Applying the relation between Euclidean on-shell action in the bulk and free energy on the holographic screen to a test charged particle in the charged R-N black hole, we show that not only gravity but also electromagnetic force can be regarded as a sort of thermal force, which accomplishes the unification of gravity and electromagnetism to some extent. In addition, taking into account the fact that both the temperature and thermal force of the dual system are measured at infinity, we argue that the dual holographic screen may be located at infinity.
By following the spirit of Verlinde's entropic force proposal arXiv:1001.0785, we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is consistent with equipartition principle and the form of Komar mass. The entropy of the holographic screen determines its area, i. e. $S=\frac{A}{4}$. And then we express the metric by thermodynamic variables, to give an illustration of how the space is foliated by the thermodynamical potentials.
We introduce higher-derivative Gauss-Bonnet correction terms in the gravity sector and we relate the modified gravity theory in the bulk to the strongly coupled quantum field theory on a de Sitter boundary. We study the process of holographic thermalization by examining three nonlocal observables, the two-point function, the Wilson loop and the holographic entanglement entropy. We study the time evolution of these three observables and we find that as the strength of the Gauss-Bonnet coupling is increased, the saturation time of the thermalization process to reach thermal equilibrium becomes s…
Gravitational collapse of a shell of dust in noncommutative geometry is probed by the renormalized geodesic length, which is dual to probe the thermalization by the two-point correlation function in the dual conformal field theory. We find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. We also investigate how the noncommutative parameter affects the thermalization velocity and thermalization acceleration.
We investigate the implications of the entropic force formalism proposed by Verlinde. We show that an UV/IR relation proposed by Cohen et al, as well as an uncertainty principle proposed by Hogan can be derived from the entropic force formalism. We show that applying the entropic force formalism to cosmology, there is an additional term in the Friedmann equation, which can be identified as holographic dark energy. We also propose an intuitive picture of holographic screen, which can be thought of as an improvement of Susskind's holographic screen.
We introduce the isothermal cavity, static holographic screen, and accelerating surface as holographic screen to study the entropic force in the presence of the Schwarzschild black hole. These may merge to provide a consistent holographic screen to define the entropic force on the stretched horizon near the event horizon. Considering the similarity between the stretched horizon of black hole and the entanglement system, we may define the entropic force in the entanglement system without referring the source mass.
We study holographic thermalization in spacetimes with a chemical potential and a non-trivial dilaton field. Three non-local observables are used to probe the whole process and investigate the effect of the ratio of the chemical potential over temperature $χ$ and the dilaton-Maxwell coupling constant $α$. It is found that the saturation time is not always a monotonically increasing function of $χ$, the situation depends on $α$. When $0 \leqα\leq 1$, larger $χ$ yields longer saturation time, while for $α>1$, the situation becomes more complex. More interesting, we found that although $α$ indeed…
We show that in the Randall-Sundrum model the Casimir energy of bulk gauge fields (or any of their supersymmetric relatives) has contributions that depend logarithmically on the radion. These contributions satisfactorily stabilize the radion, generating a large hierarchy of scales without fine-tuning. The logarithmic behaviour can be understood, in a 4D holographic description, as the running of gauge couplings with the infrared cut-off scale.
