n), n=1,2,... . A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle. [ABSTRACT FROM AUTHOR]

“ Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “ gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “ physical theories of a geometrical character.” Thence, “ physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “ differential” equations, are also being discussed. [ABSTRACT FROM AUTHOR]

We show that the inclusion of a termCabcdCabcd in the action can remove the recently described anisotropic singularity occurring on the hypersurfaceF(f) = 0 of scalar-tensor theories of gravity of the typepreserving, by construction, all of their isotropic solutions. We show that, in principle, a higher order term of this type can arise from considerations about the renormalizability of the semiclassical approach to the theory. Such result brings again into consideration the quintessential models recently proposed based in a conformally coupled scalar fieldwith potential, that have been discharged as unrealistic precisely by their anisotropic instabilities on the hypersurfaceF(f) = 0. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action $\backslash [\; S=\backslash int\; d^4x\backslash sqrt\{-g\}\backslash \{F(\backslash phi)R-\backslash partial\_a\backslash phi\backslash partial^a\backslash phi-2V(\backslash phi)\backslash \},\backslash ]$ with general F(φ) and V(φ). The dynamical nature of each singularity is elucidated, and we show that both are, in general, dynamically unavoidable, reinforcing the unstable character of previous isotropic and homogeneous cosmological results obtained for the conformal coupling case. [ABSTRACT FROM AUTHOR]

The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum violation of the classical energy conditions, and the presence of quantum fluctuations of the spacetime geometry. The possible significance of each is discussed. [ABSTRACT FROM AUTHOR]