The Interior Enviroment of a Black Hole.

Communications in Mathematical Physics, 1999

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case.

Classical and Quantum Gravity, 2000

A rigidity theorem that applies to smooth electrovac spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given in a recent work . Here we enlarge the framework of the corresponding investigations by allowing the presence of other type of matter fields. In the first part the matter fields are involved merely implicitly via the assumption that the dominant energy condition is satisfied. In the second part Einstein-Klein-Gordon (EKG),

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.

We show that, contrary to the prevailing opinion, coordinates in General Relativity do have physical meanings and that coordinates are essentially reference frames. A coordinate singularity such as an event horizon is actually a pathology in the reference frame and can be eliminated only by a velocity boost or change of reference frame. In this light we discuss the case of constant acceleration in special relativity and the Schwarzchild and Kerr metrics in General Relativity. We find, among other things, that what in the Kerr metric is often called the ergosphere is really the event horizon and that what is usually called the event horizon, being inside the real event horizon and physically inaccessible, is just another (physically uninteresting) coordinate singularity which, however, has the peculiar property of being one-dimensional rather than two-dimensional.

European Physical Journal C, 2015

Classical and Quantum …, 1999

Classical and Quantum Gravity, 2014

Within the generic null characteristic initial value problem a reduced set of the evolution equations are deduced from the coupled Newman-Penrose and Maxwell equations for smooth four-dimensional electrovacuum spacetimes allowing non-zero cosmological constant. It is shown that this reduced equations make up a first order symmetric hyperbolic system of evolution equations, and also that the solutions to this reduced system are also solutions to the full set of the Newman-Penrose and Maxwell equations provided that the inner equations hold on the initial data surfaces. The derived generic results are applied in carrying out the investigation of electrovacuum spacetimes distinguished by the existence of a pair of null hypersurfaces, H1 and H2, generated by expansion and shear free geodesically complete null congruences such that they intersect on a two-dimensional spacelike surface, Z = H1 ∩ H2. Besides the existence of this pair of null hypersurfaces no assumption concerning the asymptotic structure is made. It is shown that both the spacetime geometry and the electromagnetic field are uniquely determined, in the domain of dependence of H1 ∪ H2 once a complex vector field ξ A (determining the metric induced on Z), the τ spin coefficient and the φ1 electromagnetic potential are specified on Z. The existence of a Killing vector field-with respect to which the null hypersurfaces H1 and H2 comprise a bifurcate type Killing horizon-is also justified in the domain of dependence of H1 ∪ H2. Since, in general, the freely specifiable data on Z do not have any sort of symmetry the corresponding spacetimes do not possess any symmetry in addition to the horizon Killing vector field. Thereby, they comprise the class of generic 'stationary' distorted electrovacuum black hole spacetimes which for the case of positive cosmological constant may also (or, in certain cases, only) contain a distorted de Sitter type cosmological horizon to which our results equally apply. It is also shown that there are stationary distorted electrovacuum black hole configurations such that parallelly propagated curvature blow up occurs both to the future and to the past ends of some of the null generators of their bifurcate Killing horizon, and also that this behavior is universal. In particular, it is shown that, in the space of vacuum solutions to Einstein's equations, in an arbitrarily small neighborhood of the Schwarzschild solution this type of distorted vacuum black hole configurations always exist. A short discussion on the relation of these results and some of the recent claims on the instability of extremal black holes is also given. *

Eprint Arxiv 1108 3512, 2011

The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time-and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabés, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.

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.

2012

A solution is obtained for the interior structure of an uncharged rotating black hole that accretes a collisionless fluid. The solution is conformally stationary, axisymmetric, and conformally separable, possessing a conformal Killing tensor. The solution holds approximately if the accretion rate is small but finite, becoming more accurate as the accretion rate tends to zero. Hyper-relativistic counterstreaming between collisionless ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. As ingoing and outgoing streams approach the inner horizon, they focus into twin narrow beams directed along the ingoing and outgoing principal null directions, regardless of the initial angular motions of the streams. The radial energy-momentum of the counterstreaming beams gravitationally accelerates the streams even faster along the principal directions, leading to exponential growth in the streaming density and pressure, and in the Weyl curvature and mass function. At exponentially large density and curvature, inflation stalls, and the spacetime collapses. As the spacetime collapses, the angular motions of the freely-falling streams grow. When the angular motion has become comparable to the radial motion, which happens when the conformal factor has shrunk to an exponentially tiny scale, conformal separability breaks down, and the solution fails. The condition of conformal separability prescribes the form of the ingoing and outgoing accretion flows incident on the inner horizon. The dominant radial part of the solution holds provided that the densities of ingoing and outgoing streams incident on the inner horizon are uniform, independent of latitude; that is, the accretion flow is "monopole." The subdominant angular part of the solution requires a special non-radial pattern of angular motion of streams incident on the inner horizon. The prescribed angular pattern cannot be achieved if the collisionless streams fall freely from outside the horizon, so the streams must be considered as delivered ad hoc to just above the inner horizon.