arXiv subjects

Maulik Parikh

Publications and source records attributed to Maulik Parikh.

At least 19 recordsLinked to original sources

arXiv2025

Squeezed States in Gravity

We present a general framework for the production of squeezed quantum states of the gravitational field in linearized quantum gravity. Time-dependent couplings in the quadratic part of the action generically produce squeezed states from the vacuum. Using the harmonic oscillator as an example, we describe three techniques to obtain the squeezing parameter from such quadratic terms. For gravity, the action to quadratic order in metric perturbations contains couplings both to background curvature as well as to matter sources. Thus, both time-dependent classical spacetimes and time-dependent classical matter typically produce squeezed states of gravity.

gr-qc↗

arXiv2024

Quantum uncertainty in the area of a black hole

Quantum fluctuations of the spacetime metric induce an uncertainty in the horizon area of a black hole. Working in linearized quantum gravity, we derive the variance in the area of a four-dimensional Schwarzschild black hole from the renormalized graviton propagator. We find that the standard deviation of the horizon area scales as the product of the Schwarzschild radius and the Planck length. For macroscopic black holes, the quantum uncertainty is therefore enormous in Planck units.

hep-th↗

arXiv2023

Quantum-Gravitational Null Raychaudhuri Equation

We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity.

gr-qc↗

arXiv2023

Quantum-gravitational noise correlation in nearby detectors

We consider quantum gravity fluctuations in a pair of nearby gravitational wave detectors. Quantum fluctuations of long-wavelength modes of the gravitational field induce coherent fluctuations in the detectors, leading to correlated noise. We determine the variance and covariance in the lengths of the arms of the detectors, and thereby obtain the graviton noise correlation. We find that the correlation depends on the angle between the detector arms as well as their separation distance. Using our result, we propose an experimental setup to detect this noise. The suggested interferometer configuration can be used to distinguish quantum-gravitational noise from both correlated and uncorrelated sources of background noise.

gr-qc↗

arXiv2023

Quantum Gravity Fluctuations in the Timelike Raychaudhuri Equation

We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations of the spacetime metric. We calculate the change in the volume of a bundle of geodesics due to such fluctuations and thereby obtain a quantum-gravitationally modified timelike Raychaudhuri equation. Quantum gravity generically increases the convergence of congruences and the production of caustics.

gr-qc↗

arXiv2023

Quantum Gravity Corrections to the Fall of the Apple

We consider the motion of a massive particle in a static, weakly-curved spacetime where the gravitational field is taken to be quantized. We find that Newton's law of free-fall is modified by quantum-gravitational corrections, in addition to the known special-relativistic and post-Newtonian modifications. The quantum-gravitational corrections take the form of stochastic noise in the particle trajectory, where the statistical properties of the noise depend on the quantum state of the gravitational field.

gr-qc↗

arXiv2021

The Stringy Origins of Galileons and their Novel Limit

We show generalized Galileons -- a particular subclass of Horndeski gravity -- arise from a consistent Kaluza-Klein reduction of the low-energy effective action of heterotic string theory to first order in $α'$. This suggests Horndeski theories of gravity have a string-theoretic origin. The form of the Galileonic terms is precisely fixed by parameters of the embedding spacetime, so that only a specific subset of Horndeski theories is permitted by string theory. A novel limit of the model is considered by performing a dimensionful rescaling of $α'$.

hep-th↗

arXiv2020

A Local First Law of Gravity

We find a (quasi-)local first law of thermodynamics, $ΔE = T ΔS - W$, connecting gravitational entropy, $S$, with matter energy and work. For Einstein gravity $S$ is the Bekenstein-Hawking entropy, while for general theories of gravity $S$ is the Wald entropy, evaluated on the stretched future light cone of any point in an arbitrary spacetime, not necessarily containing a black hole. The equation can be written as $ρΔV = T ΔS - p ΔV$ by regarding the energy-momentum tensor as that of a fluid.

gr-qc↗

arXiv2020

The Noise of Gravitons

We show that when the gravitational field is treated quantum-mechanically, it induces fluctuations -- noise -- in the lengths of the arms of gravitational wave detectors. The characteristics of the noise depend on the quantum state of the gravitational field, and can be calculated exactly in several interesting cases. For coherent states the noise is very small, but it can be greatly enhanced in thermal and (especially) squeezed states. Detection of this fundamental noise would constitute direct evidence for the quantization of gravity and the existence of gravitons.

