Employing the generalized free energy landscape and solving the associated Fokker–Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation.

China

Chao Wang

Chen Ma

Meng-Ci He

Bin Wu

Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation

Quantum gravity (QG) has a natural cutoff given by the Planck scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>pl</mi></msub></math>. However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, if there are light species of particles. Here we point out that there is a third scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub><mo>≲</mo><msub><mi mathvariant="normal">Λ</mi><mi>s</mi></msub><mo>≲</mo><msub><mi>M</mi><mi>pl</mi></msub></math>, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> gets related to Gregory-Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz-Polchinski solution in the light perturbative string limits. We propose the existence of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="normal">Λ</mi><mrow><mi>BH</mi></mrow></msub></math> is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

United States

Alek Bedroya

Cumrun Vafa

David H. Wu

Tale of three scales: The Planck, the species, and the black hole scales

The maximum number of irreversible bit operations a Schwarzschild black hole can support is computed from Landauer’s principle applied at the asymptotic Hawking temperature, the frame in which the ADM mass-energy and the thermal radiation spectrum are both defined. The result is exact: <math altimg='si1.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mtext>BH</mtext></msub></mrow></math>, where <italic>N</italic> <inf>BH</inf> is the Bekenstein&#8211;Hawking entropy measured in bits. The factor of two follows algebraically from the Smarr formula <math altimg='si2.svg'><mrow><mi>M</mi><msup><mi>c</mi><mn>2</mn></msup><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>T</mi><mi>H</mi></msub><msub><mi>S</mi><mtext>BH</mtext></msub></mrow></math> and requires no assumptions beyond semiclassical black hole thermodynamics and Landauer&#8217;s principle. This identity admits a natural interpretation through the chiral structure of the two-dimensional horizon: a compact surface supports independent left-moving and right-moving excitations, doubling the processing capacity relative to single-sector storage. For Kerr black holes, the Kerr/CFT correspondence maps the rotational work term in the Smarr formula entirely to the right-moving chiral sector, yielding an asymmetric decomposition <math altimg='si3.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mi>L</mi></msub><mo linebreak='goodbreak'>+</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mi>R</mi></msub><mspace width='0.16em' /><msup><mi>M</mi><mn>2</mn></msup><mo linebreak='goodbreak'>/</mo><mrow><mo>(</mo><msup><mi>M</mi><mn>2</mn></msup><mo linebreak='badbreak'>&#8722;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in which the left-moving processing capacity is independent of spin. The processing-to-storage ratio exceeding unity has a direct bearing on the information paradox: it ensures sufficient throughput for complete information processing during Hawking evaporation.

United Kingdom

Kurtis Kemple

A Landauer bound on black hole information processing: <math altimg='si1.svg'><mrow><msub><mi>N</mi><mi>max</mi></msub><mo linebreak='goodbreak'>=</mo><mn>2</mn><mspace width='0.16em' /><msub><mi>N</mi><mtext>BH</mtext></msub></mrow></math>

We investigate the thermodynamic behavior of a spherically symmetric Anti-de Sitter black hole in Mod(A)Max electrodynamics surrounded by a cloud of strings. Within the extended phase-space framework, we treat the cosmological constant as a pressure and interpret the black-hole mass as enthalpy, which enables a unified discussion of local stability, global phase structure, and Joule–Thomson expansion. We analyze the Hawking temperature, Gibbs free energy, and heat capacity, and show how the string-cloud parameter, the Mod(A)Max deformation, and the electric charge reshape the physical domain, the stability windows, and the small/large black-hole transition pattern. We further characterize the critical behavior and demonstrate that a van der Waals–like phase structure arises only in the physical sector, while the alternate branch does not admit a genuine critical point. For the Joule-Thomson process, we determine the inversion curve and the corresponding isenthalpic trajectories, highlighting how the model parameters control the cooling/heating regimes and can generate terminating isenthalpic behavior at sufficiently large charge. Finally, we examine the sparsity of Hawking radiation and discuss how the underlying parameters influence the temporal discreteness of the emitted flux, particularly near extremality and in the large-radius AdS regime.

