🚀 go-pugleaf

Hoping to clear and not add some confusion :-)

In Newtonian physics, gravity (i.e. the scalar gravitational potential field)
is non-dynamic, since it has a time-INdependent field equation (the Poisson 
equation). Therefore, at each moment of time, this eq must be fulfilled at
arbitrary large distance, i.e. if 
  r_i(t)    is the position (at the moment t) of the i-th point particle 
(with [active] gravitational mass m_i) in a model configuration, then the
Newtonian grav'l potential U(r,t) at some position r and time t is given by

  U(r,t) = U(r,{ r_i(t) }) 

                  G * m_i
       [ = SUM  ------------ ]
            i    |r-r_i(t)|

(which you all know). If at least one test particle changes its position, 
this simultaneously changes U(r,t) in the whole spacetime, so that 
"Newtonian gravity in Galilean spacetime" has infinite propagation velocity.

On the other hand, Einsteinian metric gravity (curvature) in GR propagates 
with the velocity of light c (also wellknown, or readable in most GR books). 
Moreover, if you take a look at special-relativistic, i.e. Lorentz invariant
theories of gravity (scalar, vector, or tensor, see, e.g. MTW chapter 7;
ok, they are probably all not present in nature :-)),
then gravity gets a finite velocity ("retarded" potential), usually c [iff
"gravitons" are massless, but c_g < c iff "gravity" is mediated by massive 
particles]. Thus one can make Newtonian gravity Lorentz invariant (just 
replace the Laplace operator by the d'Alembertian and the mass density by 
the trace of the energy momentum tensor in the Poisson eq) -- this
"Newtonian gravity in Minkowsky spacetime" will then propagate with c_g == c.
--
 Hartmut Frommert                 <phfrom@nyx.uni-konstanz.de>
 Dept of Physics, Univ of Constance, P.O.Box 55 60, D-W-7750 Konstanz, Germany
                                           -- Eat whale killers, not whales --