TY - JOUR

T1 - On the ambiguity in the notion of transverse traceless modes of gravitational waves

AU - Ashtekar, Abhay

AU - Bonga, Béatrice

N1 - Funding Information:
Acknowledgements We thank Badri Krishnan, Eric Poisson, István Rácz and especially Aruna Kesavan for discussions. This work was supported in part by the NSF Grant PHY-1505411, the Eberly research funds of Penn State and Mebus Graduate Fellowship to BB. AA thanks the Erwin Schrödinger Institute in Vienna for hospitality during preparation of this manuscript.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Somewhat surprisingly, in many of the widely used monographs and review articles the term Transverse-Traceless modes of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition of the metric perturbation that is local in the momentum space (and hence non-local in physical space), and denote the resulting transverse traceless modes by habTT. However, while discussing gravitational waves emitted by an isolated system—typically in a later section—the relevant modes are extracted using a ‘projection operator’ that is local in physical space. These modes are also called transverse-traceless and again labeled habTT, implying that this is just a reformulation of the previous notion. But the two notions are conceptually distinct and the difference persists even in the asymptotic region. We show that this confusion arises already in Maxwell theory that is often discussed as a prelude to the gravitational case. Finally, we discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.

AB - Somewhat surprisingly, in many of the widely used monographs and review articles the term Transverse-Traceless modes of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition of the metric perturbation that is local in the momentum space (and hence non-local in physical space), and denote the resulting transverse traceless modes by habTT. However, while discussing gravitational waves emitted by an isolated system—typically in a later section—the relevant modes are extracted using a ‘projection operator’ that is local in physical space. These modes are also called transverse-traceless and again labeled habTT, implying that this is just a reformulation of the previous notion. But the two notions are conceptually distinct and the difference persists even in the asymptotic region. We show that this confusion arises already in Maxwell theory that is often discussed as a prelude to the gravitational case. Finally, we discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.

UR - http://www.scopus.com/inward/record.url?scp=85028374062&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028374062&partnerID=8YFLogxK

U2 - 10.1007/s10714-017-2290-z

DO - 10.1007/s10714-017-2290-z

M3 - Article

AN - SCOPUS:85028374062

VL - 49

JO - General Relativity and Gravitation

JF - General Relativity and Gravitation

SN - 0001-7701

IS - 9

M1 - 122

ER -