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===Metric signature=== In [[General relativity|relativity]], the [[metric signature]] can be either {{math|(+,β,β,β)}} or {{math|(β,+,+,+)}}. (Throughout this article, the signs of the eigenvalues of the metric are displayed in the order that presents the timelike component first, followed by the spacelike components). A similar convention is used in higher-dimensional relativistic theories; that is, {{math|(+,β,β,β,...)}} or {{math|(β,+,+,+,...)}}. A choice of signature is associated with a variety of names, physics discipline, and notable graduate-level textbooks: {| class="wikitable plainrowheaders" |+ Comparison of metric signatures in [[general relativity]] |- ! scope="row" | Metric signature ! scope="col" | {{abbr|1={{math|(+,β,β,β)}}|2=plus minus minus minus signature}} ! scope="col" | {{abbr|1={{math|(β,+,+,+)}}|2=minus plus plus plus signature}} |- ! scope="row" | [[Spacetime interval]] convention | [[timelike]], <math>\tau^2 = x^\mu x_\mu</math> | [[spacelike]], <math>\tau^2 = -x^\mu x_\mu</math> |- ! scope="row" | Subject area primarily using convention | [[Particle physics]] and [[General relativity|Relativity]] | [[General relativity|Relativity]] |- style="text-align: center" ! scope="row" | Corresponding [[metric tensor]] | <math display="inline">\begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{pmatrix}</math> | <math display="inline">\begin{pmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}</math> |- style="text-align: center" ! scope="row" | Massβ[[four momentum]] relationship | <math display="inline">m^2 = p^{\mu}p_{\mu}</math> | <math display="inline">m^2 = -p^{\mu}p_{\mu}</math> |- ! scope="row" | Common names of convention | * [[West Coast of the United States|West coast]] convention * "Mostly minuses" * [[Lev Landau|Landau]]β[[Evgeny Lifshitz|Lifshitz]] sign convention | * [[East Coast of the United States|East coast]] convention * "Mostly pluses" * Pauli convention |- ! scope="row" | Graduate textbooks using convention | * [[Course_of_Theoretical_Physics#English_editions|Landau & Lifshitz]] * ''The Mathematical Theory of Black Holes'' ([[Subrahmanyan Chandrasekhar]]) * ''Gravitation: an introduction to current research'' ([[Louis Witten|L. Witten]]) * ''Introducing Einstein's relativity'' (Ray D'Inverno) * ''General relativity'' (Michael P. Hobson, [[George Efstathiou]] & Anthony N. Lasenby) | * ''[[Gravitation (book)|Gravitation]]'' (Misner, Thorne, and Wheeler) * ''Spacetime and Geometry: An Introduction to General Relativity'' ([[Sean M. Carroll]]) * ''[[General Relativity (book)|General Relativity]]'' (Wald) (Wald changes signature to the timelike convention for Chapter 13 only) |}
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