Newtonian Modern Relativity modernrelativity special general black hole mass energy Einstein wormhole time Schwarzschild light

Appendix A

Newtonian-Relativistic Comparisons

To gain an intuitive insight into general relativity, it is helpful to have a heuristic correspondence between relativistic quantities and equations and their Newtonian counterparts. In this section we will list relativistic quantities with their Newtonian counterparts.

Relativistic Quantity

Newtonian Quantity

The Metric Tensor

g_mn

The Gravitational Potential

Forces of Affine Connection

- G^l_mnu^mpⁿ

The Gravitational Force

mg^l

The Affine Connections

- G^l_mn

The Gravitational Field

g^l

Einstein Field Equations

R_mn - (1/2)g_mnR - lg_mn = (8pG/c⁴)T_mn

The Poisson Equation

Ñ²f = kr

Gradient of Affine Forces

-(G^l_mnu^mpⁿ),_r

under particular circumstances, components of the Riemann tensor

-mc²R^l_0r0

Gravitational Force Tidal gradient

mg^l,_r

NonGeodesic Equation

F^l = Dp^l/dt

F^l = mA^l

Newton's Second Law of Motion

f^l = dp^l/dt

f^l = ma^l

182