Abstract. The evolution equation for inhomogeneous and anisotropic temperature fluctuation inside a medium is derived within the ambit of Boltzmann Transport Equation (BTE) for a hot gas of massless particles. Also, specializing to a situation created after a heavy-ion collision (HIC), we analyze the Fourier space variation of temperature fluctuation of the medium using its temperature profile. The effect of viscosity on the variation of fluctuations in the latter case is investigated and possible implications for early universe cosmology, and its connection with HICs are also explored.

If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter β, which are related to the usual Rindler vacuum by non-trivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-dependent event horizon but even an observer-dependent ergosphere. We also find rotating vacua in global AdS provided a certain region of spacetime is excluded.

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdS d+1 are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry R × H d−1 . For AdS 3 , the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT "knows" when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.super Yang-Mills theory. Thus in principle one has all the tools necessary to study event horizons in a theory of quantum gravity.While Rindler-AdS space in general dimensions has been described and studied previously, the real power of the AdS/CFT correspondence can be brought to bear when the bulk spacetime dimension is three. For that special case, the boundary theory becomes a two-dimensional CFT living in Minkowski space, with all the ensuing advantages. In particular, the two-point function can be calculated explicitly and the Rindler entropy density can be derived from the Cardy formula. The result matches the Bekenstein-Hawking entropy density of the Rindler horizon precisely, including numerical factors. Even more interestingly, one can probe the causal structure of the spacetime. Remarkably, we find that the boundary theory "knows" when a source has fallen past the Rindler horizon even though, from a bulk point of view, there are no local invariants that mark the presence of the event horizon.This paper is organized as follows. In Section 2, we present the classical geometry of Rindler-AdS space. In Section 3, we quickly review Rindler-AdS thermodynamics. Section 4 describes the boundary theory and contains our main results. The results of the paper are as follows. We calculate the bulk-boundary propagator and the two-point correlation function of operators in the boundary theory. Specializing to AdS 3 , we show that the Cardy formula precisely reproduces the Bekenstein-Hawking entropy density, including the numerical coefficient, both for nonrotating and rotating Rindler-AdS space. We then discuss the relation between Rindler-AdS space and AdS black holes. Next, we turn to perhaps our most interesting derivation. We consider a source that falls freely into the Rindler horizon. By calculating the one-point function of a boundary operator, we show that a "boundary theorist" can tell whether the source has fallen across the horizon. This is the main result of the paper. In Section 5, we consi...

We study the motion of a string in the background of Reissner-Nordstrom black hole, in both AdS as well as asymptotically flat spacetimes. We describe the phase space of this dynamical system through largest Lyapunov exponent, Poincare sections and basins of attractions. We observe that string motion in these settings is particularly chaotic and comment on its characteristics. *

We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by e −βR , where R is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably highorder loop diagrams. We also consider holographic theories in d-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in d = 2 and is below the bound for d > 2. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.