hep-th↗

arXiv2020

Signatures of the Quantization of Gravity at Gravitational Wave Detectors

We develop a formalism to calculate the response of a model gravitational wave detector to a quantized gravitational field. Coupling a detector to a quantum field induces stochastic fluctuations ("noise") in the length of the detector arm. The statistical properties of this noise depend on the choice of quantum state of the gravitational field. We characterize the noise for vacuum, coherent, thermal, and squeezed states. For coherent states, corresponding to classical gravitational configurations, we find that the effect of gravitational field quantization is small. However, the standard deviation in the arm length can be enhanced -- possibly significantly -- when the gravitational field is in a non-coherent state. The detection of this fundamental noise could provide direct evidence for the quantization of gravity and for the existence of gravitons.

hep-th↗

arXiv2020

Quantum Mechanics of Gravitational Waves

For the purpose of analyzing observed phenomena, it has been convenient, and thus far sufficient, to regard gravity as subject to the deterministic principles of classical physics, with the gravitational field obeying Newton's law or Einstein's equations. Here we treat the gravitational field as a quantum field and determine the implications of such treatment for experimental observables. We find that falling bodies in gravity are subject to random fluctuations ("noise") whose characteristics depend on the quantum state of the gravitational field. We derive a stochastic equation for the separation of two falling particles. Detection of this fundamental noise, which may be measurable at gravitational wave detectors, would vindicate the quantization of gravity, and reveal important properties of its sources.

hep-th↗

arXiv2019

Back(reaction) to the Future in the Unruh-de Sitter State

Motivated by black hole physics, we define the Unruh state for a scalar field in de Sitter space. Like the Bunch-Davies state, the Unruh-de Sitter state appears thermal to a static observer. However, it breaks some of the symmetries of de Sitter space. We calculate the expectation value of the energy-momentum tensor in the Unruh-de Sitter state in two dimensions and find a non-vanishing flux of outgoing negative energy. Extrapolating the result to four dimensions, we argue that this backreacts on the initial de Sitter geometry semi-classically. Notably, we estimate that de Sitter space is destabilized on a timescale set by the gravitational entropy; analogous to black hole evaporation, the endpoint of this instability is a singular geometry outside the regime of effective field theory. Finally, we suggest that the Unruh-de Sitter state may be a natural initial state for patches of de Sitter space, and discuss the implications for slow-roll and eternal inflation, and for de Sitter thermodynamics.

hep-th↗

arXiv2019

Rindler-AdS/CFT

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 x 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.

hep-th↗

arXiv2018

Einstein's Equations from the Stretched Future Light Cone

We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we derive Einstein's equations from the Clausius relation. Moreover, we show that the gravitational equations of motion for a broad class of diffeomorphism-invariant theories of gravity can be obtained from thermodynamics on the stretched future light cone, provided the Bekenstein-Hawking entropy is replaced by the Wald entropy.

hep-th↗

arXiv2017

Thermodynamic Origin of the Null Energy Condition

We derive the classical null energy condition, understood as a constraint on the Ricci tensor, from the second law of thermodynamics applied locally to Bekenstein-Hawking entropy associated with patches of null congruences. The derivation provides evidence that the null energy condition, which has usually been regarded as a condition on matter, is fundamentally a property of gravity.

hep-th↗

arXiv2016

Logarithmic Corrections to Gravitational Entropy and the Null Energy Condition

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.

hep-th↗

arXiv2015

Two Roads to the Null Energy Condition

The null energy condition has sweeping consequences in general relativity. I argue here that it has been misunderstood as a property exclusively of matter, when in fact it arises only in a theory of both matter and gravity. I then derive an equivalent geometric formulation of the null energy condition from worldsheet string theory, where it arises beautifully as simply Einstein's equations in two dimensions. But further, I show that this condition also has a thermodynamic origin, following from a local version of the second law of thermodynamics, applied to gravitational entropy. Thus, far from being an incidental property of matter, the validity of the null energy condition hints at the deep dual origins of gravity.

hep-th↗

arXiv2015

Derivation of the Null Energy Condition

We derive the null energy condition, understood as a constraint on the Einstein-frame Ricci tensor, from worldsheet string theory. For a closed bosonic string propagating in a curved geometry, the spacetime interpretation of the Virasoro constraint condition is precisely the null energy condition, to leading nontrivial order in the alpha-prime expansion. Thus the deepest origin of the null energy condition lies in worldsheet diffeomorphism invariance.

hep-th↗