Time dilation as an effect of energy density Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation?
i.e. Higher energy density==>Slower rate of time?
 A: The formula for gravitational time dilation1 is
$$\frac{t_0}{t_f}=\sqrt{1-\frac{2GM}{rc^2}}$$
For a sphere,
$$M=V \rho = \frac{4}{3} \pi r^3 \rho$$
So
$$\frac{t_0}{t_f}=\sqrt{1-\frac{8G \pi r^2 \rho}{3c^2}}$$
So the greater the density, the greater the time dilation.

Has any relation been observed or postulated to exist between the energy-density (or the surrounding space) of an object and time dilation?

Yes. In every single case, in fact - not just the spherically symmetric static cases, as I gave above.

1 Around a static, spherically symmetrical object.
A: In both GR and SR, the passage of time is dependent upon the energy state - in the special theory, the passage of time logged by two clocks in relative motion depends upon the kinetic energy $(v^2/c^2)$ difference whereas in the general theory, the passage of time depends upon the gravitational potential $(2GM/rc^2)$.  This in turn, is simply the escape velocity (the kinetic energy required to extricate a mass from the gravitational well).  So the bottom line is, time dilation in both SR and GR can be expressed by the same factors    
