etc ). As this gas has a finite temperature, it must radiate. However, if the object is very compact, the emitted radiation is strongly redshifted when it reaches a distant observer and the object can appear very faint. Here, I relax the quite common assumption of steady state L=M�Bc2 [9, 10, 12, 13], where L is the surface luminosity and M�B is the mass accretion rate. That would require that the accreting gas hits the ��solid surface�� of the object and then radiates to infinity all its kinetic energy. If this were the case, a very compact object would not be able to increase its mass, or at least the process would be very inefficient, likely in contradiction with the observations of the supermassive objects in galactic nuclei. Moreover, there are no reasons to assume that BH candidates have a solid surface.

In the picture in which we have a gas of particles packed in a small region by the gravitational force, the accreting gas enters into the compact object and both its rest-mass and kinetic energy contribute to increasing the mass of the BH candidate.Let us now see the constraint we can obtain in this picture from the nonobservation of thermal spectrum from BH candidates. The specific energy flux density of the compact object (often measured in erg cm?2s?1Hz?1) as detected by a distant observer is as follows:F=��Iod��,(2)where Io is the specific intensity of the radiation as measured by the distant observer and d�� is the element of the solid angle subtended by the image of the object on the observer’s sky. Ix/��x3 = const.

(Liouville’s Theorem), where ��x is the photon frequency measured by any local observer on the photon path, andd��=dx?dyD2,(3)where x and y are the Cartesian coordinates on the observer’s sky and D is the distance of the compact object from the observer. The equivalent isotropic luminosity of the BH candidate is thusL=4�С�g3Ie?dx?dy?d��.(4)Here, g = ��o/��e is the redshift factor, ��o is the photon frequency measured by the distant observer, and ��e and Ie are, respectively, the photon frequency and the specific intensity of the radiation measured by an observer located at the point of emission of Anacetrapib the photon, on the surface of the compact object, and corotating with the surface of the compact object. The emission should be like the one of a blackbody; that is,Ie=2h��e3c21exp?(h��e/kBTe)?1,(5)where Te is the temperature of the surface of the BH candidate measured by a locally corotating observer.

For the sake of simplicity, we now consider a spherically-symmetric nonrotating object. The geometry of the spacetime around the BH candidate will be described by the Schwarzschild solution, which is valid till the radius of the compact object, R. The luminosity becomes as follows:L=4��g4Te4��dx?dy,(6)where �� is the Stefan-Boltzmann constant andg=(1?2MR)1/2.