The American scientist John Wheeler coined the phrase “black hole” in 1969 to describe a massively compact star with such a strong gravitational field that light cannot escape. When a star’s central reserve of hydrogen is depleted, the star begins to die. Gravity causes the center to contract to higher and higher temperatures, while the outer regions swell up, and the star becomes a red giant. The star then evolves into a white dwarf, where most of its matter is compressed into a sphere roughly the size of Earth. Some stars continue to evolve, and their centers contract to even higher densities and temperatures until their nuclear reserves are exhausted and only their gravitational energy remain. The core then rushes inward while the mantle explodes outward, creating neutron stars in the form of rapidly rotating pulsars. Imploding stars overwhelmed by gravity form black holes, where the core hits infinite density and becomes a singularity (some estimate it at 10^94 times the density of water).
John Michell and Pierre de Laplace, in 1783, showed that when the escape speed from the surface of a body equals the speed of light, Newtonian theory breaks down. According to general relativity, spacetime is curved and the curvature is a measure of the strength of gravity. Thus as a star contracts, its surface gravity increases and spacetime becomes more curved. At the Schwartzschild radius (Rs=2GM/c^2) spacetime is so curved that the body is enclosed, becoming a black hole wrapped in curved spacetime where not even light can escape it. Also, as a mass contracts, its surface gravity increases in strength and light rays emitted from the surface are increasingly redshifted and deflected (gravitational redshift=(l0-l)/l=1/(1- Rs/R)^.5-1 where l is the emitted wavelength, l0 is the received wavelength, and R is the radius of a body whose Schwartzschild radius is Rs ). Rays of light leaving a gravitating body are curved, and become more curved as the body shrinks. When the radius of the body is less than the radius of the photon sphere, a radius 1.5 times the Schwartzschild radius where the light rays circularly orbit a black hole, the exit cone begins to close. Rays within the exit cone escape while those outside are trapped and fall back. Since the photon sphere orbits are unstable, if a circulating rays is disturbed slightly, it either spirals around and is captured or spirals out and escapes at radius 3^.5=1.732 times that of the photon sphere. Both redshift and deflection allow no radiation to escape (Harrison 248-250).
At large distances from the black hole, gravity is weak and spacetime is the same as spacetime in special relativity. Close to the black hole, however, spacetime is deformed, causing differences in space and time between the stationary and distant observer. The effect of spacetime curvature near a black hole is such that lightcones are tilted so that the future lightcones tip toward the black hole. ...