Matching Items (14)
Description
This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter β. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R × Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT “knows” when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements.
ContributorsSamantray, Prasant (Author) / Parikh, Maulik (Thesis advisor) / Davies, Paul (Committee member) / Vachaspati, Tanmay (Committee member) / Easson, Damien (Committee member) / Alarcon, Ricardo (Committee member) / Arizona State University (Publisher)
Created2012
Description
A problem of interest in theoretical physics is the issue of the evaporation of black holes via Hawking radiation subject to a fixed background. We approach this problem by considering an electromagnetic analogue, where we have substituted Hawking radiation with the Schwinger effect. We treat the case of massless QED in 1+1 dimensions with the path integral approach to quantum field theory, and discuss the resulting Feynman diagrams from our analysis. The results from this thesis may be useful to find a version of the Schwinger effect that can be solved exactly and perturbatively, as this version may provide insights to the gravitational problem of Hawking radiation.
ContributorsDhumuntarao, Aditya (Author) / Parikh, Maulik (Thesis director) / Davies, Paul C. W. (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
With the discovery of the Higgs Boson in 2012, particle physics has decidedly moved beyond the Standard Model into a new epoch. Though the Standard Model particle content is now completely accounted for, there remain many theoretical issues about the structure of the theory in need of resolution. Among these is the hierarchy problem: since the renormalized Higgs mass receives quadratic corrections from a higher cutoff scale, what keeps the Higgs boson light? Many possible solutions to this problem have been advanced, such as supersymmetry, Randall-Sundrum models, or sub-millimeter corrections to gravity. One such solution has been advanced by the Lee-Wick Standard Model. In this theory, higher-derivative operators are added to the Lagrangian for each Standard Model field, which result in propagators that possess two physical poles and fall off more rapidly in the ultraviolet regime. It can be shown by an auxiliary field transformation that the higher-derivative theory is identical to positing a second, manifestly renormalizable theory in which new fields with opposite-sign kinetic and mass terms are found. These so-called Lee-Wick fields have opposite-sign propagators, and famously cancel off the quadratic divergences that plague the renormalized Higgs mass. The states in the Hilbert space corresponding to Lee-Wick particles have negative norm, and implications for causality and unitarity are examined.
This dissertation explores a variant of the theory called the N = 3 Lee-Wick
Standard Model. The Lagrangian of this theory features a yet-higher derivative operator, which produces a propagator with three physical poles and possesses even better high-energy behavior than the minimal Lee-Wick theory. An analogous auxiliary field transformation takes this higher-derivative theory into a renormalizable theory with states of alternating positive, negative, and positive norm. The phenomenology of this theory is examined in detail, with particular emphasis on the collider signatures of Lee-Wick particles, electroweak precision constraints on the masses that the new particles can take on, and scenarios in early-universe cosmology in which Lee-Wick particles can play a significant role.
This dissertation explores a variant of the theory called the N = 3 Lee-Wick
Standard Model. The Lagrangian of this theory features a yet-higher derivative operator, which produces a propagator with three physical poles and possesses even better high-energy behavior than the minimal Lee-Wick theory. An analogous auxiliary field transformation takes this higher-derivative theory into a renormalizable theory with states of alternating positive, negative, and positive norm. The phenomenology of this theory is examined in detail, with particular emphasis on the collider signatures of Lee-Wick particles, electroweak precision constraints on the masses that the new particles can take on, and scenarios in early-universe cosmology in which Lee-Wick particles can play a significant role.
ContributorsTerBeek, Russell Henry (Author) / Lebed, Richard F (Thesis advisor) / Alarcon, Ricardo (Committee member) / Belitsky, Andrei (Committee member) / Chamberlin, Ralph (Committee member) / Parikh, Maulik (Committee member) / Arizona State University (Publisher)
Created2015
Description
Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$ gravity allows for traversable wormholes among its vacuum solutions. This is surprising to find in such simple setting as these type of solutions usually requires fairly complex constructions to satisfy the equations of motion of a gravitational theory. The second idea is the matter bounce description of the early universe where a fairly unique feature of the model is identified. Consequences of this feature could allow the paradigm to distinguish itself from other alternative descriptions, such as inflation, through late time observations. An explicit example of this claim is worked out by studying a model involving an interaction in the dark sector. Results of a more astrophysical nature, where a careful analysis of the morphology of blazar halos is performed, are also presented in the Appendix. The analysis determined that the $Q$-statistic is an appropriate tool to probe the properties of the intergalactic magnetic fields responsible for the halos formation.
