However, according to Padmanabhan , there exists a suitable definition for what we will call an energy current four-vector G of the gravitational field, such that the total energy current P := G + P is conserved:
This four-vector P should not be confused with the three-vector P in [(22).
In particular, in the Minkowski space-time and taking for v the four-velocity field of some inertial reference frame, the gravitational current G vanishes; hence, conservation (56) of the (matter) current is exactly the same equation as the local energy conservation (19) with definitions (20), whence our use of the expression "matter energy current" to designate the four-vector field (57).
micro]] is the electromagnetic potential four-vector ([phi],[?
2 Maxwell's equations and the current density four-vector
micro]] and using the Lorentz condition of (16), we obtain the well-known wave equation for the four-vector potential [14, see pp.
Using (20) into (17) and making use of the Lorentz condition, the wave equation for the four-vector potential becomes
Proper treatment of the general case requires that the current density four-vector be proportional to the RHS of (21) as follows ([[F.
Some applications have reached over 100Mflops for 16 processors, which is about the speed a four-vector
processor system of comparable speed achieves.
In Chapter 2, the four-vector
representation of events will be introduced.
By analogy with the current density four-vector