Some galaxies have redshifts \(z\) that if equated to \(v_{\mathrm{r}} / \mathrm{c}\) correspond to velocities greater than the speed of light. Special relativity is not violated in this case a. because of relativistic beaming. b. because of superluminal motion. c. because redshifts carry no information. d. because these velocities do not measure motion through space

Relativistic beaming is a phenomenon that occurs when an object is moving towards an observer at speeds close to the speed of light. This causes the emitted radiation to be concentrated in the direction of motion, making it appear much brighter to the observer. The effect is due to the relativistic Doppler effect and aberration of light. Relativistic beaming is often observed in astrophysical jets, such as those emitted by active galactic nuclei and gamma-ray bursts. It helps astronomers understand the orientation and speed of these ejected particles, but it is not directly related to redshift or the expansion of the universe.

Superluminal motion refers to the apparent faster-than-light motion seen in some astronomical objects, especially jets from quasars and microquasars. This illusion occurs because of the relativistic speeds of the jets, combined with the angle at which we observe them. Even though the particles are moving at speeds less than the speed of light, their rapid motion and our perspective can make them appear as though they are exceeding this universal speed limit.
It is crucial to understand that superluminal motion does not violate the principles of special relativity. It is an effect of the time delay in receiving the light emitted from different parts of the jet. The light from the parts moving towards us reaches us much sooner than the light from the parts moving away. Thus, it gives the illusion of superluminal travel.

Cosmic expansion refers to the observation that the universe is expanding over time. First discovered by Edwin Hubble, it means that galaxies are moving away from us, which results in the redshift of their light. This expansion is described by the Big Bang theory and is supported by the Cosmological Principle, which states that the universe is homogeneous and isotropic on large scales.
In terms of redshift, when we observe distant galaxies, the redshift we measure is not due to their local motion through space, but rather, it is a result of the space itself expanding. This expansion can make it seem like some galaxies are moving away from us faster than the speed of light, but in reality, the galaxies are relatively stationary in their local space. Instead, it is the fabric of space-time that is stretching, which is described by general relativity.

General relativity, formulated by Albert Einstein, is the theory that provides a comprehensive description of gravity. Unlike Newtonian gravity, which describes gravity as a force, general relativity describes it as the curvature of space-time caused by mass and energy. This curvature dictates the paths that objects take in space-time.
An important aspect of general relativity is that it describes how space-time itself can expand, which is key to understanding cosmic expansion and the redshift of light from distant galaxies. The velocities indicated by redshifts due to cosmic expansion do not indicate actual motion through space but rather the stretching of space-time. These redshift-induced velocities can exceed the speed of light without violating the principles of special relativity because they do not represent any physical object moving through space faster than light.