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A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1134\/1.558646","article-title":"Symmetries and causes of the coincidence of the radiation spectra of mirrors and charges in (1 + 1) and (3 + 1) spaces","volume":"87","author":"Ritus","year":"1998","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_10","first-page":"615","article-title":"Emission of scalar photons by an accelerated mirror in (1 + 1) space and its relation to the radiation from an electrical charge in classical electrodynamics","volume":"81","author":"Nikishov","year":"1995","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_11","first-page":"20200656","article-title":"The relation between quantum and classical field theory with a classical source","volume":"476","author":"Fulling","year":"2020","journal-title":"Proc. R. Soc. Lond. A Math. Phys. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"045020","DOI":"10.1103\/PhysRevD.100.045020","article-title":"Classical and quantum aspects of the radiation emitted by a uniformly accelerated charge: Larmor-Unruh reconciliation and zero-frequency Rindler modes","volume":"100","author":"Landulfo","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105016","DOI":"10.1103\/PhysRevD.102.105016","article-title":"Uniformly accelerated classical sources as limits of Unruh-DeWitt detectors","volume":"102","author":"Cozzella","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1103\/PhysRevD.14.870","article-title":"Notes on black-hole evaporation","volume":"14","author":"Unruh","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_15","unstructured":"Birrell, N., and Davies, P. (1984). Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press."},{"key":"ref_16","unstructured":"Lin, K.N., Chou, C.E., and Chen, P. (2020). Particle Production by a Relativistic Semi-Transparent Mirror in 1 + 3D Minkowski Spacetime. arXiv."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"045001","DOI":"10.1103\/PhysRevLett.118.045001","article-title":"Accelerating Plasma Mirrors to Investigate Black Hole Information Loss Paradox","volume":"118","author":"Chen","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"123106","DOI":"10.1063\/5.0012374","article-title":"Trajectory of a flying plasma mirror traversing a target with density gradient","volume":"27","author":"Chen","year":"2020","journal-title":"Phys. Plasmas"},{"key":"ref_19","first-page":"2015","article-title":"Smooth and sharp creation of a Dirichlet wall in 1 + 1 quantum field theory: How singular is the sharp creation limit?","volume":"61","author":"Brown","year":"2015","journal-title":"J. High Energ. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"67","DOI":"10.3390\/physics2010007","article-title":"Fifty Years of the Dynamical Casimir Effect","volume":"2","author":"Dodonov","year":"2020","journal-title":"Physics"},{"key":"ref_21","unstructured":"Kosyakov, B.P. (2007). Introduction to the Classical Theory of Particles and Fields, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2019.03.002","article-title":"Self-interaction in classical gauge theories and gravitation","volume":"812","author":"Kosyakov","year":"2019","journal-title":"Phys. Rept."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2942","DOI":"10.1007\/s10773-019-04176-7","article-title":"Stationary Worldline Power Distributions","volume":"58","author":"Good","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"059","DOI":"10.1007\/JHEP06(2020)059","article-title":"Unruh-like effects: Effective temperatures along stationary worldlines","volume":"06","author":"Good","year":"2020","journal-title":"JHEP"},{"key":"ref_25","unstructured":"McDonald, K.T. (2017, April 28). Radiated-Power Distribution in the Far Zone of a Moving System, (Unpublished) 2017. Available online: http:\/\/kirkmcd.princeton.edu\/examples\/moving_far.pdf."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rohrlich, F. (2007). Classical Charged Particles, World Scientific. [3rd ed.].","DOI":"10.1142\/6220"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1103\/PhysRevD.31.767","article-title":"Particle and energy creation by moving mirrors","volume":"31","author":"Walker","year":"1985","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fabbri, A., and Navarro-Salas, J. (2005). Modeling Black Hole Evaporation, Imperial College Press.","DOI":"10.1142\/9781860947223"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"025023","DOI":"10.1103\/PhysRevD.88.025023","article-title":"Time dependence of particle creation from accelerating mirrors","volume":"88","author":"Good","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1023\/A:1015278813573","article-title":"Black holes are one-dimensional","volume":"33","author":"Bekenstein","year":"2001","journal-title":"Gen. Rel. Grav."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rindler, W.A. (1977). Essential Relativity: Special, General and Cosmological, Springer. [2nd ed.]