A photon sphere is a spherical region of space where gravity is strong enough that photons are forced to travel in orbits. The radius of the photon sphere, which is also the lower bound for any stable orbit, is:
which is one and half times the Schwarzschild radius.
This equation entails that photon spheres can only exist in the space surrounding an extremely compact object (a black hole or possibly a neutron star).
As photons travel near the event horizon of a black hole they can escape being pulled in by the gravity of a black hole by traveling at a nearly vertical direction known as an exit cone. A photon on the boundary of this cone will not completely escape the gravity of the black hole. Instead it orbits the black hole. These orbits are not stable.
The photon sphere is located farther from the center of a black hole than the event horizon and ergosphere. Within a photon sphere it is possible to imagine a photon that starts at the back of your head and orbits around a black hole only then be seen by your eyes. For non-rotating black holes, the photon sphere is a sphere of radius 3/2 Rs, where Rs denotes the Schwarzschild radius (the radius of the event horizon) - see below for a derivation of this result. There are no stable free fall orbits that exist within or cross the photon sphere. Any free fall orbit that crosses it from the outside spirals into the black hole. Any orbit that crosses it from the inside escapes to infinity. No unaccelerated orbit with a semi-major axis less than this distance is possible, but within the photon sphere, a constant acceleration will allow a spacecraft or probe to hover above the event horizon.
A rotating black hole has two photon spheres. As a black hole rotates, it drags space with it. The photon sphere that is closer to the black hole is moving in the same direction as the rotation, whereas the photon sphere further away is moving against it. The greater the angular velocity of the rotation of a black hole the greater distance between the two photon spheres. Since the black hole has an axis of rotation, this only holds true if approaching the black hole in the direction of the equator. If approaching at a different angle, such as one from the poles of the black hole to the equator, there is only one photon sphere. This is because approaching at this angle the possibility of traveling with or against the rotation does not exist.
Other articles related to "photon sphere, photons, sphere":
... The photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit ... For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius ... While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole ...
Famous quotes containing the word sphere:
“If today there is a proper American sphere of influence it is this fragile sphere called earth upon which all men live and share a common fatea sphere where our influence must be for peace and justice.”
—Hubert H. Humphrey (19111978)