Abstract
We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations for stationary black holes and the spectrum of linearised spectrum about black string configurations has been obtained using the membrane equation for EGB gravity. All our results are worked out to linear order in the Gauss-Bonnet parameter.
Highlights
In the limit of spacetime dimensions (D) going to infinity, the late time dynamics (at time scales of order O(1)) of black holes consists of only a finite number of degrees of freedom
We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations
We find the spectrum of light quasi-normal modes of static black holes in EGB gravity in the large D limit from the linearised fluctuations of the membrane about a static spherical configuration
Summary
In the limit of spacetime dimensions (D) going to infinity, the late time dynamics (at time scales of order O(1)) of black holes consists of only a finite number of degrees of freedom. There are an infinitely large number of heavy quasi-normal modes of frequency of the order O(D) which die off in time intervals of the order of O(1/D) Motivated by this the authors of [2] derived a set of effective non-linear equations determining this late time dynamics in terms of variables of a membrane propagating in flat spacetime. The large D effective equations of dynamics within a region of width O(1/D) about static black holes in presence of a GB term was obtained in [21].Further a detailed analysis of linearised modes about Static black holes was carried out and it was shown that the spectrum matches the gravitational computation of QNMs in [19].Similar effe√ctive equations of dynamics about black strings with spatial derivatives of the order O( D) has been worked out in [22] and the Hydro-elastic complementarity study of [14] and the study of turbulent regime of fluid dynamics in large D initiated in [16] was extended to Einstein-Gauss-Bonnet (EGB) gravity in [23]. In addition we analyse the spectrum of linearised fluctuations about a membrane dual to black strings [12] using the modified membrane equations and find that the spectrum matches with the corresponding answers in [22] under a rescaling of spatial derivatives
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