Answers

ConceptChecks

ConceptCheck 21-1: For anyone riding on the speeding train, the train is not moving relative to the riders. They observe no length contraction or time dilation, so their hearts do not beat more slowly.

ConceptCheck 21-2: All observers, whether moving or not, see light travel at the same speed through the vacuum of space: They all see light travel at c = 3×10⁸ m/s.

ConceptCheck 21-3: Less time has passed on the clock near the planet—the planet’s gravity slows down time; the stronger the gravity, the more time slows down.

ConceptCheck 21-4: No. As the radio waves “climb” out of the gravitational field of the planet, they experience a gravitational redshift—the frequency decreases and the wavelength increases.

ConceptCheck 21-5: Neutron stars can support up to 2 to 3 M_⊙ without collapsing further. Masses larger than this can collapse into black holes, so these are the lowest black hole masses expected from stellar core-collapse.

ConceptCheck 21-6: If an object is compressed, its escape speed increases, and the escape speed also increases if more mass is added to the object while maintaining its size. When an object’s escape speed exceeds the speed of light, no light can escape, and the object becomes a black hole.

ConceptCheck 21-7: Stars do not emit strongly in X-rays, as Cygnus X-1 does. More importantly, fast variations in the X-ray brightness tell us that the mass of Cygnus X-1 is smaller than Earth—far too small for any type of star or other object.

ConceptCheck 21-8: The collapsar supernova model for gamma-ray bursts involves the special case in which jets are formed during the collapse, and one jet of gamma rays points toward Earth. Without the formation and enhanced intensity of jets, a regular supernova (of Type I or II) would be too weak to account for the strength of the observed gamma rays.

ConceptCheck 21-9: No. The larger the mass of a black hole, the lower the average density required to form the black hole. If it could be carried out, filling our solar system with water would produce a very large black hole.

ConceptCheck 21-10: No. Theoretically speaking, the laws of gravity allow a black hole to exist with any mass. However, natural processes in the cosmos might only produce black holes in certain mass ranges.

ConceptCheck 21-11: A black hole’s event horizon is a spherical boundary with a radius given by the Schwarzschild radius. Objects getting closer to the Schwarzschild radius have fallen irreversibly within the event horizon.

ConceptCheck 21-12: At such large distances, the gravitational force is the same from each object. Stronger forces and other effects only show up much closer to a black hole.

ConceptCheck 21-13: It would be safer to fly by the event horizon of the larger black hole, where the gravitational force is actually weaker.

ConceptCheck 21-14: No. Once matter enters a black hole, the only properties of the black hole are its mass, charge, and angular momentum.

ConceptCheck 21-15: Maybe, as it depends on the mass of the black hole. For a supermassive black hole with weak tidal forces, they would not notice their feet being tugged with a greater force than any other part of their body. However, for a stellar-mass black hole, their feet could be pulled relative to their legs by deadly forces.

ConceptCheck 21-16: The smaller the black hole, the larger its temperature. Therefore, the stellar-mass black hole is hotter and radiates more intensely.

ConceptCheck 21-17: No. As black holes lose mass through Hawking radiation, they heat up to even greater temperatures. This causes them to lose even more mass in a process of evaporation, which is more noticeable for smaller black holes.

ConceptCheck 21-18: Small black holes evaporate more quickly and a black hole of this extraordinarily small size would have evaporated long ago if it were produced during the Big Bang. Therefore, the black hole would have been created more recently.