We study the thermal helicity, defined in arXiv:1211.3850, of a conformal field theory with anomalies in the context of AdS$_{2n+1}$/CFT$_{2n}$. To do so, we consider large charged rotating AdS black holes in the Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant using fluid/gravity expansion. We compute the anomaly-induced current and stress tensor of the dual CFT in leading order of the fluid/gravity derivative expansion and show their agreement with the field theoretical replacement rule for the thermal helicity. Such replacement rule is reflected in the bulk by new …
We determine holographically 2-point correlators of gauge invariant operators with large conformal weights and entanglement entropy of strips for a time-dependent anisotropic 5-dimensional asymptotically anti-de Sitter spacetime. At the early stage of evolution where geodesics and extremal surfaces can extend beyond the apparent horizon all observables vary substantially from their thermal value, but thermalize rapidly. At late times we recover quasi-normal ringing of correlators and holographic entanglement entropy around their thermal values, as expected on general grounds. We check the beha…
We propose a new holographic program of gravity in which we introduce a surface stress tensor. Our proposal differs from Verlinde's in several aspects. First, we use an open or a closed screen, a temperature is not necessary but a surface energy density and pressure are introduced. The surface stress tensor is proportional to the extrinsic curvature. The energy we use is Brown-York energy and the equipartiton theorem is violated by a non-vanishing surface pressure. We discuss holographic thermodynamics of a gas of weak gravity and find a chemical potential, and show that Verlinde's program doe…
Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynamical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature $T_D$. The modified entropic force returns to the Newton's law of gravitation whi…
We show how the maximum force principle can be derived from the holographic principle and vice versa, thus demonstrating equivalence of the two principles.
We study the mixed state entanglement in a holographic axion model. We find that the holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) exhibit very distinct behaviors with system parameters. The HEE exhibits universal monotonic behavior with system parameters, while the behaviors of MI and EoP relate to the specific system parameters and configurations. We find that MI and EoP can characterize mixed state entanglement better than HEE since they are less affected by thermal effects. Moreover, we argue that EoP is more suitable for describing …
We investigate a possibility of realizing the entropic force into the cosmology. A main issue is how the holographic screen is implemented in the Newtonian cosmology. Contrary to the relativistic realization of Friedmann equations, we do not clarify the connection between Newtonian cosmology and entropic force because there is no way of implementing the holographic screen in the Newtonian cosmology.
We study holographic phase transitions in (2+1) dimensions that possess interacting phases which result from a direct coupling between the two U(1) gauge fields. This can be interpreted as a non-minimal interaction between the electric and spin motive forces of the dual model. We first present a new analytical solution of the Einstein-Maxwell equations that describes a black hole with charge non-equivalent to the sum of the asymptotic charges of the two U(1) gauge fields and briefly discuss formation of uncharged scalar hair on this solution. We then study the formation of charged scalar hair …
Assuming gauge/gravity correspondence we study reheating of the Universe using its holographic dual. Inflaton decay and thermalisation of the decay products correspond to collapse of a spherical shell and formation of a blackhole in the dual anti-de Sitter (AdS) spacetime. The reheating temperature is computed as the Hawking temperature of the developed blackhole probed by a dynamical boundary, and is determined by the inflaton energy density and the AdS radius, with corrections from the dynamics of the shell collapse. For given initial energy density of the inflaton field the holographic mode…
Recently it has been shown that the thermal holographic fluctuations can give rise to an almost scale invariant spectrum of metric perturbations since in this scenario the energy is proportional to the area of the boundary rather than the volume. Here we calculate the non-Gaussianity of the spectrum of cosmological fluctuations in holographic phase, which can imprint on the radiation dominated universe by an abrupt transition. We find that if the matter is phantom-like, the non-Gaussianity $f_{NL}^{equil}$ can reach ${\cal O}(1)$ or even be larger than ${\cal O}(1)$. Especially in the limit $ω…
We investigate the temperature and energy on holographic screens for 4-dimensional black holes with the entropic force idea proposed by Verlinde. We find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature on the horizon and can be considered as a generalized Hawking temperature on the holographic screen outside the horizons. The energy on the holographic screen is not the black hole mass $M$ but the reduced mass $M_0$, which is related to the black hole parameters. With the replacement of the black hole mass $M$ by the reduced mass $M_0$, the entropic force can be writte…
Recently, Verlinde conjectured that gravity may be an entropic force, arising from thermodynamics on the holographic screen. We investigate the implications of the entropic force formalism for inflationary cosmology. We find the background dynamics of inflation can be dually described in the holographic language. At the perturbation level, two kinds of novel scale invariant scalar fluctuations arise from thermal fluctuations on the holographic screen. These fluctuations can be responsible for CMB anisotropy and structure formation.
