As we have described a black hole we could never observe one of them since they would not reflect or emit any type of radiation or particle. But there are certain effects that could be detected. One of these effects is the gravitational effect on one neighboring star.
Supposes a binary system of stars (two very near stars rotating one around the other) in which one of the stars is visible and from which we could calculate its distance to the Earth and their mass. This visible star will carry out some oscillatory movements in the space due to the gravitational attraction with the invisible star. From these movements the mass of the invisible star could be calculated.
If this invisible star have a mass greater than 2.5 times the mass of our sun, we will have to suppose that is a black hole.
Also if the visible star is close
enough, it could being transferring a part of its mass that would
fall toward the black hole being accelerated to such speed that
it would reach as high temperature as in order to emit X rays.
But this would also happen if it were a neutrons star instead of
a black hole.
One example of detected object that fulfil the two conditions exposed above is the binary star called Cignus-X1, that is a source of very intense X rays formed by a visible star and an invisible star with a calculated mass greater than 2.5 solar masses
Furthermore, also it's necessary to keep in mind that S. Hawking deduced that a black hole would produce subatomic particles in their vicinities, losing mass and irradiating this particles. This may be another way of detection.
We could read in Black Holes and Small Universes of Stehen Hawking, in their lecture "The Future of the universe" saying:
"The indetermination principle of the quantum mechanics indicates that the particles could not have simultaneously very defined the position and the velocity. As greater is the precision with is defined the position of a particle, lesser will be the accuracy with which is determined their velocity and "vicebersa". If a particle is in a black hole, their position is very defined there, what it means that their velocity can't be exactly defined. It is possible that the speed of the particle were greater than that of the light, in this way it could escape from the black hole."
But we should not think that the hole would lose mass, since a black hole with few solar masses would emit a radiation lesser than the Cosmic Microwave Background (CMB), an then it would receive more energy than the emited, and therefore their mass would increase.
In addition to observing the movement of stars to detect invisible neighboring stars that could be mass black holes, or by the radiation emitted by accretion disks, we also have tracks of black holes by mean of gravitational lensing, thus a black hole may distort the light from a nebula that was behind so as to produce some figures in an arc or circle shape, visible enough.
[black holes index]
INTRODUCTION / HOW THE BLACK HOLES ARE FORMED / SPECIAL RELATIVITY AND BLACK HOLES / GENERAL RELATIVITY AND BLACK HOLES / BLACK HOLES DETECTION / The NON- PUNCTUAL BLACK HOLE / SPACE-TIME graphics on STAR COLLAPSE / HOLES In ETERNAL FORMACION, ETERNAL BLACK HOLES And OTHER MATHEMATICAL CONCEPTS