arXiv subjects
Publications and source records attributed to Maulik Parikh.
We show that effective theories of matter that classically violate the null energy condition cannot be minimally coupled to Einstein gravity without being inconsistent with both string theory and black hole thermodynamics. We argue however that they could still be either non-minimally coupled or coupled to higher-curvature theories of gravity.
We study the power - and bi -spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one -parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch -Davies vacuum state. Selecting the Bunch -Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch -Davies state the hyperbolic de Sitter $n$-point correlation functions have to match the planar de Sitter $n$-point correlation functions. The expressions for the planar and hyperbolic Bunch -Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power - and bi -spectrum. For the bi -spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch -Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.
The topological contribution to black hole entropy of a Gauss-Bonnet term in four dimensions opens up the possibility of a violation of the second law of thermodynamics in black hole mergers. We show, however, that the second law is not violated in the regime where Einstein-Gauss-Bonnet holds as an effective theory and black holes can be treated thermodynamically. For mergers of AdS black holes, the second law appears to be violated even in Einstein gravity; we argue, however, that the second law holds when gravitational potential energy is taken into account.
The null energy condition, in its usual form, can appear to be violated by transformations in the conformal frame of the metric. We propose a generalization of the form of the null energy condition to Jordan frame, in which matter is non-minimally coupled, which reduces to the familiar form in Einstein frame. Using our version of the null energy condition, we provide a direct proof of the second law of black hole thermodynamics in Jordan frame.
We obtain all the stationary vacua of de Sitter space by classifying the inequivalent timelike isometries of the de Sitter group. Besides the static vacuum, de Sitter space also admits a family of rotating vacua, which we use to obtain Kerr-de Sitter solutions in various dimensions. By writing the metric in a coordinate system adapted to the rotating Hamiltonian, we show that empty de Sitter space admits not only an observer-dependent horizon but also an observer-dependent ergosphere.
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 beta, 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.
The topology of extra dimensions can break global Lorentz invariance,singling out a globally preferred frame even in flat spacetime. Through experiments that probe global topology, an observer can determine her state of motion with respect to the preferred frame. This scenario is realized if we live on a brane universe moving through a flat space with compact extra dimensions. We identify three experimental effects due to the motion of our universe that one could potentially detect using gravitational probes. One of these relates to the peculiar properties of the twin paradox in multiply-connected spacetimes. Another relies on the fact that the Kaluza-Klein modes of any bulk field are sensitive to boundary conditions. A third concerns the modification to the Newtonian potential on a moving brane. Remarkably, we find that even small extra dimensions are detectable by brane observers if the brane is moving sufficiently fast.
To an outside observer, a black hole's event horizon appears to behave exactly like a dynamical fluid membrane. We extend this membrane paradigm to black holes in general $f(R)$ theories of gravity. We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity. Using Euclidean methods, we study the thermodynamics of the membrane. We speculate on what theories of gravity admit horizons with fluid properties.
Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. Einstein's equations are not modified and no selection principle is applied to their solutions; Mach's principle is realized wholly within Einstein's general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Specification of both boundary and bulk stress tensors uniquely specifies the geometry and thereby the inertial frames. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically AdS space-times, is consistent with holographic duality.
The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor $\exp(-βω_k)$ replaced by $\exp(ΔS)$, where $S$ is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an ${\cal O} (H/M_p)^2$ modification of the primordial power spectrum of inflationary perturbations, which we determine.