. Texts and Monographs in Physics.","DOI":"10.1119\/1.10693"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Rahaman, F. (2014). The Special Theory of Relativity: A Mathematical Approach, Springer.","DOI":"10.1007\/978-81-322-2080-0"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jackson, J.D. (1999). Classical Electrodynamics, Wiley. [3rd ed.].","DOI":"10.1119\/1.19136"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zangwill, A. (2013). Modern Electrodynamics, Cambridge Univ. Press.","DOI":"10.1017\/CBO9781139034777"},{"key":"ref_35","unstructured":"Griffiths, D.J. (2013). Introduction to Electrodynamics, Pearson. [4th ed.]. Re-published by Cambridge University Press in 2017."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1103\/PhysRevLett.59.1369","article-title":"Gravitational Particle Production in the Formation of Cosmic Strings","volume":"59","author":"Parker","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/0003-4916(60)90105-6","article-title":"Classical radiation from a uniformly accelerated charge","volume":"9","author":"Fulton","year":"1960","journal-title":"Ann. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/0003-4916(80)90360-7","article-title":"Radiation from a uniformly accelerated charge","volume":"124","author":"Boulware","year":"1980","journal-title":"Ann. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Singal, A.K. (2020). Discrepancy between power radiated and the power loss due to radiation reaction for an accelerated charge. Symmetry, 12.","DOI":"10.3390\/sym12111833"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"215001","DOI":"10.1088\/0264-9381\/33\/21\/215001","article-title":"Non-existence of isometry-invariant Hadamard states for a Kruskal black hole in a box and for massless fields on 1 + 1 Minkowski spacetime with a uniformly accelerating mirror","volume":"33","author":"Kay","year":"2016","journal-title":"Class. Quant. Grav."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"024021","DOI":"10.1103\/PhysRevD.67.024021","article-title":"Uniformly accelerated mirrors. Part 1. Mean fluxes","volume":"67","author":"Obadia","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"024022","DOI":"10.1103\/PhysRevD.67.024022","article-title":"Uniformly accelerated mirrors. Part 2. Quantum correlations","volume":"67","author":"Obadia","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.newast.2016.10.003","article-title":"The relativistic blackbody spectrum in inertial and non-inertial reference frames","volume":"52","author":"Lee","year":"2017","journal-title":"New Astron."},{"key":"ref_44","first-page":"411","article-title":"On the relativity principle and the conclusions drawn from it","volume":"4","author":"Einstein","year":"1907","journal-title":"Jahrb. Radioakt. Elektron"},{"key":"ref_45","first-page":"1","article-title":"Zur dynamik bewegter systeme","volume":"26","author":"Planck","year":"1908","journal-title":"Ann. Phys. (Liepzig)"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/BF01375397","article-title":"Lorentz-Transformation der W\u00e4rme und der Temperatur","volume":"175","author":"Ott","year":"1963","journal-title":"Z. Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1038\/214903a0","article-title":"Does a Moving Body appear Cool?","volume":"214","author":"Landsberg","year":"1967","journal-title":"Nature"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2327","DOI":"10.1103\/PhysRevD.36.2327","article-title":"Reflections on moving mirrors","volume":"36","author":"Carlitz","year":"1987","journal-title":"Phys. Rev. D"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"065010","DOI":"10.1103\/PhysRevD.94.065010","article-title":"Mirror Reflections of a Black Hole","volume":"94","author":"Good","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1140\/epjc\/s10052-020-08761-7","article-title":"Particle spectrum of the Reissner\u2013Nordstr\u00f6m black hole","volume":"80","author":"Good","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Foo, J., Good, M.R., and Mann, R.B. (2020). Particle production model for general classes of Taub-NUT black holes. arXiv.","DOI":"10.3390\/universe7090350"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Good, M.R., Foo, J., and Linder, E.V. (2020). Accelerating boundary analog of a Kerr black hole. arXiv.","DOI":"10.1088\/1361-6382\/abebb6"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"045020","DOI":"10.1103\/PhysRevD.102.045020","article-title":"Mirror at the edge of the universe: Reflections on an accelerated boundary correspondence with de Sitter cosmology","volume":"102","author":"Good","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0375-9601(00)00515-6","article-title":"Nonthermal nature of extremal Kerr black holes","volume":"273","author":"Rothman","year":"2000","journal-title":"Phys. Lett. A"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"104050","DOI":"10.1103\/PhysRevD.101.104050","article-title":"Extremal Hawking radiation","volume":"101","author":"Good","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"024005","DOI":"10.1103\/PhysRevD.62.024005","article-title":"Nonthermal nature of incipient extremal black holes","volume":"62","author":"Liberati","year":"2000","journal-title":"Phys. Rev. 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