India

Faizuddin Ahmed

Jordan

Ahmad Al-Badawi

Brazil

Edilberto O. Silva

Thermal analysis, Joule-Thomson expansion and Hawking sparsity of Mod(A)Max-AdS black hole immersed in a cloud of strings

We present the CET Ω framework, a causal-informational extension of standard cosmology that predicts a universal doubly logarithmic correction to the radiation energy density in the early Universe: <display><formula id='ueq0001'><math altimg='si4.svg'><mrow><msub><mi>&#961;</mi><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle></msub><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>&#961;</mi><mi>r</mi></msub><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mrow><mo stretchy='true'>[</mo><mn>1</mn><mo linebreak='badbreak'>+</mo><msub><mi>&#945;</mi><mi>log</mi></msub><mspace width='0.16em' /><mi>log</mi><mi>log</mi><mrow><mo>(</mo><mi>a</mi><mo linebreak='badbreak'>/</mo><msub><mi>a</mi><mi>i</mi></msub><mo>)</mo></mrow><mo stretchy='true'>]</mo></mrow><mo>.</mo></mrow></math></formula></display>This correction arises naturally from scale-invariant spectral sectors with logarithmically-running infrared scales and represents a low-energy manifestation of the full CET &#937; theory. We derive the doubly logarithmic form from two complementary perspectives&#8212;spectral integration and renormalization group flow&#8212;and perform a full Markov Chain Monte Carlo analysis jointly varying six &#923;CDM parameters and <italic>&#945;</italic> <inf>log</inf>, using Planck 2018 TT,TE,EE+lowE likelihoods and BBN constraints. The result, <math altimg='si5.svg'><mrow><msub><mi>&#945;</mi><mi>log</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>0.008</mn><mo>&#177;</mo><mn>0.006</mn></mrow></math> (68% C.L.), is consistent with zero. We identify the expected <italic>N</italic> <inf>eff</inf> degeneracies with <italic>H</italic> <inf>0</inf> and <italic>n<inf>s</inf></italic>, establish the first observational bound | <italic>&#945;</italic> <inf>log</inf>|&#8239;&#8818;&#8239;0.006, and demonstrate that future CMB-S4 measurements can probe <math altimg='si6.svg'><mrow><mrow><mo stretchy='false'>|</mo></mrow><msub><mi>&#945;</mi><mi>log</mi></msub><mrow><mo>|</mo><mo>&#8764;</mo></mrow><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>3</mn></mrow></msup></mrow></math>.

Argentina

Christian Balfagon

Doubly logarithmic corrections to radiation domination from CET Ω: Theory and Planck/BBN constraints

The Jiangmen Underground Neutrino Observatory (JUNO) started physics data taking on 26 August 2025. JUNO consists of a 20-kton liquid scintillator central detector, surrounded by a 35 kton water pool serving as a Cherenkov veto, and almost 1000 m$^{2}$ of plastic scintillator veto on top. The detector is located in a shallow underground laboratory with an overburden of 1800 m.w.e. This paper presents the performance results of the detector, extensively studied during the commissioning of the water phase, the subsequent liquid scintillator filling phase, and the first physics runs. The liquid scintillator achieved an attenuation length of 20.6 m at 430 nm, while the high coverage PMT system and scintillator together yielded about 1785 photoelectrons per MeV of energy deposit at the detector centre, measured using the 2.223 MeV $\textit{γ}$ from neutron captures on hydrogen with an Am-C calibration source. The reconstructed energy resolution is 3.4% for two 0.511 MeV $\textit{γ}$ at the detector centre and 2.9% for the 0.93 MeV quenched $^{214}$Po alpha decays from natural radioactive sources. The energy non-linearity is calibrated to better than 1%. Intrinsic contaminations of $^{238}$U and $^{232}$Th in the liquid scintillator are below 10$^{-16}$ g/g, assuming secular equilibrium. The water Cherenkov detector achieves a muon detection efficiency better than 99.9% for muons traversing the liquid scintillator volume. During the initial science runs, the data acquisition duty cycle exceeded 97.8%, demonstrating the excellent stability and readiness of JUNO for high-precision neutrino physics.

