Black hole perturbation in parity violating gravitational theories

Journal Article · Sat Oct 15 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.84.084041· OSTI ID:21607924

Motohashi, Hayato ^[1]; Suyama, Teruaki ^[2]

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1. Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan)
2. Research Center for the Early Universe (RESCEU), Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan)

We study linear perturbations around static, spherically symmetric spacetimes in f(R,C) gravitational theories whose Lagrangians depend on the Ricci scalar R and the parity violating Chern-Simons term C. By an explicit construction, we show that the Hamiltonian for the perturbation variables is not bounded from below, suggesting that such a background spacetime is unstable against perturbations. This gives a strong limit on a phenomenological gravitational model which violates parity. We also show that either R=const or ({partial_derivative}{sup 2}f/{partial_derivative}R{partial_derivative}C)=0 is a necessary and sufficient condition for the stability. We then implement in detail the perturbation analysis for such theories which satisfy the stability conditions. For l{>=}2, where l is the usual integer for the multipole expansion, the number of propagating modes is three, one from the odd and the other two from the even, all of which propagate at the speed of light. Unlike in the case of f(R) theories, these modes are coupled to each other, which can be used as a distinctive feature to test the parity violating theories from observations. The no-ghost conditions and no-tachyon conditions are the same as those in f(R) theories. For the dipole perturbations, the odd and the even modes completely decouple. The odd mode gives a slowly rotating black hole solution whose metric is linearized in its angular momentum. We provide an integral expression of this solution. On the other hand, the even mode propagates at the speed of light. For the monopole perturbation, in addition to a mode which simply shifts the mass of the background black hole, there also exists one even mode that propagates at the speed of light.

• OSTI ID: 21607924
• Journal Information: Physical Review. D, Particles Fields, Vol. 84, Issue 8; Other Information: DOI: 10.1103/PhysRevD.84.084041; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BLACK HOLES
DIPOLES
DISTURBANCES
EXPANSION
GRAVITATION
HAMILTONIANS
LAGRANGIAN FUNCTION
MASS
MATHEMATICAL SOLUTIONS
METRICS
PARITY
PERTURBATION THEORY
QUANTUM FIELD THEORY
RICCI TENSOR
SPACE-TIME
STABILITY
SYMMETRY
VELOCITY
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MULTIPOLES
PARTICLE PROPERTIES
QUANTUM OPERATORS
TENSORS