A white dwarf is a planet-sized star supported by degenerate electrons. Massive white dwarfs are smaller than low-mass white dwarfs. The Chandrasekhar limit, the greatest mass that a white dwarf can have, is about 1.4 solar mass.
A white dwarf keeps a constant size as it evolves. It radiates away its heat and grows cooler and dimmer simultaneously. After billions of years, a white dwarf becomes so dim it is difficult to detect.
White dwarf stars evolve from the cores of asymptotic giant branch stars that have lost their outer layers as cool winds. A star like the Sun will produce a white dwarf of about 0.6 solar mass. The most massive white dwarfs originate in main sequence stars of about 8 solar mass.
A type II supernova is the result of the collapse of the core of a massive star. As the core collapses, its protons and electrons combine to form neutrons. The inner core becomes a neutron star. Infalling matter rebounds from the neutron star and produces a shock wave that moves outward rapidly through the star. After a few hours, the shock wave expands the surface of the star and produces a great brightening.
Supernova 1987A, in the Large Magellanic Cloud, a nearby galaxy, was the first supernova visible to the naked eye in nearly 400 years. Neutrinos, which were detected almost a day before the supernova brightened, marked the time of core collapse and confirmed the idea that type II supernovae result from the collapse of the cores of stars.
The blast of gas ejected from a supernova sweeps up the surrounding interstellar gas and heats it to produce a luminous supernova remnant. Highenergy electrons in the supernova remnant emit synchrotron radiation, which makes a supernova remnant visible using radio telescopes. After about 10,000 to 100,000 years, the supernova remnant merges into the interstellar gas.
Neutron stars, about 10 km in radius, are supported by degenerate neutrons. Like white dwarf stars, the more massive neutron stars are the smallest. The greatest mass that a neutron star can have is estimated to be 1.5 to 2.7 solar mass. A newly formed neutron star spins very rapidly and has a large magnetic field.
Pulsars are rotating neutron stars that emit beams of radiation. The rotation of the neutron star causes the beams to sweep past the Earth, causing us to observe pulses of radiation as often as one thousand times per second.
The beamed radio emission from pulsars is probably produced by energetic electrons in regions near the magnetic poles, which are tipped with respect to the rotation axis of a pulsar. Pulsars lose rotational energy as time passes and, after perhaps 10 million years, slow to periods of a few seconds. Magnetars are highly magnetized neutron stars that produce gamma-ray bursts.
The rotation of the magnetic field of a pulsar produces low-frequency electromagnetic radiation that carries off the rotational energy of the pulsar. The radiation energizes electrons, which emit synchrotron radiation that fills in the center of the surrounding supernova remnant.
Spacetime is the combination of three space coordinates and one time coordinate that locates events in space and time. A geodesic, the shortest distance between two points, is a straight line in flat spacetime, but a curved path in curved spacetime. Geometric quantities, such as the sum of the angles of a triangle, depend on the curvature of spacetime.
According to general relativity, gravity is a consequence of the curvature of spacetime by mass. Objects and light follow geodesics in curved spacetime near massive objects. We cannot see that spacetime is curved, so we have invented the force of gravity to account for the motion of light and moving bodies.
A black hole forms as a result of the collapse of the core of a star when the core is too massive to become a neutron star. The black hole is bounded by its event horizon, through which nothing can emerge, not even light. The Schwarzschild radius, the radius of the event horizon, is 3 km times the mass of the black hole in solar masses.
All that we can ever learn about a black hole is its mass, angular momentum, and electrical charge. We can detect the presence of black holes, however, by looking for the strong gravitational influence that they have on their immediate surroundings.
