Abstract
The effect of massive scalar perturbations on neutral black string in de Rham–Gabadadze–Tolley (dRGT) massive gravity is investigated through the study of the quasi-normal modes (QNMs). Due to the similarity between the equation of motion of the field in the black-string and black-hole background, similar numerical and analytical techniques can be used to explore the behaviour of the QNMs. We use the asymptotic iteration method (AIM) and the WKB method to numerically calculate the QNMs of scalar perturbation in the black string background with positive cosmological constant. High-momentum behaviour of such QNMs can be analytically approximated by the first-order WKB method with excellent accuracy. For near-extremal black string with event horizon very close to the cosmological horizon, the Pöschl–Teller technique gives accurate analytic formula for the QNMs. When massive-gravity-parameter gamma increases, we found that the scalar modes oscillate with higher frequencies and decay faster. The QNMs of black string in spacetime with negative cosmological constant are explored in all range of possible gamma using the spectral method. We found the movement of the holographic sound poles to collide and form diffusive poles as gamma changes from positive to negative values. We observe no evidence of instability of neutral black string in both positive and negative cosmological constant cases.
Highlights
Four dimensional static spherically symmetric black holes in de Rham–Gabadadze–Tolley (dRGT) massive gravity with and without U (1) charge are constructed explicitly in [11]
Unlike the black string in general relativity, there exists dRGT black string solution even with a positive cosmological constant effectively contributed by the graviton mass
We investigate a rich structure of dRGT massive gravity by calculating the effect of massive charged scalar perturbation on charged dRGT black hole [19]
Summary
Four dimensional static spherically symmetric black holes in dRGT massive gravity with and without U (1) charge are constructed explicitly in [11]. Unlike the black string in general relativity, there exists dRGT black string solution even with a positive cosmological constant effectively contributed by the graviton mass. Similar behaviours are found for the QNMs of black string in the dRGT background, the near-horizon modes of the event horizon and cosmic horizon for positive cosmological constant case are purely diffusive (or negative imaginary) but we will present more detailed analysis elsewhere. Black brane and black string in asymptotically anti de-Sitter (AdS) space with negative cosmological constant are interesting from the holographic duality viewpoint They are dual to the thermal field theory on the boundary whose temperature is identified with the Hawking temperature of the spacetime.
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