Behind the Schwarzschild horizon

Foundations of Physics, 2008

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.

International Journal of Modern Physics A, 2015

We discuss a sufficiently large four-dimensional Schwarzschild black hole which is in equilibrium with a heat bath. In other words, we consider a black hole which has grown up from a small one in the heat bath adiabatically. We express the metric of the interior of the black hole in terms of two functions: One is the intensity of the Hawking radiation, and the other is the ratio between the radiation energy and the pressure in the radial direction. Especially in the case of conformal matters we check that it is a self-consistent solution of the semiclassical Einstein equation, Gμν = 8πG〈Tμν〉. It is shown that the strength of the Hawking radiation is proportional to the c-coefficient, that is, the coefficient of the square of the Weyl tensor in the four-dimensional Weyl anomaly.

It is shown that inconsistencies arise when we look upon the Schwarzschild solution as the space-time arising from a localized point singularity. The notion of black holes is critically examined, and it is argued that, since black hole formation never takes place within the past light cone of a typical external observer, the discussion of physical behavior of black holes, classical or quantum, is only of academic interest. It is suggested that problems related to the source could be avoided if the event horizon did not form and that the universe only contained quasi-black holes.

An investigation on black holes reveals interesting new data. Due to the many speculations about the inside of black holes a concept is developed to allow consideration of the properties occuring inside on a model consisting of an electromagnetic wave. The advantage of the current model is that the investigation is based on a mass originated from even that wave and rather avoids to base the study on an already existing massive mass, which then preliminary excludes any transparent imagination in that field. The theory starts on a classical treatment to later incorporate relativistic considerations leading finally to the transformation equations appropriate for a description of an anti-world. On the basis of the photo sphere the Schwarzschild radius can be determined, which is completely free and independent then on any preliminary given conditions those could ban further in-depth treatment of that task. It is shown each of the two frames reveals individually its own Schwarzschild radius, both of them being reciprocal to each other. In spite of their distinct characteristics of the frames inside and outside a black hole it can be stated out those radii touch each other. A comparison of the two frames can be established by a set of transformation equations to justify the physical properties of the two frames are ideally mirrored in accordance to CPT-operation. The possibility of an anti-universe inside a black hole is discussed.

Advances in Astrophysics, Vol. 4, No. 1, February 2019

The article gives the metric of the Schwarzschild black hole, consistent with the fact that the electromagnetic vacuum is unstable under its horizon. A similar metric was previously obtained in the author's work when studying the dynamics of a vortex. This metric is characterized by the absence of many familiar concepts intrinsic to hyperbolic space-time: light-like geodesics, light cone, etc. The thermodynamic aspect of this black hole model is also considered.

International Journal of Astronomy and Astrophysics, 2013

Presented herein is a new and independent derivation of equation for the radius of Black Holes, i.e. the event horizon of black holes. The equation has been derived by formulating the relativistic equation of escape velocity derived from the relativistic equations for gravitational potential and kinetic energy. Based upon that, it is now shown that the actual size of a black hole, as determined by its event horizon, is exactly half the value predicted by the escape velocity equation used in the Newtonian mechanics. It proves that the actual radius of a black hole is exactly one half of the Schwarzschild radius.

We consider the case of constantly accelerated frames and rotating frames in the Special Theory of Relativity. We find that both cases have surfaces homologous to an event horizon at the point where the velocity of the non-inertial reference frame, , with respect to an arbitrary but fixed global inertial frame, , becomes and space variables become time-like and the time variable becomes space-like. We conjecture that this is impossible and that one must transfer to another reference frame which becomes non-rigid at least slightly before reaching the event horizon and where space variables are globally space-like and never null or time-like and time variables are globally time-like, never null or space-like. We conjecture, moreover, that in relativity any rigid non-inertial reference frame must have an event horizon somewhere; we also conjecture that this is not a reference frame that could occur in nature and whose space and time variables could be used for meaningful physical analysis. In that case, one must transfer to another reference frame which is non-rigid and in which no event horizon occurs. Mathematical

We will show that the Schwarzschild interior and exterior solution can be represented by a common formal system if one uses the methodology of 5-dimensional embedding. Black holes are excluded from the outset. Moreover, it is not possible to approach the event horizon. The interior part of the solution covers that critical region.

2005

In a previous paper I derived the general solution for the simple point-mass in a true Schwarzschild space. I extend that solution to the point-charge, the rotating pointmass, and the rotating point-charge, culminating in a single expression for the general solution for the point-mass in all its configurations when Λ = 0. The general exact solution is proved regular everywhere except at the arbitrary location of the source of the gravitational field. In no case does the black hole manifest. The conventional solutions giving rise to various black holes are shown to be inconsistent with General Relativity.

We present a pedagogically sound derivation of the most general solution of the time-independent, spherically-symmetric gravitational field equations. We use that solution, the Combridge-Janne solution, as a basis for evaluating the original and textbook Schwarzschild solutions. We demonstrate that both versions of the Schwarzschild solution are valid, are distinct and not equivalent to each other, but are related by means of a one-parameter family of solutions. We explicitly show that the original solution is the appropriate solution for a point mass source while the textbook solution is the appropriate solution for a wormhole source. In addition, the textbook solution necessarily has a time-dependent aspect while the original solution is truly time-independent. A number of issues surrounding these two solutions are clarified and resolved.