Chile

Angel Abusleme

France

Thomas Adam

Germany

Kai Adamowicz

David Adey

Pakistan

Shakeel Ahmad

Rizwan Ahmed

Finland

Timo Ahola

Italy

Sebastiano Aiello

Fengpeng An

Guangpeng An

Costas Andreopoulos

Giuseppe Andronico

João Pedro Athayde Marcondes de André

Russia

Nikolay Anfimov

Vito Antonelli

Tatiana Antoshkina

Thailand

Burin Asavapibhop

Didier Auguste

Margherita Buizza Avanzini

Slovakia

Andrej Babic

Jingzhi Bai

Weidong Bai

Nikita Balashov

Roberto Barbera

Andrea Barresi

Davide Basilico

Eric Baussan

Beatrice Bellantonio

Marco Bellato

JeanLuc Beney

Marco Beretta

Antonio Bergnoli

Enrico Bernieri

Nikita Bessonov

David Biaré

Daniel Bick

Lukas Bieger

Svetlana Biktemerova

Thilo Birkenfeld

David Blum

Simon Blyth

Sara Boarin

Manuel Boehles

Anastasia Bolshakova

Mathieu Bongrand

Aurélie Bonhomme

Clément Bordereau

Matteo Borghesi

Augusto Brigatti

Timothee Brugiere

Riccardo Brugnera

Riccardo Bruno

Jonas Buchholz

Antonio Budano

Max Buesken

Mario Buscemi

Severino Bussino

Jose Busto

Ilya Butorov

Marcel Büchner

Anatael Cabrera

Barbara Caccianiga

Boshuai Cai

Hao Cai

Xiao Cai

Yanke Cai

Yi-zhou Cai

Zhiyan Cai

Stéphane Callier

Steven Calvez

Antonio Cammi

Agustin Campeny

Dechang Cai

Chuanya Cao

Dewen Cao

Guofu Cao

Jun Cao

Yaoqi Cao

Rossella Caruso

Aurelio Caslini

Cédric Cerna

Vanessa Cerrone

Daniele Cesini

Chi Chan

Jinfan Chang

Yun Chang

Milo Charavet

Tim Charissé

Auttakit Chatrabhuti

Chao Chen

Guoming Chen

Haitao Chen

Haotian Chen

Jiahui Chen

Jian Chen

Jing Chen

Junyou Chen

Lihao Chen

Mali Chen

Mingming Chen

Initial performance results of the JUNO detector * We acknowledge financial and institutional supportfrom the Chinese Academy of Sciences, the National KeyR&D Program of China, the People's Government of Guangdong Province, and the Tsung–Dao Lee Institute of Shanghai Jiao Tong University in China.We appreciate the contributions from the Institut Na-tional de Physique Nucléaire et de Physique des Partic-ules (IN2P3) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, the Fonds de la Recherche Sci-entifique (F.R.S.–FNRS) and the Institut Interuni-versitaire des Sciences Nucléaires (IISN) in Belgium, and the Conselho Nacional de Desenvolvimento Científico eTecnológico (CNPq) in Brazil.We also acknowledge the support of the AgenciaNacional de Investigación y Desarrollo (ANID) and the ANID–Millennium Science Initiative Program (ICN2019044) in Chile; the European Structural and In-vestment Funds, the Ministry of Education, Youth and Sports, and the Charles University Research Center inthe Czech Republic; the Deutsche Forschungsgemeinsch-aft (DFG), the Helmholtz Association, and the Cluster ofExcellence PRISMA+ in Germany; and the Joint Insti-tute for Nuclear Research (JINR) and Lomonosov Mo-scow State University in Russia.We further thank the Slovak Research and Develop-ment Agency in the Slovak Republic, the National Science and Technology Council (NSCT) and MOE, China, the Program Management Unit for Hu-man Resources & Institutional Development, Research and Innovation (PMU–B), Chulalongkorn University, and Suranaree University of Technology in Thailand, the Science and Technology Facilities Council (STFC) in the United Kingdom, and the University of California atIrvine and the National Science Foundation (NSF) in the United States

We investigate the impact of one-loop radiative corrections in a nonsupersymmetric model of hybrid inflation with a chaotic (polynomial-like) potential, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>V</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math>, in the light of the latest constraints from Planck and Atacama Cosmology Telescope (ACT) observations. Here, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>V</mi><mn>0</mn></msub></math> denotes the energy scale of inflation, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mi>p</mi></msub></math> is a coupling associated with the polynomial term of power <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>. These corrections can naturally arise from couplings of the inflaton to other matter fields, which also facilitate the reheating process. At the tree level, the predictions of such models for the scalar spectral index <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub></math> and the tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math> typically lie outside the current observational bounds. However, incorporating one-loop radiative corrections modifies the potential to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>V</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>+</mo><mi>A</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>ln</mi><mo stretchy="false">(</mo><mi>ϕ</mi><mo>/</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi></math> characterizes the strength of the inflaton’s coupling to other fields, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math> is an appropriate renormalization scale. This radiatively corrected potential can reconcile the model with the combined <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Planck</mi><mo>+</mo><mi>ACT</mi></mrow></math> data over a suitable range of parameter space explored in this work. In particular, radiative corrections from fermionic loops (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mo>&lt;</mo><mn>0</mn></math>) suppress the tensor-to-scalar ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>r</mi></math>, while simultaneously yielding a red-tilted spectrum with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>s</mi></msub><mo>&lt;</mo><mn>1</mn></math>, even for sub-Planckian field excursions. This brings the prediction in line with current observations, while still allowing for potentially detectable signatures of primordial gravitational waves. Furthermore, the inflaton’s couplings enable successful reheating and naturally accommodate nonthermal leptogenesis, providing a unified framework for inflation and baryogenesis.