ContributorsDuplessis, Francis (Author) / Easson, Damien (Thesis advisor) / Vachaspati, Tanmay (Committee member) / Mauskopf, Philip (Committee member) / Parikh, Maulik (Committee member) / Arizona State University (Publisher)
Created2017
ContributorsDebussy, Claude, 1862-1918 (Composer) / Hamelin, Gaston (Arranger)
Description
Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC. Using the same argument, I show logarithmic quantum corrections to the Bekenstein-Hawking entropy formula do not alter the form of the Ricci convergence condition, but obscure its connection to the NEC. Then, by attributing thermodynamics to the stretched horizon of future lightcones -- a timelike hypersurface generated by a collection of radially accelerating observers with constant and uniform proper acceleration -- I derive Einstein's equations from the Clausius relation. Based on this derivation I uncover a local first law of gravity, connecting gravitational entropy to matter energy and work. I then provide an entanglement interpretation of stretched lightcone thermodynamics by extending the entanglement equilibrium proposal. Specifically I show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. Using the AdS/CFT correspondence, I then provide a microscopic explanation of the 'thermodynamic volume' -- the conjugate variable to the pressure in extended black hole thermodynamics -- and reveal the super-entropicity of three-dimensional AdS black holes is due to the gravitational entropy overcounting the number of available dual CFT states. Finally, I conclude by providing a recent generlization of the extended first law of entanglement, and study its non-trivial 2+1- and 1+1-dimensional limits. This thesis is self-contained and pedagogical by including useful background content relevant to emergent gravity.
ContributorsSvesko, Andrew (Author) / Parikh, Maulik (Thesis advisor) / Vachaspati, Tanmay (Thesis advisor) / Keeler, Cynthia (Committee member) / Easson, Damien (Committee member) / Arizona State University (Publisher)
Created2020
Description
In this dissertation I discuss about calculating one-loop partition function on curved spacetimes and various approaches to build symmetries of gravitational systems, and extending the analysis to the large dimensional spacetimes. I show the calculations pertaining to the contributions to the one-loop determinant for transverse trace-less gravitons in an $n + 3$-dimensional Schwarzschild black hole background in the large dimension limit, due to the $SO(n+2)$-type tensor and vector fluctuations, using the quasinormal mode method. Accordingly I find the quasinormal modes for these fluctuations as a function of a fiducial mass parameter $\Delta$. I show that the behavior of the one-loop determinant at large $\Delta$ accords with a heat kernel curvature expansion in one lower dimension, lending further evidence towards a membrane picture for black holes in the large dimension limit. I also find that the analysis of building one-loop determinants is similar to that of the AdS, thus serving as a motivation to explore this emergent symmetry in detail. For this, I first build these symmetries for Kerr-(A)dS black holes in arbitrary dimensions and then extend this analysis to the large dimensional Schwarzschild black hole. To study the former, in this dissertation, I discuss how to generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions. I also discuss the results on building the $SL(2, R)$ generators directly from the Killing tower, whose Killing tensors and Killing vectors enforce the separability of the equations of motion. This construction amounts to an explicit relationship between hidden conformal symmetries and Killing tensors: I use the Killing tower to build a novel tensor equation connecting the $SL(2,R)$ Casimir with the radial Klein-Gordon operator. For asymptotically flat black holes in four and five dimensions I discuss that the previously known results that were obtained using the ``near-region'' limit and the monodromy method, were recovered. I also perform a monodromy evaluation of the Klein-Gordon scalar wave equation for all Kerr-(A)dS black holes, finding explicit forms for the zero mode symmetry generators.
Lastly, I discuss the work on extending this analysis to the large-dimensional Schwarzschild black hole as a step towards building a Large-D/CFT correspondence.
ContributorsPriya, Alankrita (Author) / Keeler, Cynthia (Thesis advisor) / Baumgart, Matthew (Committee member) / Parikh, Maulik (Committee member) / Vachaspati, Tanmay (Committee member) / Arizona State University (Publisher)
Created2021
Description
The double copy is a procedure that relates gravity to simpler gauge and scalar field theories. Double copy structure was first discovered in the context of scattering amplitudes, and has since been realized at the level of classical fields and curvatures. This dissertation focuses on mappings between fields (the Kerr-Schild double copy) and curvatures (the Weyl double copy). First, the connection between non-singular black holes and non-singular gauge theories is made, which illuminates a subtlety between gravitational horizons and the gauge field strength. Then, a perturbative double copy in the context of the fluid/gravity duality is presented, where the associated gauge theory quantities have surprisingly elegant interpretations in terms of certain classes of Navier-Stokes solutions. Finally, a new formula that provides a consistent treatment of external sources in the Weyl double copy is introduced. After illustrating its consistency with the Kerr-Schild double copy, the sourced Weyl double copy is applied to the most general Petrov type D electro-vac spacetime. Various limits of the general solution are analyzed, including the Kerr-Newman metric and the charged, accelerating black hole.
ContributorsManton, Tucker Daniel (Author) / Easson, Damien A (Thesis advisor) / Keeler, Cynthia (Committee member) / Parikh, Maulik (Committee member) / Wilczek, Frank (Committee member) / Arizona State University (Publisher)
Created2022
Description
Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein–Hawking entropy.
ContributorsParikh, Maulik (Author) / Svesko, Andrew (Author) / College of Liberal Arts and Sciences (Contributor)
Created2016-08-01
Description
We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.
ContributorsParikh, Maulik (Author) / Sarkar, Sudipta (Author) / College of Liberal Arts and Sciences (Contributor)
Created2016-03-31