Changes

Black holes have never been directly observed, and there is no direct evidence for their existence.  Even believers in black holes should admit that there are far fewer than predicted by theory, and they lose credibility when they fail to address that undisputed truth.  They will cite evidence of observations of radiation from accretion disks, motion of stars near the center of the galaxy, and "gravitational lensing," around places where there are no visible objects.  But at most the evidence for the existence of black holes is circumstantial, with heavy reliance on speculation.

Black holes have never been directly observed, and there is no direct evidence for their existence.  Even believers in black holes should admit that there are far fewer than predicted by theory, and they lose credibility when they fail to address that undisputed truth.  They will cite evidence of observations of radiation from accretion disks, motion of stars near the center of the galaxy, and "gravitational lensing," around places where there are no visible objects.  But at most the evidence for the existence of black holes is circumstantial, with heavy reliance on speculation.

Black holes are conceptually associated with "[[wormhole]]s",<ref name="nytimes.com"/> which never caught on with the public, perhaps due to its unattractive terminology. The prediction of the existence of wormholes, and its naming in 1957, predates the prediction and naming (1967) of a black hole.

Black holes are conceptually associated with "[[wormhole]]s",<ref name="nytimes.com"/> which never caught on with the public, perhaps due to its unattractive terminology.

 

==Mathematical description==

==Mathematical description==

A '''black hole''' is any object that lies entirely inside its own Schwarzschild radius, given by

A '''black hole''' is any object that lies entirely inside its own Schwarzschild radius, given by