All Writings

Linearized Einstein field equations, wave solutions in the weak-field limit, the transverse-traceless (TT) gauge, quadrupole radiation generation, and orbital decay.

General relativistic hydrostatic equilibrium, the TOV maximum mass limit, internal superfluidity, nuclear pasta phases, and the ultra-strong magnetic fields of magnetars.

Quantum Fermi-Dirac statistics, the relativistic equation of state, polytropic hydrostatic equilibrium, and the 1.44 solar mass threshold for white dwarf collapse.

Quasars, blazars, and radio galaxies; the Eddington accretion limit; supermassive black hole seed formation; and feedback-driven galactic coevolution.

Keplerian shear flows, the alpha-viscosity prescription, Balbus-Hawley magnetorotational instability (MRI), and the Blandford-Znajek relativistic jet mechanism.

The four laws of black hole mechanics, holographic horizon area entropy, quantum vacuum particle creation, black hole evaporation, and the Page curve.

The Raychaudhuri equation, trapped 2-surfaces, global hyperbolicity, null energy conditions, and the topological inevitability of gravitational singularities.

Stationary axisymmetric rotating black holes, the Kerr metric in Boyer-Lindquist coordinates, the static limit surface, Lense-Thirring precession, and extraction of rotational energy.

Exact spherically symmetric vacuum solutions, the Schwarzschild radius, coordinate vs curvature singularities, gravitational time dilation, and photon orbits.

Foundations of general relativity, pseudo-Riemannian geometry, the metric tensor, geodesic motion, and the geometric derivation of the Einstein field equations.