Physics of Electron Black Holes: From Event Horizons to Quantum Effects

 Extremal Event Horizon

Definition: The Extremal Event Horizon marks the boundary beyond which escape velocity equals the speed of light, preventing anything from escaping.

Formalism: Schwarzschild metric describes spacetime around non-rotating black holes:

ds^2 = -(1 - 2GM / (c^2r))dt^2 + dr^2 / (1 - 2GM / (c^2r)) + r^2(dθ^2 + sin^2θdϕ^2)

Example: For a black hole with M = 3M⊙, the Schwarzschild radius rs is approximately 4.43 kilometers.

Spin-Orbit Nexus

Definition: Spin-Orbit Nexus describes how a rotating Electron Black Hole influences nearby objects.

Formalism: Kerr metric characterizes spacetime around rotating black holes:

ds^2 = -(1 - 2GM / (c^2r))dt^2 - (4aGMr / c^2)sin^2θdtdϕ + (r^2Δ / Σ)dr^2 + Σdθ^2 + sin^2θ(r^2 + a^2 + (2GMr / c^2))dϕ^2

Example: A black hole with a = 0.9 exhibits pronounced frame-dragging effects.

Electro-Gravitational Node

Definition: Electro-Gravitational Node represents equilibrium between gravity and electromagnetism near an Electron Black Hole.

Formalism: Combine Einstein's field equations for gravity and Maxwell's equations for electromagnetism:

Einstein's field equations:

Gμν = (c^4 / (8πG))Tμν

Maxwell's equations:

∇μFμν = (c^4 / (4π))Jν

Dyonic Ergosphere

Definition: Dyonic Ergosphere is the region affected by both electric and magnetic charges around an Electron Black Hole.

Formalism: Modify the Kerr-Newman metric to include electric (Q) and magnetic (P) charges:

ds^2 = ... + c^2Qrsin^2θdtdϕ - c^2Prsin^2θdtdθ

Planckian Core

Definition: Planckian Core is the central region where quantum effects dominate.

Formalism: Quantum field theory in curved spacetime describes phenomena:

∇μ∇μφ - (1 / c^2)∇μ∇νφgμν - (1 / (ħc))(1/2)∇μ(∇μφ) - (1 / (ħc))(1/2)∇μ(∇νφ)gμν - (1 / (ħc))(1/2)(∇μφ)(∇μφ) = 0

Example: Inside the Planckian Core, Hawking radiation arises from quantum fluctuations near the event horizon.

Supersymmetric Kernel

Definition: Supersymmetric Kernel explores connections between Electron Black Holes and supersymmetry.

Formalism: Integrate supersymmetry equations into black hole physics:

Qsusy = {Q^α, Q^β} = γμC^αβPμ

Microscopic Kerr Singularity

Definition: Microscopic Kerr Singularity is the central singularity within an Electron Black Hole.

Formalism: Analyze the Kerr metric near the singularity:

Rμν - (1/2)Rgμν = (c^4 / (8πG))Tμν

Nanocharged Spacetime

Definition: Nanocharged Spacetime results from tiny electric charges modifying spacetime.

Formalism: Modify Einstein-Maxwell equations for nanocharges:

Gμν = (c^4 / (8πG))Tμν

Maxwell's equations:

∇μFμν = Rμν - (1/2)Rgμν = (c^4 / (8πG))Tμν

Exotic Limit Point

Definition: Exotic Limit Point represents unique boundary conditions in Electron Black Hole physics.

Formalism: Investigate mathematical properties of the Exotic Limit Point within black hole models.

Quantum Mechanics and General Relativity Interplay

Definition: Quantum Mechanics and General Relativity Interplay combines quantum field theory with general relativity.

Formalism: Apply quantum field theory in curved spacetime:

∇μ∇νφ - (1 / c^2)∇μ∇νφgμν - (1 / (ħc))(1/2)∇μ(∇μφ) - (1 / (ħc))(1/2)∇μ(∇νφ)gμν - (1 / (ħc))(1/2)(∇μφ)(∇μφ) = 0

Example: Hawking radiation, predicted by this formalism, demonstrates quantum effects near black holes.