data/43.json
{
"definitions": {
"f^{\\mu}": [
"4-acceleration",
{}
],
"G": [
{
"Q18373": " gravitational constant (empirical physical constant)"
}
],
"c": [
{
"Q2111": "speed of light (speed at which all massless particles and associated fields travel in vacuum)"
}
],
"A": [
{
"Q1289248": "scalar (real numbers in the context auf linear algebra)"
}
],
"T_{\\alpha\\beta}": [
{
"Q876346": "Stress–energy tensor"
}
],
"B": [
{
"Q1289248": "scalar (real numbers in the context auf linear algebra)"
}
],
"T": [
"trace of the stress energy tensor",
{}
],
"\\eta_{\\alpha\\beta}": [
"Minkowski metric",
{
"Q464794": "Minkowski spacetime (mathematical space setting which eases explanation of special relativity)"
}
],
"\\delta _{\\nu}^{\\mu}": [
{
"Q193794": "identity matrix (n × n square matrix with ones on the main diagonal and zeros elsewhere)",
"Q192826": "Kronecker delta (function)"
}
],
"u^{\\mu}": [
"4-velocity",
{}
],
"u_{\\nu}": [
"4-velocity",
{}
],
"u^{\\alpha}": [
"4-velocity",
{}
],
"x^{\\nu}": [
"4-position",
{}
],
"u^{\\beta}": [
"4-velocity",
{}
]
},
"constraints": [],
"math_inputtex": " f^{\\mu} = - 8\\pi { G \\over { 3 c^4 } } \\left ( {A \\over 2} T_{\\alpha \\beta} + {B \\over 2} T \\eta_{\\alpha \\beta} \\right ) \\left ( \\delta^{\\mu}_{\\nu} + u^{\\mu} u_{\\nu} \\right ) u^{\\alpha} x^{\\nu} u^{\\beta} ",
"math_inputtex_semantic": "\\wDef{Q2283172}{f}\\wDef{Q1738991}{\\mu}} \\tensor{f}{\\mu}{} = - 8\\pi {\\w{Q18373}{G} \\over { 3 \\w{Q2111}{c}^4 } } \\left ( {\\w{Q1289248}{A} \\over 2} \\w{Q876346}{T}_{\\alpha \\beta} + {\\w{Q1289248}{B} \\over 2} \\w{Q47004388}{T} \\w{Q464794}{\\eta}_{\\alpha \\beta} \\right ) \\left ( \\w{Q192826}{\\delta}^{\\mu}_{\\nu} + \\w{Q1322540}{u}^{\\mu} \\w{Q1322540}{u}_{\\nu} \\right ) \\w{Q1322540}{u}^{\\alpha} \\w{Q844610}{x}^{\\nu} \\w{Q1322540}{u}^{\\beta}",
"correct_tex": "f^{\\mu} = - 8\\pi { G \\over { 3 c^4 } } \\left ( {A \\over 2} T_{\\alpha \\beta} + {B \\over 2} T \\eta_{\\alpha \\beta} \\right ) \\left ( \\delta^{\\mu}_{\\nu} + u^{\\mu} u_{\\nu} \\right ) u^{\\alpha} x^{\\nu} u^{\\beta}",
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"title": "Theoretical_motivation_for_general_relativity",
"comment": "einstein notation",
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}