General Relativity for Mathematicians：Graduate Texts in Mathematics

Thisisabookaboutphysics,writtenformathematicians.Thereaderswehaveinmindcanberoughlydescribedasthosewho:I.aremathematicsgraduatestudentswithsomeknowledgeofglobaldifferentialgeometry2.havehadtheequivalentoffreshmanphysics,andfindpopularaccountsofastrophysicsandcosmologyinteresting3.appreciatemathematicalelarity,butarewillingtoacceptphysicalmotivationsforthemathematicsinplaceofmathematicalones4.arewillingtospendtimeandeffortmasteringcertaintechnicaldetails,suchasthoseinSection1.1.Eachbookdisappointssomereaders.Thisonewilldisappoint:1.physicistswhowanttousethisbookasafirstcourseondifferentialgeometry2.mathematicianswhothinkLorentzianmanifoldsarewhollysimilartoRiemannianones,orthat,givenasufficientlygoodmathematicalbackground,theessentialsofasubject!ikecosmologycanbelearnedwithoutsomehardworkonboringdetaiis3.thosewhobelievevaguephilosophicalargumentshavemorethanhistoricalandheuristicsignificance,thatgeneralrelativityshouldsomehowbe"proved,"orthataxiomatizationofthissubjectisuseful4.thosewhowantanencyclopedictreatment(thebooksbyHawking-Ellis[1],Penrose[1],Weinberg[1],andMisner-Thorne-Wheeler[I]gofurtherintothesubjectthanwedo;seealsothesurveyarticle,Sachs-Wu[1]).5.mathematicianswhowanttolearnquantumphysicsorunifiedfieIdtheory(unfortunateIy,quantumphysicstextsallseemeithertobeforphysicists,ormerelyconcernedwithformaImathematics).