Torsion mass generation induced by Einstein–Cartan gravity with a Barbero–Immirzi Higgs field analogue

Abstract It is well known that torsion waves in teleparallel Einstein gravity may induce gravitational waves (GWs). In this paper we show that a modification to Holst gravity induces low-frequency torsion waves of torsional frequency $$\sim {10^{12}Hz}= 1THz$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> <mml:mi>H</mml:mi> <mml:mi>z</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mi>T</mml:mi> <mml:mi>H</mml:mi> <mml:mi>z</mml:mi> </mml:mrow> </mml:math> as GWs sourced from astrophysical black holes. Of course, since here we use the almost Riemann-flat manifold approximation, there are no Riemannian GWs as in teleparallel spacetime but only torsionful gravitational waves. This result in Holst gravity allows us to determine an upper bound for the Barbero–Immirzi (BI) parameter as $$\gamma&lt;&lt;&lt;10^{-58}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mo>&lt;</mml:mo> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>58</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , which agrees with the BI bound obtained by Aliberti and Lambiase by considering matter–anti-matter asymmetry in Holst gravity. Unfortunately, this very interesting result suffers from the usual torsion ambiguity. To remedy this situation, we proceed with the BI parameter promoted to a field ore BI scalarization. Again we find a BI parameter with a bound of $$10^{-58}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>58</mml:mn> </mml:mrow> </mml:msup> </mml:math> from a terahertz-frequency torsion wave. The BI parameter is promoted to a field, and with specific approximation one obtains a BI wave equation with a plane wave solution, similar to those obtained by Taveras and Yunes. From this wave equation constant the BI parameter implies zero torsion, and consequently general relativity (GR), but the converse is not true. Higgs field variation is regarded as responsible for massive torsion. This comes from an analogy between the Higgs field and BI scalar.