AST-08

Schwarzschild radius

r_s = 2 G M / c². Event-horizon scale of a non-spinning black hole.

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GravitySchwarzschild

Governing equation

r_s=2GM/c^2

where

M: Mass (M_\odot)
r_s: Schwarzschild radius (km)

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-08 — Schwarzschild radius) is the form associated with Schwarzschild. Working symbols: $M$ $\rightarrow$ $r_s$ . The Sun's r_s is 3 km. Nothing inside r_s communicates with infinity.

Purpose

Purpose: compute

r_s

from

M

in Astrophysics via

r_s=2GM/c^2

r_s = 2 G M / c². Event-horizon scale of a non-spinning black hole. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 10.000\,\mathrm{M_odot}

, the governing relation

r_s=2GM/c^2

yields

r_s = 29.53\,\mathrm{km}

. A hole, a photon sphere, an r_s ring. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass M10 M_\odot

Outputs

Schwarzschild radius r_s29.53 km

Reading speed

Watch on YouTube

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00:0 / 00:08

Narration of this film

A hole, a photon sphere, an r_s ring.

The Sun's r_s is 3 km. Nothing inside r_s communicates with infinity.

Reading speed

Watch on YouTube