Schwarzschild radius
Definition: The Schwarzschild radius R_s = 2GM/c² gives the event horizon radius for a non-rotating black hole of mass M; it scales linearly with mass, so more massive black holes have larger (not smaller) event horizons.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.
event horizon
Definition: A black hole’s event horizon is the boundary within which the escape velocity exceeds the speed of light, so no light or information can escape from inside it.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: The Schwarzschild radius R_s = 2GM/c² gives the event horizon radius for a non-rotating black hole of mass M; it scales linearly with mass, so more massive black holes have larger (not smaller) event horizons.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.
singularity
Definition: Black holes form when a collapsing core exceeds the maximum mass supportable by neutron degeneracy pressure (roughly 2-3 M☉); above that, general relativity predicts unstoppable collapse to a singularity cloaked by an event horizon.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: A black hole’s event horizon is the boundary within which the escape velocity exceeds the speed of light, so no light or information can escape from inside it.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.
stellar-mass black hole
Definition: For a 10 M☉ stellar-mass black hole: M = 10 × 1.989e+30 kg = 1.989e+31 kg.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: The Schwarzschild radius R_s = 2GM/c² gives the event horizon radius for a non-rotating black hole of mass M; it scales linearly with mass, so more massive black holes have larger (not smaller) event horizons.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.
supermassive black hole
Definition: The Event Horizon Telescope imaged the shadow of the supermassive black hole in M87 (2019) and Sagittarius A* at the Milky Way’s center (2022), both consistent with the predicted size for their independently measured masses.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: For the Milky Way’s central supermassive black hole, Sagittarius A* (mass ≈ 4.3 × 10⁶ M☉): R_s = 2 × 6.674e-11 × (4.3e6 × 1.989e+30) / (2.998e+08)² ≈ 1.27e+07 km — roughly 430000 times larger than the 10 M☉ case, directly illustrating that R_s scales linearly with mass.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.
gravitational wave
Definition: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Why it matters here: Black holes are the endpoint of collapse for cores too massive for neutron degeneracy pressure to support, with an event horizon size (Schwarzschild radius) that scales linearly with mass and is now directly probed by gravitational-wave and imaging observations.
Relationship: LIGO and Virgo have directly detected gravitational waves from dozens of merging black hole pairs since 2015, with masses and waveforms matching general-relativistic predictions for black hole inspiral and merger.
Boundary or common confusion: Imagining a black hole as a "cosmic vacuum cleaner" that pulls in everything nearby with unusually strong gravity. Outside the event horizon, a black hole’s gravity is identical to that of any other object of the same mass; a Sun-mass black hole at the Sun’s current distance would not pull Earth in any harder than the Sun already does.