I've read in some texts that we can't directly observe a black hole in space because not even light can escape from its gravity. Some of the indirect observational methods mentioned are, gravitational lensing and gamma ray outbursts created by swirling matter into the event horizon. My question is, if a black hole is surrounded by glowing matter, it should appear just like a star (except with a different spectral signature), and it should be fairly easy to detect. I don't understand the statement: "If you find an object orbiting around nothing, there's likely to be a black hole at the center". Though a black hole is invisible, the enveloping matter should reveal its identity... What am I missing here? Please answer!
The reason has to do with time dilation, and specifically, with the resulting red shift.
A black hole forms from a collapsing star, which is of course made of brightly glowing matter. The event horizon forms in the centre and moves outwards while the star-matter falls towards it. Because of gravitational time dilation, the infalling matter never crosses the event horizon from the outside perspective, and thus can technically still be "seen."
However, this time dilation also causes the light the matter emits to be redshifted. Essentially, every photon the matter emits is reduced in frequency due to the time dilation, and the time in between photons also reduces, asymptotically approaching infinity. This means that the black hole very rapidly converges to something that would appear completely black to an outside observer - the matter falling into it can only be seen by someone with the patience to collect many very low frequency photons over many billions of years.
That said, matter that falls into the black hole after it's been formed can certainly glow brightly enough to be detected - very much so in the case of an active galactic nucleus.
This is a curious question. Many black holes are detected and identified due to light emitted from material falling into them.
When black holes accrete matter, conservation of angular momentum would usually lead to the formation of an accretion disk. The release of gravitational potential energy as material falls means that this disk can be hot, and it is radiation from this hot disk that is one of the ways in which black holes are identified.
Examples would include most stellar-sized black hole binary systems - these are among the most powerful X-ray sources in our Galaxy. ((For example: Cygnus X-1).
In terms of super-massive black holes, accretion of matter is responsible for powering active galactic nuclei and quasars.
So yes, if a black hole is surrounded by a significant amount of matter which it is accreting, then it will be observable and may actually be quite bright.
There are examples of "dark" black holes. These would be black holes that are not accreting matter at any significant rate. An example would be the black hole at the center of our Galaxy - whose identity is only revealed by observing the motion of stars around it.
I think you should be more specific in the type of black hole, because the spinning (and spinning-charged) black holes can make light reach the photonsphere and not be swallowed by the black hole, but enter an orbit around it. Eventually debris that are also in orbit will be heated up and started to glow, and it's the first step for a quasar to be born.