Phase transition of holographic entanglement entropy in massive gravity

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculate the minimal surface area for a black hole and black brane respectively. In the entanglement entropy$-$temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy$-$temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.Comment: 15 pages, many figures, some statments are adde

Electromagnetic counterparts of high-frequency gravitational waves having additional polarization states: distinguishing and probing tensor-mode, vector-mode and scalar-mode gravitons

GWs from extra dimensions, very early universe, and some high-energy astrophysical process, might have at most six polarizations: plus- and cross-type (tensor-mode gravitons), x-, y-type (vector-mode), and b-, l-type (scalar-mode). Peak or partial peak regions of some of such GWs are just distributed in GHz or higher frequency band, which would be optimal band for electromagnetic(EM) response. In this paper we investigate EM response to such high-frequency GWs(HFGWs) having additional polarizations. For the first time we address:(1)concrete forms of analytic solutions for perturbed EM fields caused by HFGWs having all six possible polarizations in background stable EM fields; (2)perturbed EM signals of HFGWs with additional polarizations in three-dimensional-synchro-resonance-system(3DSR system) and in galactic-extragalactic background EM fields. These perturbative EM fields are actually EM counterparts of HFGWs, and such results provide a novel way to simultaneously distinguish and display all possible six polarizations. It is also shown: (i)In EM response, pure cross-, x-type and pure y-type polarizations can independently generate perturbative photon fluxes(PPFs, signals), while plus-, b- and l-type polarizations produce PPFs in different combination states. (ii) All such six polarizations have separability and detectability. (iii)In EM response to HFGWs from extra-dimensions, distinguishing and displaying different polarizations would be quite possible due to their very high frequencies, large energy densities and special properties of spectrum. (iv)Detection band(10^8 to 10^12 Hz or higher) of PPFs by 3DSR and observation range(7*10^7 to 3*10^9 Hz) of PPFs by FAST (Five-hundred-meter-Aperture-Spherical Telescope, China), have a certain overlapping property, so their coincidence experiments will have high complementarity.Comment: 27 pages, 16 figure