Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wald's definition of the Cauchy Horizon

  1. Nov 20, 2011 #1


    User Avatar
    Science Advisor
    Gold Member

    Hello, Wald defines, on page 203 the future Cauchy Horizon of a set [itex]S\subset M[/itex] as:


    Where the overline means the closure of the set. D+ is the future domain of dependence (i.e. all points in the manifold which can be connected to S by a past inextendible causal curve), and I- is the chronological past.

    It seems to me that the closure of the set D+ does not include some parts of the set I-(D+) since the second term is the entire chronological past including the chronological past of the points on S.

    Is there a mistake in this definition? I would have thought (intuitively) that the future Cauchy Horizon of a set S would simply be the boundary of the Future domain of dependence of S minus S itself. In that case, Wald defined the interior of D+ as:

    [tex]int(D^+(S))=I^-[D^+(S)]\cap I^+(S)[/tex]

    Perhaps he meant this as the second term? Am I missing something here?
  2. jcsd
  3. Nov 20, 2011 #2


    User Avatar
    Science Advisor
    Gold Member

    Nevermind, I figured it out......my set theory knowledge was weak apparently haha.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Wald's definition Cauchy Date
I "General Relativity" by Wald -- question Feb 22, 2017
I Did Wald make a mistake here? Jun 19, 2016
A Covariant derivative definition in Wald May 6, 2016
Wald Chapter 10 Problem 2 Feb 2, 2014
Linearized Gravity Wald Jan 28, 2014