arXiv subjects

Debarshi Mukherjee

Publications and source records attributed to Debarshi Mukherjee.

5 recordsLinked to original sources

arXiv2026

The Derivation of Phase-Space Metric in a Geometric Quantization Approach: General Relativity with Quantized Phase-Space Metric and Relative Spacetime

Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static) spacetime. Apparently, this seems to enable the principles of GR and quantum mechanics (QM) to be reconciled into a coherent relativity and quantum theory. A canonical geometric quantization approach that presents kinematics of free-falling quantum particles within a tangent bundle, expands QM to incorporate relativistic gravitational fields, and generalizes the four-dimensional Riemann manifold into an eight-dimensional one likely discretizes, if not fully quantizes, the Finsler and Hamilton structures. The Finsler and Hamilton metrics can be directly derived from the Hessian matrix. As introduced in [Physics, 7 (2025) 52], the quantized four-dimensional metric tensor can be deduced by means of approximations including proper parameterization of coordinates and the equating line elements on all these manifolds including Riemann manifold. This research, on the contrary, goes beyond all these approximations and proposes the incorporation of a phase-space metric tensor into GR. The derivation of a quantized eight-dimensional metric tensor is not only presented, but also the implications of it and the corresponding relative spacetime are examined.

physics.gen-ph↗

arXiv2025

Simple Analytic Estimate of Black Hole Shadow Size in an Expanding Universe

The apparent shadow of a black hole provides one of the most direct probes of strong-field general relativity. While the shadow size in asymptotically flat spacetimes is well understood, the influence of cosmic expansion on its apparent angular diameter remains less explored. In this work, we present a simple analytic framework to estimate the shadow size of a non-rotating black hole embedded in an expanding universe. By combining the local Schwarzschild geometry with large-scale cosmological dynamics through the McVittie and Kottler metrics, we derive a compact relation between the shadow angular size and the angular diameter distance $D_A(z)$. This approach captures the essential dependence on cosmological parameters such as the Hubble constant $H_0$ and the cosmological constant $\Lambda$, while remaining analytically tractable. We further perform numerical estimates to quantify the redshift dependence of the apparent shadow size, showing that the effect of cosmic expansion is negligible for nearby sources but becomes relevant for high-redshift black holes. Our results demonstrate a clear conceptual connection between strong-gravity optics and cosmological expansion, providing a pedagogically transparent and physically motivated extension of black hole shadow theory to a cosmological context.

gr-qc↗

arXiv2025

Theoretical Signatures of QCD Phase Transitions in Compact Astrophysical Systems

We investigate theoretical signatures of first-order QCD phase transitions in high-density astrophysical systems through a framework combining lattice QCD, effective field theories, and multimessenger constraints. Hybrid equations of state with Maxwell and Gibbs constructions, constrained by lattice QCD at finite temperature and baryon chemical potential up to mu_B/T < 3, interpolate consistently between chiral effective field theory at nuclear densities and perturbative QCD at asymptotic densities. Applying these models to static neutron stars via Tolman-Oppenheimer-Volkoff equations and to binary mergers via relativistic hydrodynamics, we find distinctive signatures: (i) twin star branches with 0.5-2.0 km radius differences at fixed mass, (ii) equation of state softening in coexistence regions reducing maximum masses by 0.2-0.4 solar masses, (iii) delayed post-merger gravitational-wave frequency shifts of 200-400 Hz, and (iv) enhanced neutrino emission during phase transitions. Confronted with multimessenger constraints from GW170817, NICER observations of PSR J0740+6620 and PSR J0030+0451, and perturbative QCD, our models suggest strong first-order transitions are marginally consistent with current data but produce signatures detectable by next-generation detectors. Neutron star core sound speeds satisfy c_s^2 < 0.5c^2, with transient conformal bound violations in 2-4 times saturation density. This framework yields quantitative predictions for the Einstein Telescope and Cosmic Explorer, establishing foundations for precision QCD matter tests and possible quark matter discovery.

nucl-th↗

arXiv2025

Systematic Effects of Chaotic Magnetic Fields on Neutron Star Tidal Deformability: Implications for Gravitational Wave Constraints on Dense Matter

We investigate the effects of strong magnetic fields on the equation of state (EoS) of neutron star matter and the resulting implications for tidal deformability measurements in binary neutron star (BNS) mergers. A critical issue with previous magnetized neutron star studies is the treatment of magnetic field anisotropy in the Tolman-Oppenheimer-Volkoff (TOV) equations. To address this fundamental problem, we employ the chaotic magnetic field approximation, which allows for a self-consistent treatment of magnetic pressure while maintaining isotropy. Using a relativistic mean field approach with properly implemented magnetic field corrections, we compute mass-radius relations and tidal deformability parameters for neutron stars with magnetic field strengths ranging from $10^{15}$ to $10^{16}$ G. Our systematic study reveals that magnetic fields induce increases in both stellar radii (0.8--2.3\%) and tidal deformabilities (4.2--18.1\%) compared to field-free cases, with effects scaling approximately as $B^{1/2}$. These modifications, while modest, are potentially detectable with current and next-generation gravitational wave detectors. For a canonical $1.4\,M_\odot$ neutron star, the tidal deformability increases from $\Lambda_{1.4} = 678 \times 10^6$ in the absence of magnetic fields to $\Lambda_{1.4} = 803 \times 10^6$ for $B = 10^{16}$ G. We demonstrate that magnetic field effects must be considered when constraining the neutron star equation of state using gravitational wave observations, particularly for populations including highly magnetized neutron stars. Our results suggest that the current GW170817 constraint on tidal deformability may require systematic corrections when accounting for magnetic field effects. We provide scaling relations for magnetic field corrections and discuss the implications for population studies of neutron star mergers with next-generation detectors.

astro-ph.HE↗

arXiv2025

The Energy Spectrum of the Pion from Lattice QCD

In this report, computational techniques are employed to extract the energy eigenvalues of the pion from two-point correlation function data that has been simulated using the lattice formulation of Quantum Chromodynamics (QCD) across various momentum values for the particle. The analysis focuses on systematically obtaining these eigenvalues to understand better the behavior of the pion under different kinematic conditions. Once extracted, these energy eigenvalues obtained through plateau fitting of the Energy vs Time graph, are utilized to plot the dispersion relation of the pion. This resulting dispersion relation is then compared with theoretical predictions to assess the accuracy and validity of the computational approach. The comparison provides insights into how well the lattice QCD simulations align with established theoretical expectations, and what range of kinematic variables are reliable.

hep-lat↗