  Does a dynamical black hole embedded in a cosmological FRW background emit
Hawking radiation where a globally defined event horizon does not exist? What
are the differences to the Schwarzschild black hole? What about the first law
of black hole mechanics? We face these questions using the LTB cosmological
black hole model recently published. Using the Hamilton-Jacobi and radial null
geodesic-methods suitable for dynamical cases, we show that it is the apparent
horizon which contributes to the Hawking radiation and not the event horizon.
The Hawking temperature is calculated using the two different methods giving
the same result. The first law of LTB black hole dynamics and the thermal
character of the radiation is also dealt with.
