If a photon is massless how can the intense gravity of a black hole have any affect it?

 

Ta

Because the notion that gravity only affects massive objects is a Newtonian one, but a better description of gravity is General Relativity. In that, gravity is due to/manifests itself as the curvature of space.

And in any case you can consider photons to have (relativistic) mass since they have momentum and energy. Their rest mass is zero, however.

And in any case you can consider photons to have (relativistic) mass since they have momentum and energy. Their rest mass is zero, however.

 

I do not think that relativistic mass is a useful concept in this situation.

 

As swansont has stated, gravity is best thought of a the local geometry of space-time. In particular, that geometry need not be flat.

 

Now it turns out that photons travel along the next best thing to a straight line on a space-time: a null geodesic. To be a little more careful, we are thinking of photons as test particles, that is they do not effect the space-time themselves.

 

The energy-momentum is what acts as a source of gravity. Although photons are massless they carry energy-momentum and can act as a source of gravity.

Even Newtonian gravity predicted the deflection of light by gravity (though only half as much as General Relativity predicted).