Message: 6 Date: Sun, 20 Oct 2013 06:03:58 -0700 From: Henry Baker <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Subject: [math-fun] Stupid GR question Message-ID: <E1VXsgM-0003Il-25@elasmtp-banded.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii"
I've been watching Leonard Susskind's lectures on GR (available on the Internet) & had a question.
A non-rotating black hole is completely characterized by its mass & therefore its Schwarzschild radius.
A bigger black hole has a bigger Schwarzschild radius, and space in the vicinity of the Schwarzschild radius of a very large black hole is relatively flat.
Q: Can a point observer outside the Schwarzschild radius of a black hole tell how big the black hole is by examining the curvature of space very near the observer?
--time the period of your circular orbit about the hole and measure the length of your orbital path, thus deducing, e.g. your acceleration (which is a "local curvature" measure) and the mass of the hole. If that was not local enough, then measure your acceleration directly by moving your arm in a straight line (following light beam) while rest of you moves in orbit; difference is acceleration to good approximation anyhow. Also, several copies of you slightly displaced will move apart (differing orbits) at a rate of acceleration (tidal) which again allows inference both of local curvature & the hole mass, at least if you know your orbit circular.