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edited Sep 28 at 13:57

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is there a way to define Defining a perturbation of metric which is not symmetric in lower indices in xAct

I am doing variation and perturbation in xAct, when perturb the metric, can I set the perturbation of metric is not symmetric in lower indices?

DefConstantSymbol[dim, PrintAs -> "D"]
DefManifold[M4, 
  dim, {\[Alpha]α, \[Beta]β, \[Gamma]γ, \[Mu]μ, \[Nu]ν, \[Rho]ρ, \[Sigma]σ, \
\[Kappa]κ, \[Xi]ξ, \[Zeta]ζ, \[Delta]δ}];
DefMetric[-1, Met[-\[Mu]μ, -\[Nu]]ν], 
  CD, {";", "\!\(\*OverscriptBox[\(\[Del]\∇\), \(-\)]\)"}, 
  PrintAs -> "\!\(\*OverscriptBox[\(g\), \(_\)]\)"];
DefMetricPerturbation[Met, \[Delta]MetδMet, \[Tau]τ, PrintAs -> "h"];
DefTensor[h1[-\[Alpha]α, -\[Beta]]β], M4]  ;M4];

is there a way to define a perturbation of metric is not symmetric in lower indices in xAct

I am doing variation and perturbation in xAct, when perturb the metric, can I set the perturbation of metric is not symmetric in lower indices?

DefConstantSymbol[dim, PrintAs -> "D"]
DefManifold[M4, 
  dim, {\[Alpha], \[Beta], \[Gamma], \[Mu], \[Nu], \[Rho], \[Sigma], \
\[Kappa], \[Xi], \[Zeta], \[Delta]}];
DefMetric[-1, Met[-\[Mu], -\[Nu]], 
  CD, {";", "\!\(\*OverscriptBox[\(\[Del]\), \(-\)]\)"}, 
  PrintAs -> "\!\(\*OverscriptBox[\(g\), \(_\)]\)"];
DefMetricPerturbation[Met, \[Delta]Met, \[Tau], PrintAs -> "h"];
DefTensor[h1[-\[Alpha], -\[Beta]], M4]  ;

Defining a perturbation of metric which is not symmetric in lower indices in xAct

I am doing variation and perturbation in xAct, when perturb the metric, can I set the perturbation of metric is not symmetric in lower indices?

DefConstantSymbol[dim, PrintAs -> "D"]
DefManifold[M4, dim, {α, β, γ, μ, ν, ρ, σ, κ, ξ, ζ, δ}];
DefMetric[-1, Met[-μ, -ν], 
  CD, {";", "\!\(\*OverscriptBox[\(∇\), \(-\)]\)"}, 
  PrintAs -> "\!\(\*OverscriptBox[\(g\), \(_\)]\)"];
DefMetricPerturbation[Met, δMet, τ, PrintAs -> "h"];
DefTensor[h1[-α, -β], M4];

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asked Sep 28 at 13:04

Jh Wang

is there a way to define a perturbation of metric is not symmetric in lower indices in xAct

I am doing variation and perturbation in xAct, when perturb the metric, can I set the perturbation of metric is not symmetric in lower indices?

DefConstantSymbol[dim, PrintAs -> "D"]
DefManifold[M4, 
  dim, {\[Alpha], \[Beta], \[Gamma], \[Mu], \[Nu], \[Rho], \[Sigma], \
\[Kappa], \[Xi], \[Zeta], \[Delta]}];
DefMetric[-1, Met[-\[Mu], -\[Nu]], 
  CD, {";", "\!\(\*OverscriptBox[\(\[Del]\), \(-\)]\)"}, 
  PrintAs -> "\!\(\*OverscriptBox[\(g\), \(_\)]\)"];
DefMetricPerturbation[Met, \[Delta]Met, \[Tau], PrintAs -> "h"];
DefTensor[h1[-\[Alpha], -\[Beta]], M4]  ;

xact