Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
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Springer
Received: February 17, Revised: May 17, Accepted: June 3, Published: July 3,
2020 2020 2020 2020
Krishnakanta Bhattacharya,a,b Bibhas Ranjan Majhia and Douglas Singletonb a
Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India b Department of Physics, California State University, Fresno, 2345 East San Ramon Avenue, M/S MH 37, Fresno, CA 93740, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: The duality of gravitational dynamics (projected on a null hypersurface) and of fluid dynamics is investigated for the scalar tensor (ST) theory of gravity. The description of ST gravity, in both Einstein and Jordan frames, is analyzed from fluid-gravity viewpoint. In the Einstein frame the dynamical equation for the metric leads to the Damour-NavierStokes (DNS) equation with an external forcing term, coming from the scalar field in ST gravity. In the Jordan frame the situation is more subtle. We observe that finding the DNS equation in this frame can lead to two pictures. In one picture, the usual DNS equation is modified by a Coriolis-like force term, which originates completely from the presence of a non-minimally coupled scalar field (φ) on the gravity side. Moreover, the identified fluid variables are no longer conformally equivalent with those in the Einstein frame. However, this picture is consistent with the saturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find the standard DNS equation (i.e. without the Coriolis-like force), with the fluid variables conformally equivalent with those in Einstein frame. But, the second picture, may not agree with the KSS bound for some values of φ. We conclude by rewriting the Raychaudhuri equation and the tidal force equation in terms of the relevant parameters to demonstrate how the expansion scalar and the shear-tensor evolve in the spacetime. Although, the area law of entropy is broken in ST gravity, we show that the rewritten form of Raychaudhuri’s equation correctly results in the generalized second law of black hole thermodynamics. Keywords: Black Holes, Classical Theories of Gravity, Gauge-gravity correspondence ArXiv ePrint: 2002.04743
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)018
JHEP07(2020)018
Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
Contents 1 Introduction
1
2 Brief review: equations of motion in the two frames
3 5 5 6 9 9 12
4 The entropy increase theorem 4.1 Einstein frame 4.2 Jordan frame
17 17 18
5 Tidal force equation
19
6 Summary and conclusions
20
1
Introduction
Despite the enormous success of Einstein’s theory of general relativity (GR), there are several indications [1–9] implying that Einstein’s GR might not be a complete theory of gravity. There are several motivations, emerging from both theory [10–13] and from experiment [1, 4, 5], that motivate the study of alternative theories of gravity
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