Waqas Ahmed

Saudi Arabia

Saleh O. Allehabi

Mansoor Ur Rehman

Revisiting polynomial hybrid inflation: Planck and ACT compatibility via radiative corrections

We investigate the quasinormal modes (QNMs) of Planck stars within the framework of scale-dependent gravity (SDG). In our setup, the running parameter $$\alpha $$ is fixed to a negative value by matching the effective Newtonian potential to the one-loop EFT result. As a consequence, the associated running Newton coupling does not realise the ultraviolet fixed point of asymptotically safe gravity, and the geometry should be interpreted as an SDG-inspired effective metric rather than a realisation of asymptotically safe gravity itself. We focus on the resulting renormalisation-group-improved Schwarzschild metric, which naturally yields a finite-size Planck-density core. Building on this background, we compute the QNM spectrum for scalar, electromagnetic, and gravitational perturbations using the Spectral Method (SM). This approach, known for its superior accuracy over high-order WKB schemes, enables the detection of fundamental modes, large families of overtones, and purely imaginary overdamped modes that are entirely missed in previous analysis. Our results reveal a robust $\textit{Martini glass}$ morphology of the oscillatory spectrum across perturbation sectors, nearly equally spaced overdamped modes with characteristic anomalous gaps, and the emergence, in the gravitational sector, of isolated overdamped modes separated from the main sequence by exceptionally large frequency intervals. These features, resolved here for the first time in the Planck-star context, underscore the importance of high-precision spectral techniques in probing subtle signatures of quantum-gravity-inspired black hole models.

