REL-25

Gravitational redshift

Weak-field photon climb.

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GoverningGravitational redshift

Governing equation

z=GM/(rc^2)

$r \in \left[3, 2\times 10^{5}\right]$

where

M: M (Msun)
r: r (km)
z: Gravitational redshift (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

z=GM/(rc^2)

$r \in \left[3, 2\times 10^{5}\right]$

$r = 3$ $z = 0.491$

Along the curve

②

Domain of the variable — blue

r_{\min} = 3,\quad r_{\max} = 2\times 10^{5}

$r \in \left[3, 2\times 10^{5}\right]$

$r = 3$ $r = 3$

Along the curve

③

Response curve — green

z=GM/(rc^2)

$r \in \left[3, 2\times 10^{5}\right]$

$r = 3$ $z = 0.491$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}z}{\mathrm{d}r}

$r \in \left[3, 2\times 10^{5}\right]$

$r = 1260.8$ $z^{\prime} = -1.95\times 10^{-4}$

Along the curve

Lecture brief

Historical brief

Einstein’s 1905 Lorentz kinematics and 1915 field equation, then Schwarzschild (1916) and Hawking temperature, recast time, mass and gravity. The lab computes dilation, E=mc² and horizon scales. This sheet (REL-25 — Gravitational redshift) is the form associated with Gravitational redshift. Working symbols: $M$ , $r$ $\rightarrow$ $z$ . Weak-field photon climb. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

z

from

M

r

in Relativity via

z=GM/(rc^2)

Weak-field photon climb. Use it when a real relativity question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 1.000\,\mathrm{Msun}

r = 7000.000\,\mathrm{km}

, the governing relation

z=GM/(rc^2)

yields

z = 2.106e-4\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

M M1 Msunr r7000 km

Outputs

Gravitational redshift z0.000 —

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Weak-field photon climb. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube