Remarks on infinite towers of gravitational memories
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Springer
Received: September 9, 2020 Accepted: October 13, 2020 Published: November 20, 2020
Pujian Mao Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, P.R. China
E-mail: [email protected] Abstract: An infinite tower of gravitational memories was proposed in [1] by considering the matter-induced vacuum transition in the impulsive limit. We give an alternative realization of the infinite towers of gravitational memories in Newman-Penrose formalism. We also demonstrate that the memories at each order can be associated to the same supertranslation instead of infinite towers of supertranslations or superrotations. Keywords: Classical Theories of Gravity, Gauge Symmetry ArXiv ePrint: 2008.12109
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)102
JHEP11(2020)102
Remarks on infinite towers of gravitational memories
Contents 1
2 Infinite towers of gravitational memories in Newman-Penrose formalism
2
3 The relation to supertranslations
3
4 Infinite towers of conservation laws
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5 Comment on the relation to soft theorems
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6 Conclusion
7
A Spin-weighted derivative operators
7
1
Introduction
Gravitational memory [2–5] obtained rewed attentions in recent years since its intrinsic connections to BMS supertranslations and soft graviton theorem were revealed [6]. The gravitational memory formula is a Fourier transformation of soft graviton theorem. While the memory effect is a consequence of the fact that the gravitational radiation induces transitions among two different vacua that are connected by BMS supertranslations. The triangle relation [7] has accumulated considerable evidence in its favor in particular in discovering new features of gravitational memory. In [1], it was reported that infinite towers of gravitational memory effects can be generated by matter-induced transitions (see also [8] from the soft theorem side). In this paper, we show that the infinite towers of gravitational memories can be derived in the Newman-Penrose (NP) formalism [9]. The gravitational wave is characterized by the asymptotic shear σ 0 and σ 0 in the NP formalism. The infinite towers of gravitational memories are derived from the evolution of the components of the Weyl tensor. The memory effect at each order is encoded in different choices of σ 0 and σ 0 . The infinite towers of gravitational memories can be associated to the unique BMS supertranslation rather than infinite towers of supertranslations and superrotations proposed in [1]. There are infinite conserved quantities in NP formalism at each order [10] which can be associated to the unique supertranslation charge [11]. The gravitational memories are equivalent to soft graviton theorems at the first two orders [6, 12]. We show that the derivation of equivalence for the first two orders is not valid at the third order. Thus the connection beyond the second order is still obscure. In the present work, we are restricted in linearized gravitat
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