Accelerating mirrors to investigate black hole radiation and cosmological thermodynamics

Project: FDCRGP

Project Details

Grant Program

Faculty Development Competitive Research Grant Program 2021-2023

Project Description

2.1 Brief description
Einstein used a moving mirror in his seminal 1905 work to derive the relativistic Doppler effect. Schrödinger, in 1939, determined that our expanding universe results in particle creation. A beautiful union of these seemingly disparate ideas occurred in the 1970s when it was calculated that an accelerating mirror [Moore1970] could also produce its own radiation, in close analog [Fulling1976] to black hole particle creation [Hawking1975].

How can this be? The vacuum of space is not empty. It can be excited, under just the right conditions, to radiate. As one of the most extraordinary predictions of quantum field theory, there is still much mystery surrounding how quantum fields in the vacuum are alive with virtual particles emanating in and out of existence. Any sufficiently disrupting external effect, like a moving mirror [Davies1977], expanding universe [Parker1968], or a black hole [Hawking1975], can stimulate the vacuum this way, amplifying fluctuations into real particles, but direct measurement is hard.

In the early 1900s, these vacuum effects were just a curiosity, but it became apparent that special select non-radiative cases of vacuum fluctuations are measurable, for instance, the attractive force for two closely held uncharged mirrors (Casimir effect, 1948) or the Lamb shift of atomic spectra (Nobel Prize, 1955). The usual renormalization techniques used in this context to handle divergences are now central to our basic understanding of nature. However, in the last two decades incredible progress has been made culminating in a stunning direct measurement of the dynamical Casimir effect (DCE), by [Wilson2011]. The DCE is the general name given to the effect of a moving mirror that converts virtual photons directly into observable real photons, like a knife slicing through the vacuum of space [Good2017a].

It is always pleasant to have exact solutions in simple form at your disposal. – Schwarzschild, 1916.

On the theory side, a single moving mirror shining light into the vacuum is a wonderfully rich toy model for calculating analytic results like the particle spectrum and energy flux that can be used to understand the less accessible astrophysical regimes of black holes thermodynamics and the expanding universe. Recently, in fact, certain mirror motions have been found to emit radiation in exact one-to-one correspondences to many of the most well-known black hole spacetimes:

(1) Schwarzschild [Good2016a], (2) Reissner-Nordström (RN) [Good2020e], (3) Extremal RN [Good2020c],

Moreover, these accelerated boundary correspondences (ABCs), exist for the cosmologies of de-Sitter and Anti-de Sitter space [Good2020f]. Tightening the connection between the realms of laboratory table-top physics of moving mirrors and cosmological observations of an expanding universe and the astrophysical environment of black holes, this project aims to investigate how the physics of moving mirrors can help bridge the gap between these seemingly separate realms. These recent ABC solutions provide a probe for the unknown and fascinating areas of laboratory physics and astrophysics related to acceleration radiation, cosmological expansion, black hole evaporation and the light from accelerated boundaries.

We will produce accurate predictions, using ABCs, of the particle count, energy emission and entanglement entropy from the single moving mirror, through the use of state-of-the-art computer simulations and mathematical techniques. These tools will find applications in a wide range of scientific contexts and will ultimately benefit the economic development of Kazakhstan. The funding offered by this university grant, while modest (see the strict University-wide limits for each spending category in Sec 4.2), will mostly go toward young Kazakh scientists who have excellent scientific potential. The projects will be developed with different renowned international institutions and will offer opportunities to young Kazakh researchers to engage in cutting edge research on the international arena. The computations will be performed both locally in Nur-Sultan and internationally, with emphasis on engaging opportunities for younger students on numerous fronts and challenges. The educational aim is to help catalyze and increase the intellectual horsepower of the next generation of Kazakh leaders as problem solvers, one small step at a time.

This will strengthen the reputation of Nazarbayev University and Kazakhstan at international level and enhance the scientific ties of this young University (10 years) with international institutions. The proposed work will be performed in collaboration with other research teams in world-renowned institutions such as the Nanyang Technological University in Singapore, University of California at Berkeley, USA, the University of Queensland, Australia and the University of Waterloo, Canada.
Short titleAccelerating mirrors
Effective start/end date1/1/2112/31/23