Geometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime

The geometrical Kosambi–Cartan–Chern approach has been applied to study the systems of differential equations which arise in quantum-mechanical problems of a particle on the background of non-Euclidean geometry. We calculate the geometrical invariants for the radial system of differential equations arising for electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Because the second invariant is associated with the Jacobi field for geodesics deviation, we analyze its behavior in the vicinity of physically meaningful singular points r = M, ∞. We demonstrate that near the Schwarzschild horizon r = M the Jacobi instability exists and geodesics diverge for both considered problems.

Explicit microstates at the Schwarzschild horizon

The claim that the microstates of Schwarzschild black holes in perturbative string theory amount to the modes of long folded strings in the vicinity of its horizon is supported by more evidence.

The Ether Theory Unifying the Relativistic Gravito-Electromagnetism Including also the Gravitons and the Gravitational Waves

In previous publications, we showed that Maxwell’s equations are an approximation to those of General Relativity when V<<c, where V is the velocity of the particle submitted to the electromagnetic field. This was demonstrated by showing that the Lienard-Wiechert potential four-vector A_u created by an electric charge is the equivalent of the gravitational four-vector G_u created by a massive neutral point when V<<c. In the present paper, we generalize these results for V non-restricted to be small. To this purpose, we show first that the exact Lagrange-Einstein function of an electric charge q submitted to the field due an immobile charge q_0 is of the same form as that of a particle of mass m submitted to the field created by an immobile particle of mass m_0. Maxwell’s electrostatics is then generalized as a case of the Einstein’s general relativity. In particular, it appears that an immobile q_0 creates also an electromagnetic horizon that behaves like a Schwarzschild horizon. Then, there exist ether gravitational waves constituted by gravitons in the same way as the electromagnetic waves are constituted by photons. Now, since A_u and G_u, are equivalent, and as we show, G_u produces the approximation, for V<<c, of g_u4 created by m_0 mobile, where the g_uv are the components of Einstein’s fundamental tensor, it follows that A_u+u_u produces the approximation, for V<<c, of Bet_u4 , where the Bet_uv created by m_0 and by q_0, generalize the g_uv.

Gravitational waves, gamma ray bursts, and black stars

Stars that are collapsing towards forming a black hole but appear frozen near their Schwarzschild horizon are termed “black stars”. The collision of two black stars leads to gravitational radiation during the merging phase followed by a delayed gamma ray burst during coalescence. The recent observation of gravitational waves by LIGO, followed by a possible gamma ray counterpart by Fermi, suggests that the source may have been a merger of two black stars with profound implications for quantum gravity and the nature of black holes.

HIDING AND CONFINING CHARGES VIA "TUBE-LIKE" WORMHOLES

We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source of gravity and electromagnetism may appear electrically neutral to an external observer — a phenomenon opposite to the famous Misner–Wheeler "charge without charge" effect. We show that this phenomenon takes place when coupling a bulk gravity/nonlinear-gauge-field system self-consistently to a codimension-one charged lightlike brane as a matter source. The "charge-hiding" effect occurs in a self-consistent wormhole solution of the above coupled gravity/nonlinear-gauge-field/lightlike-brane system which connects a noncompact "universe," comprising the exterior region of Schwarzschild–(anti-)de Sitter (or purely Schwarzschild) black hole beyond the internal (Schwarzschild) horizon, to a Levi-Civita–Bertotti–Robinson-type ("tube-like") "universe" with two compactified dimensions via a wormhole "throat" occupied by the charged lightlike brane. In this solution the whole electric flux produced by the charged lightlike brane is expelled into the compactified Levi-Civita–Bertotti–Robinson-type "universe" and, consequently, the brane is detected as neutral by an observer in the Schwarzschild–(anti-)de Sitter "universe." Next, the above "charge-hiding" solution can be further generalized to a truly charge-confining wormhole solution when we couple the bulk gravity/nonlinear-gauge-field system self-consistently to two separate codimension-one charged lightlike branes with equal in magnitude but opposite charges. The latter system possesses a "two-throat" wormhole solution, where the "left-most" and the "right-most" "universes" are two identical copies of the exterior region of the neutral Schwarzschild–de Sitter black hole beyond the Schwarzschild horizon, whereas the "middle" "universe" is of generalized Levi-Civita–Bertotti–Robinson "tube-like" form with geometry dS2 ×S2 (dS2 being the two-dimensional de Sitter space). It comprises the finite-extent intermediate region of dS2 between its two horizons. Both "throats" are occupied by the two oppositely charged lightlike branes and the whole electric flux produced by the latter is confined entirely within the middle finite-extent "tube-like" "universe." A crucial ingredient is the special form of the nonlinear gauge field action, which contains both the standard Maxwell term as well as a square root of the latter. This theory was previously shown to produce a QCD-like confining dynamics in flat space–time.

Black holes in the varying speed of light theory

We consider the effect of the varying speed of light theory on nonrotating black holes. We show that in any varying-c theory, the Schwarzschild solution is neither static nor stationary. For a no-charged black hole, the singularity in the Schwarzschild horizon cannot be removed by coordinate transformation. Hence, no matter can enter the horizon, and the interior part of the black hole is separated from the rest of the Universe. If ċ < 0, then the size of the Schwarzschild radius increases with time. The higher value of the speed of light in the very early Universe may have caused a large reduction in the probability of the creation of the primordial black holes and their population. The same analogy is also considered for charged black holes. PACS No.: 04.70.–s