Astronomy Bizarre Wheeler309N FALL 2004 October 25, 2004(47855)Review for Test #3Neutron Stars and Black HolesNeutron stars – mass of sun, radius ~ 10km, density like atomic nucleus, huge gravity at surface.Discovery of pulsars – pulsating radio sourcesInterpretation of pulsars as rotating magnetized neutron starsRole of magnetic field to cause radiation, misalignment of rotation axis, magnetic axisProduction of pulses – probably related to strong electric, magnetic fields at magnetic poles, ejection ofelectrons, annihilation of positronsAbout 600 pulsars known, perhaps a billion neutron stars in the Galaxy.Pressure support from quantum pressure of neutrons plus nuclear repulsion. Maximum mass of neutronstar about 2 solar masses.Neutron stars as binary X-rays sources.X-ray pulsars – accreted gas channeled to magnetic poles, neutron star spins faster as it accretes.X-ray transients – 4 or 5 in Galaxy. Outburst every few years for a month. Probably a disk instabilitylike a dwarf nova, but with the white dwarf replaced by a neutron star.X-ray Bursters – about 30 in the Galaxy. Burst every few hours for minutes. Probably the neutron staranalog of a classical nova. Matter accretes on surface of neutron star. Hydrogen is supported by thermalpressure, burns to helium. Helium is supported by quantum pressure and is unregulated and explodes.Often found in globular clusters.Black Hole History – Mitchell, Laplace, escape velocity.Event Horizon —Since nothing with velocity less than or equal to the speed of light can pass backwardthrough an event horizon, the information that an event occurred cannot pass through, so an event on thewrong side of an event horizon can never be known to an observer on the opposite side, hence the name.Schwarzschild Radius—the distance of the event horizon from the center of a black hole. For a non-rotating, non-charged, black hole the size of the event horizon is 3 kilometers x (mass/solar mass) i.e. ifthe Sun were a black hole its event horizon would be 3 kilometers in radius (the Sun is actually about amillion kilometers in radius).Singularity—region in center of black hole where ordinary space and time cannot exist because of severespace time curvature and quantum uncertainty. The boundary of physics as we currently know it.Tidal forces tend to draw any object into a “noodle” shape for two reasons: the force closer to the center isstronger and because two separated points the same distance from the hole tend to approach one anotheras they both try to fall directly toward the center.Conceptual problems with Newton’s Theory of GravityEinstein says there is no “force” of gravity. Matter curves space and curved space tells matter how tomove.Einstein says the space around a gravitating object (Earth, a star, a black hole) is curved in the same senseas a cone poked in a rubber sheet. The circumference of a circle drawn around such an object is less than2π times the radius and “straight lines,” the shortest distance between two points, curve around the object.One type of straight line in this kind of curved space follows the curved space and closes on itself. Anorbit is interpreted as this kind of straight line.Space versus HyperspaceEinstein says space around gravitating object “flows” inward, cause of free fall inward.Einstein says that all objects accelerate at the same rate near a gravitating object because that objectcurves the space around it and everything falls on the same “straight” line, independent of their ownnature.Far away from a gravitating object, space is “flat” and there is no gravity. Black holes are “safe” from adistance.Nature of Time in the vicinity of a black hole. Any observer always senses his or her own time asperfectly normal. But an observer at a large distance from the black hole where the force of gravity issmall sees time passing more slowly for events occurring deep in the gravitational field of a black hole.Events right at the event horizon would show no passage of time to a distant observer. A distant observerwatching another person falling toward the event horizon would perceive (other effects not interfering)that this second person gradually approached but never crossed the event horizon. An observer freelyfalling under the influence of no forces would plunge into the black hole after a finite (and normallyshort) passage of their own time.Redshift—the redshift of the wavelength of photons received at a distance gets very large as the point ofemission of the photon gets more deep in a gravitational field.“Black Hole”—the large redshift of photons emitted near the event horizon coupled with the long passageof time between the arrival of these photons at a distant observer due to the apparent slowing of timemeans that events happening just outside the event horizon cannot, in practice, be “seen” by a distantobserver—hence, “black hole” is a more accurate term than “frozen star” which does not connote theblackness.Temperature of a black hole—according to Stephen Hawking, if one studies the event horizon with theQuantum Theory one finds that the gravitation energy (and hence mass) of a black hole can be convertedinto matter and anti-matter (mostly photons) with some of this material being ejected carrying off themass of the hole.Black Hole Evaporation—For a black hole of ordinary stellar mass or larger the amount of mass loss isnegligible in the age of the Universe and may be ignored. A black hole of less than asteroid size couldtotally evaporate within the age of the Universe.The three fundamental properties of a Black Hole are those which can be measured from a distance -mass, charge, and spin. Other properties such as size and shape are specified once these basic propertiesare set.Information Loss in Black HolesTime-like space—interior to event horizon space drags in one direction, just as time drags you older.Schwarzschild black hole—mass but no spin, no charge.Rotating or Kerr black hole—the idealized mathematical solution of Einstein's equations developed byKerr in which one assumes that all the mass is in the rotating singularity and that there is vacuumeverywhere else.Singularity in a rotating black hole—shaped like a ring, surrounded by “normal ” space so that it can beavoided in principle.Time-like space in rotating black hole—the “in-going” time-like space is bounded on both sides by anevent horizon so