Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity
arXiv:2401.00967 · doi:10.1103/PhysRevD.109.084019
Abstract
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 ADM 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 gravity to a completely generic higher derivative theory, the gravity. We present an algorithm for calculation of the -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.
arXiv commentTypos corrected
References in corpus (60)
- Gauging the Carroll Algebra and Ultra-Relativistic Gravity
- Newtonian Gravity and the Bargmann Algebra
- Carrollian Physics at the Black Hole Horizon
- Flat holography and Carrollian fluids
- Carroll Structures, Null Geometry and Conformal Isometries
- Action Principle for Newtonian Gravity
- Carroll versus Galilei Gravity
- Dynamics of Carroll Particles
- Field Theories with Conformal Carrollian Symmetry
- Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids
- Non-Relativistic Gravity and its Coupling to Matter
- Carroll Expansion of General Relativity
- Consistent Higher Derivative Gravitational theories with stable de Sitter and Anti-de Sitter Backgrounds
- Torsional Newton-Cartan gravity from the large expansion of General Relativity
- Magic Fermions: Carroll and Flat Bands
- Aspects of Nonrelativistic Strings
- Field Theories on Null Manifolds
- Newton-Cartan (super)gravity as a non-relativistic limit
- Carrollian and celestial spaces at infinity
- Dynamics of Carroll Strings
- Review on Non-Relativistic Gravity
- A new formulation of non-relativistic diffeomorphism invariance
- Two-dimensional fluids and their holographic duals
- Post-Newtonian extension of the Newton-Cartan theory
- A Non-Relativistic Limit of NS-NS Gravity
- Non-Boost Invariant Fluid Dynamics
- Carrollian Origins of Bjorken Flow
- Carrollian manifolds and null infinity: A view from Cartan geometry
- Interacting Conformal Carrollian Theories: Cues from Electrodynamics
- The tensionless path from closed to open strings
- Non-linear black hole dynamics and Carrollian fluids
- Planar Carrollean dynamics, and the Carroll quantum equation
- Gauges in Three-Dimensional Gravity and Holographic Fluids
- Superconductivity in type-II Weyl-semimetal WTe2 induced by a normal metal contact
- A Rindler Road to Carrollian Worldsheets
- Near horizon dynamics of three dimensional black holes
- BMS-like symmetries in cosmology
- Covariant formulation of the post-1-Newtonian approximation to General Relativity
- Torsional Newton-Cartan geometry from Galilean gauge theory
- Non-Lorentzian theories with and without constraints
- Nonrelativistic Approximations of Closed Bosonic String Theory
- Galilean Anomalies and Their Effect on Hydrodynamics
- Carrollian Origin of Spacetime Subsystem Symmetry
- Galilean first-order formulation for the non-relativistic expansion of general relativity
- Carroll versus Galilei from a Brane Perspective
- Carrollian Motion in Magnetized Black Hole Horizons
- General theory of Galilean gravity
- Existence and Construction of Galilean invariant Theories
- On the subtelties of nonrelativistic reduction and applications
- Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
- Non-relativistic limits and three-dimensional coadjoint Poincare gravity
- BMS Field Theories and Weyl Anomaly
- A closer glance at black hole pair creation
- Migrating Carrollian particles on magnetized black hole horizons
- Giant thermopower and power factor in magic angle twisted bilayer graphene at low temperature
- A 3+1 formulation of the 1/c expansion of General Relativity
- Carrollian limit of quadratic gravity
- New formulation of Galilean relativistic Maxwell theory
- Non-relativistic limit of gravity theories in the first order formalism
- Non-relativistic gravity theories in four spacetime dimensions