Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity - INSPIRE

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Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity

Poula Tadros
(
- Charles U.
)
,
Ivan Kolář
(
- Charles U.
)

Jan 1, 2024

16 pages

Published in:

Phys.Rev.D 109 (2024) 8, 084019

Published: Apr 10, 2024

e-Print:

2401.00967 [gr-qc]

DOI:

10.1103/PhysRevD.109.084019 (publication)

View in:

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Abstract: (APS)

We show that the seemingly different methods used to derive non-Lorentzian (Galilean and Carrollian) gravitational theories from Lorentzian ones are equivalent. Specifically, the pre-nonrelativistic and the pre-ultralocal parametrizations can be constructed from the gauging of the Galilei and Carroll algebras, respectively. Also, the pre-ultralocal approach of taking the Carrollian limit is equivalent to performing the Arnowitt-Deser-Misner decomposition and then setting the signature of the Lorentzian manifold to zero. We use this uniqueness to write a generic expansion for the curvature tensors and construct Galilean and Carrollian limits of all metric theories of gravity of finite order ranging from the

f (R)

gravity to a completely generic higher derivative theory, the

f (g_{μ ν}, R_{μ ν σ ρ}, \nabla_{μ})

gravity. We present an algorithm for calculation of the

n

th order of the Galilean and Carrollian expansions that transforms this problem into a constrained optimization problem. We also derive the condition under which a gravitational theory becomes a modification of general relativity in both limits simultaneously.

derivative: high
curvature: tensor
gravitation: model
Galilei
algebra
general relativity
parametrization
optimization
signature
asymptotic behavior

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Figures(0)

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