From db3fd3abc7af0fb85949f373747caf117719f08a Mon Sep 17 00:00:00 2001 From: Vasko Date: Sun, 1 Aug 2021 16:26:30 +0200 Subject: [PATCH] adding calculation of the Euclidean action of the Kerr-Newman black hole --- kerr_newman.nb | 22955 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 22955 insertions(+) create mode 100644 kerr_newman.nb diff --git a/kerr_newman.nb b/kerr_newman.nb new file mode 100644 index 0000000..93b3171 --- /dev/null +++ b/kerr_newman.nb @@ -0,0 +1,22955 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 12.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 833356, 22947] +NotebookOptionsPosition[ 800512, 22502] +NotebookOutlinePosition[ 801053, 22521] +CellTagsIndexPosition[ 801010, 22518] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell[TextData[StyleBox["Kerr-Newman", "Title"]], "Section", + CellChangeTimes->{{3.833209877876775*^9, + 3.8332098887602873`*^9}},ExpressionUUID->"68739284-c599-4be5-8113-\ +ca0ae03ad3e0"], + +Cell[TextData[{ + "Author : Vasil Dimitrov (", + ButtonBox["vasko.dimitrov@kuleuven.be", + BaseStyle->"Hyperlink", + ButtonData->{ + URL["mailto:vasko.dimitrov@kuleuven.be"], None}, + ButtonNote->"mailto:vasko.dimitrov@kuleuven.be"], + ")\nDate: June 2021\nThis notebook first checks that the Kerr-Newman \ +spacetime is a solution to Einstein-Maxwell gravity. Then computes the \ +surface gravity, horizon area, asymptotic charges, Euclidean on-shell action \ +and entropy of the Kerr-Newman black hole. The notebook is composed of \ +independent sections. Each section begins with a preamble (marked by blue \ +lines) where we define the objects that will be needed and ends with Exit \ +(also marked in blue). If you have the auxiliary files in the same folder as \ +the notebook, in principle each section can be evaluated completely \ +independently from the remaining sections. If you want to generate the \ +auxiliary files from scratch then you should evaluate the sections \ +sequentially. The entire notebook takes about 8min to run on my machine. Note \ +that because of the Exit at the end of each section you cannot evaluate the \ +entire notebook at once, but should really do it section by section." +}], "Affiliation", + CellChangeTimes->{{3.833210138233946*^9, 3.83321023715668*^9}, { + 3.833210392952175*^9, 3.8332103929660473`*^9}, {3.8332107147917137`*^9, + 3.8332107161719007`*^9}, {3.833630064452053*^9, 3.83363020686747*^9}, { + 3.8336302772196407`*^9, 3.833630532387092*^9}, {3.8336345234746428`*^9, + 3.833634529586273*^9}},ExpressionUUID->"9073bae4-0b67-4449-bca8-\ +b47e79d7a38e"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["1. 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signs that prevent collisions of indices, then \ +note that at this point `xAct` knows nothing about the following functions\ +\>", "Text", + CellChangeTimes->{{3.833456157425642*^9, + 3.833456247464014*^9}},ExpressionUUID->"2dffc5f5-95c3-491c-9cd3-\ +461a0d159399"], + +Cell[CellGroupData[{ + +Cell[BoxData[{ + RowBox[{"g", "[", + RowBox[{ + RowBox[{"-", "\[Mu]"}], ",", + RowBox[{"-", "\[Nu]"}]}], "]"}], "\[IndentingNewLine]", + RowBox[{"A", "[", + RowBox[{"-", "\[Mu]"}], "]"}], "\[IndentingNewLine]", + RowBox[{ + RowBox[{"PD", "[", + RowBox[{"-", "\[Mu]"}], "]"}], "[", + RowBox[{"A", "[", "\[Mu]", "]"}], "]"}]}], "Input", + CellChangeTimes->{{3.8334562535913553`*^9, 3.8334563004321203`*^9}, { + 3.8334566407446527`*^9, 3.833456644030827*^9}, {3.83361577279951*^9, + 3.833615777475033*^9}, {3.833615943981687*^9, 3.83361594938564*^9}}, + CellLabel->"In[18]:=",ExpressionUUID->"fa545d16-fbde-4f07-890d-c22844cdd6b7"], + +Cell[BoxData[ + RowBox[{"g", "[", + RowBox[{ + RowBox[{"-", "\[Mu]"}], 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