1. Gravity ≡ a field (not a force) which causes distortions (i.e., curvatures and dilation) in spacetime.
• Corollary 1: Gravity is a wave with λ = v/f. Specifically, it is a low frequency (103Hz), long wavelength (λ ≥ 105m) field that is observed at macroscale levels. (f ≈ 1KHz, λ ≈ 100-1000 km)
• Corollary 2: Gravitational waves travel at the speed of light. Therefore λgravity = c/f
• Corollary 3: Gravitational waves behave similar to electromagnetic waves.
• Corollary 4: The closer one moves to the point-source of the gravity field, the “strength” of the field (amplitude of the gravity wave) increases.
• Corollary 4b: Distortions (curves and expansion-dilation) in space and time increase (become more pronounced) as one moves closer to the point source of the gravitational wave
2. Gμν=(8πG/c4)×Tμν
3. Location of an arbitrary point called s in 2-d (x, y), 3-d (x, y, z), and 4-d (x, y, z, t):
• 2-d: s2 = x2 + y2
• 3-d: s2 = x2 + y2 + z2
• 4-d: s2 = x2 + y2 + z2 – c2t2
• Past influences the present, and present influence the future (Minkowski lightcone)
• General Relativity tells us we live in a spacetime geometry. It applies to accelerating frames of reference.
• Special relativity applies to inertial, constant velocity, non-accelerating frames of reference
4. Strong Nuclear Force: Within the nucleus of atoms (i.e., at subatomic, nanoscale levels) the force field that binds protons together within a nucleus (via neutrons) is multiple orders of magnitude “stronger” than gravitational fields.
• Corollary 1: spacetime distortions (and constraints) don’t exist at the subatomic level. At the subatomic level all effects of gravity are canceled out. Thus particle theory (i.e., quantum mechanics) takes over.

Where:

• defined as
• equivalent to
• f: frequency in Hertz
• λ: wavelength
• v: velocity
• c: velocity of light = 2.998×108m/s
• x, y, z: arbitrary coordinates in 3-dimensional space
• t: time
• Fμν: electromagnetic field tensor, all the information about the electric and magnetic field
• Tμν: energy-stress tensor, describes the mass-energy, momentum, and stress density
• Gμν: Einstein tensor, curvature of space-time
• (8πG/c4)Tμν: coupling of energy, momentum, stress and strain from matter to curvature
• 8πG/c4: matter-gravity coupling (coupling of energy-momentum) to curvature = 2.077×10-43 1/Newton
• G: Newton’s Gravitational Constant = 6.674×104 Newton⋅meter2/kilogram2