  An analysis of all known spherically symmetric solutions to the field
equations originating from the Riemann tensor quadratic curvature Lagrangian is
presented. A new exact solution is found for the field equation originating
from the "energy-momentum" equation of the gauge gravity theory. Imposing
equivalence between the Palatini and standard variational field equations
yields an algebraic condition that restricts the number spacetime solutions to
gauge gravity. An analysis of a new spherically symmetric solution to the
conformal gravity field equations is also presented. Point particle orbital
dynamics in both the Schwarzschild and Reissner-Nordstrom black hole spacetimes
are analyzed as 2-d conservative bifurcation phenomena. The Schwarzschild
dynamics exhibit both saddle-center and transcritical bifurcation points and a
calculation of periastron precession is presented that incorporates a
phase-plane analysis of the relativistic equations of motion. Level curves of
constant energy are illustrated for both timelike and null geodesics and a
phase-plane analysis of dynamical invariance between the proper and coordinate
time reference frames is discussed. The Reissner-Nordstrom dynamics exhibit
saddle-center, transcritical, pseudo-transcritical, and additional bifurcations
that combine all three previous bifurcations in various combinations.
Periastron precession in the Reissner-Nordstrom spacetime is analyzed using the
phase-plane and bifurcation techniques and extended to include a bifurcation
point of the dynamics. A numerical solution at these parameter values
illustrates that such orbits typically yield a much larger precession value
compared to the standard value for timelike, precession. The acausal geodesics
considered by Brigman are also discussed and their precession value is
calculated.
