According to the ever faithfull E=mc2, a massive body increases mass when accelerated. I just wonder if it gravity increases as well?

Yes. It does. The abstract to the article

**Measuring the active gravitational mass of a moving object,** D.W. Olson and R.C. Guarino, Am. J. Phys. 53(7), July 1985

If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that Mrel = g(1 + b)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not gM but is 2gM .

where g = gamma, b = beta = v/c

Think of it like this - Since the inertial mass of a body increases with speed inertial mass is proportional to (active) gravitational mass, and the source of gravity is (active) gravitational mass then the strength of the gravitational field increaseses as well.

On a similar note - since light has inertial mass it too generates a gravitational field. E.g. the inertial mass, m, of a photon is defined by m = p/c where p = magnitude of momentum and c = speed of light. This comes from the defining relationship for inertial mass, i.e.

**p** =

*m***v**. Therefore whatever has momentum has inertial mass.

Please note: By "inertial mass" I am not referring to proper mass, aka rest mass. These are different quantities. Photons have zero proper mass and non-zero inertial mass. This is why a beam of light, where all the photons are moving in the same direction, generates a gravitational field.

It's bit more complicated that that of course. The mathematical object which completely defines mass is the stress-energy-momentum tensor,

**T**. This is the source of gravity in the same way that the 4-current is the source of the electromagnetic field.