United Arab Emirates

Davide Batic

Denys Dutykh

Canada

Fabio Scardigli

Spectral analysis of quasinormal modes of Planck stars

We investigate the propagation of a massless scalar field in the Gödel universe and demonstrate that the rotating spacetime functions as an intrinsically optically active medium, characterized by a refractive index that depends on both position and frequency. Starting from the covariant Klein-Gordon equation, we derive a generalized Helmholtz-type radial equation in which the effective refractive index <italic>n</italic> <inf>&#8728;</inf>( <italic>r, &#969;</italic>) explicitly depends on the radial coordinate <italic>r</italic> and frequency <italic>&#969;</italic>. Consequently, the G&#246;del geometry manifests as a rotation-induced optical medium: scalar modes are confined within a finite radial domain bounded by turning points where <math altimg='si19.svg'><mrow><msubsup><mi>n</mi><mrow><mo>&#8728;</mo></mrow><mn>2</mn></msubsup><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>&#969;</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>. Depending on the rotation rate &#937;, the frequency <italic>&#969;</italic>, and the azimuthal quantum number <italic>m</italic>, the medium supports either propagating <math altimg='si20.svg'><mrow><mo>(</mo><msubsup><mi>n</mi><mrow><mo>&#8728;</mo></mrow><mn>2</mn></msubsup><mo linebreak='goodbreak'>&gt;</mo><mn>0</mn><mo>)</mo></mrow></math> or evanescent <math altimg='si21.svg'><mrow><mo>(</mo><msubsup><mi>n</mi><mrow><mo>&#8728;</mo></mrow><mn>2</mn></msubsup><mo linebreak='goodbreak'>&lt;</mo><mn>0</mn><mo>)</mo></mrow></math> behavior. Near the rotational axis, a centrifugal singularity emerges, producing strongly evanescent regions for | <italic>m</italic>|&#8239;&gt;&#8239;1/2, whereas for <math altimg='si22.svg'><mrow><mi>m</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, propagation persists near the axis but confinement still occurs due to the evanescent asymptotics at large <italic>r</italic>. Asymptotically, <math altimg='si23.svg'><mrow><msubsup><mi>n</mi><mrow><mo>&#8728;</mo></mrow><mn>2</mn></msubsup><mrow><mo>(</mo><mi>r</mi><mspace width='-0.16em' /><mo>&#8594;</mo><mspace width='-0.16em' /><mi>&#8734;</mi><mo>,</mo><mi>&#969;</mi><mo>)</mo></mrow><mo>&#8771;</mo><mo>&#8722;</mo><mn>3</mn><mo linebreak='goodbreak'>&#8722;</mo><mfrac><msup><mstyle mathvariant='normal'><mi>&#937;</mi></mstyle><mn>2</mn></msup><mrow><mn>4</mn><msup><mi>&#969;</mi><mn>2</mn></msup></mrow></mfrac></mrow></math>, rendering all modes evanescent. Planck-scale corrections are incorporated within the framework of rainbow gravity, employing energy-dependent functions <italic>f</italic>(&#1013;) and <italic>g</italic>(&#1013;), where <math altimg='si24.svg'><mrow><mi>&#1013;</mi><mo linebreak='goodbreak'>=</mo><mi>&#969;</mi><mo linebreak='goodbreak'>/</mo><msub><mi>&#969;</mi><mi>p</mi></msub></mrow></math>. We consider (i) loop-quantum-gravity-inspired functions <math altimg='si25.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>&#1013;</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mn>1</mn><mo>,</mo><mspace width='0.28em' /><mi>g</mi><mrow><mo>(</mo><mi>&#1013;</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msqrt><mrow><mn>1</mn><mo linebreak='badbreak'>&#8722;</mo><mi>&#951;</mi><mi>&#1013;</mi></mrow></msqrt></mrow></math> and (ii) doubly special relativity-inspired functions <math altimg='si26.svg'><mrow><mi>f</mi><mo>(</mo><mi>&#1013;</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><mo>(</mo><mn>1</mn><mo linebreak='goodbreak'>&#8722;</mo><mi>&#951;</mi><mi>&#1013;</mi><mo>)</mo><mo>,</mo><mspace width='0.28em' /><mi>g</mi><mo>(</mo><mi>&#1013;</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></math>, which induce the frequency deformation <math altimg='si27.svg'><mrow><mi>&#969;</mi><mspace width='-0.16em' /><mo>&#8594;</mo><mspace width='-0.16em' /><mover accent='true'><mi>&#969;</mi><mo>&#732;</mo></mover><mo linebreak='goodbreak'>=</mo><mi>&#969;</mi><mspace width='0.16em' /><mi>f</mi><mrow><mo>(</mo><mi>&#1013;</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>/</mo><mi>g</mi><mrow><mo>(</mo><mi>&#1013;</mi><mo>)</mo></mrow></mrow></math> and lead to a modified refractive index <math altimg='si28.svg'><mrow><mover accent='true'><mi>n</mi><mo>&#732;</mo></mover><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>&#969;</mi><mo>,</mo><msub><mi>&#969;</mi><mi>p</mi></msub><mo>)</mo></mrow></mrow></math>. First-order corrections ( <italic>&#951;</italic>&#1013;&#8239;&#8810;&#8239;1) yield analytic shifts of the turning points, while exact closed-form expressions allow precise numerical treatment. The resulting rainbow-induced deformations generate frequency-dependent modifications to the propagation thresholds, which become particularly pronounced near the axis ( <italic>r</italic>&#8239;&#8594;&#8239;0) and in near-Planckian regimes. Furthermore, we demonstrate that these results generalize to <italic>z</italic>-polarized electromagnetic wave modes and show the smooth recovery of scalar-like propagation in the G&#246;del universe. Finally, when <math altimg='si16.svg'><mrow><mi>&#951;</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, we establish that in the high-frequency limit ( <italic>&#969;</italic>&#8239;&#8594;&#8239;&#8734;), the effective refractive index accurately reproduces the null geodesics of the spacetime.

Türkiye

Omar Mustafa

Abdullah Guvendi

Semra Gurtas Dogan

Optics in the Gödel universe: Effects of global rotation and Planck-scale corrections

Pulsars convert a significant fraction of their total spin-down power into very high-energy electrons, leading to the formation of TeV halos. While these halos are well characterized at TeV energies, it remains unclear whether pulsars also accelerate electrons efficiently at lower energies and how these particles propagate through their surrounding environments. We aim to test whether synchrotron emission from $$\sim 50$$ – $$300 \, \textrm{GeV}$$ electrons around the Geminga pulsar can be detected in the frequency range observed by the Planck satellite. This would help constrain low-energy particle acceleration and diffusion in the vicinity of pulsars. We model the expected synchrotron emission from Geminga’s TeV halo based on various diffusion and injection spectrum scenarios and compare these predictions to publicly available multi-frequency Planck data. We find no conclusive evidence of spatially extended synchrotron emission associated with Geminga in any of Planck’s frequency bands. Our calculations show that even under favorable diffusion and injection conditions, the predicted synchrotron flux lies well below Planck’s measured background levels.

D. Hooper

E. Pinetti

A. Sokolenko

Searching for synchrotron emission from the geminga TeV halo using the planck satellite