Using gauge/gravity duality, we study the thermalization of strongly coupled N = 4 supersymmetric Yang-Mills plasma. We analyze the expectation value of the stress tensor and scalar correlation functions and the applicability of the fluctuation dissipation theorem. Via gauge/gravity duality, this maps into studying the equilibration of a black hole geometry and its Hawking radiation.
Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
In this paper, we suppose that the universe begins in a holographic thermal equilibrium phase with the diverged correlation length, and the phase transition to the radiation phase of standard cosmology goes with the abrupt reducing of correlation length. In this case, the primordial perturbations may be induced by thermal fluctuations in this holographic phase. We calculate the spectra of this holographic primordial perturbations, and find that the scalar spectrum has a slightly red tilt and the tensor perturbation amplitude has a moderate ratio, which may be tested in coming observations. The…
The Schwarzschild singularity is known to be classically unstable. We demonstrate a simple holographic consequence of this fact, focusing on a perturbation that is uniform in boundary space and time. Deformation of the thermal state of the dual CFT by a relevant operator triggers a nonzero temperature holographic renormalization group flow in the bulk. This flow continues smoothly through the horizon and, at late interior time, deforms the Schwarzschild singularity into a more general Kasner universe. We show that the deformed near-singularity, trans-horizon Kasner exponents determine specific…
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Minsner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theor…
Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh-Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable…
We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated…
A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum correction to the partition function in the bulk and the corresponding subleading correction at large N on the boundary. In this paper we probe this prediction for a class of quotients of hyperbolic space by a discrete subgroup of isometries. We restrict to the simplest situation of a…
We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to th…
We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI) and the holographic entanglement of purification (EoP) over the superconductivity phase transition. We find that HEE, MI and EoP can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with…
Holographic duality provides a first-principles approach to investigate real time processes in quantum many-body systems, in particular at finite temperature and far-from-equilibrium. We use this approach to study the dynamical evolution of vortex number in a two-dimensional (2D) turbulent superfluid through numerically solving its gravity dual. We find that the temporal evolution of the vortex number can be well fit statistically by two-body decay due to the vortex pair annihilation featured relaxation process, thus confirm the previous suspicion based on the experimental data for turbulent s…
Time dependent perturbations of states in the holographic dual of a 3+1 dimensional confining theory are considered. The perturbations are induced by varying the coupling to the theory's most relevant operator. The dual gravitational theory belongs to a class of Einstein-dilaton theories which exhibit a mass gap at zero temperature and a first order deconfining phase transition at finite temperature. The perturbation is realized in various thermal bulk solutions by specifying time dependent boundary conditions on the scalar, and we solve the fully backreacted Einstein-dilaton equations of moti…
The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: $S\leq S_{\text{max}}={\cal A}/4{\ell^2_P}$ (here $\ell_P$ is the Planck length). An intriguing possible counter-example to this fundamental entropy bound, which involves {\it homogenous} weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, has been proposed almost a decade ago. Interestingly, in the present paper we shall prove t…
We develop a new method for computing the holographic retarded propagator in generic (non-)equilibrium states using the state/geometry map. We check that our method reproduces the thermal spectral function given by the Son-Starinets prescription. The time-dependence of the spectral function of a relevant scalar operator is studied in a class of non-equilibrium states. The latter are represented by AdS-Vaidya geometries with an arbitrary parameter characterising the timescale for the dual state to transit from an initial thermal equilibrium to another due to a homogeneous quench. For long quenc…
We introduce a new interpretation of chemical potential and show that holographic entropy is entropy bound, which is supported by two ideal cases discussed in detail. One is sparse but incompressible liquid like a star of uniform density and the other is a screen at infinity in spherically symmetric sapcetime. Our work is based on the new scenario of entropy force and holographic thermodynamics, and the Brown-York quasi-local energy.
