arXiv subjects
Publications and source records attributed to Tian-Shun Chen.
This comment gives dimension-independent analytic proofs of the local inequalities arising in the odd- and even-dimensional constructions of higher-dimensional partition charge functions. The prior works established these inequalities by exhaustive computation in low dimensions and tested them numerically in selected higher dimensions.
Timelike entanglement entropy (TEE) provides a Lorentzian boundary probe of bulk geometry, but its use for metric reconstruction depends on the holographic prescription and on the extremal-surface branch selected by that prescription. We study this inverse problem for strip-shaped TEE data and make these dependencies explicit. In the complex-valued weak extremal surface (CWES) prescription, the time-width dependence of TEE determines an Abel density $H(W)$ on a selected real branch; for Bañados-Teitelboim-Zanelli (BTZ) black holes this gives an analytic reconstruction of the blackening factor once the singularity endpoint fixes the radial origin. After developing a forward numerical method for the complex-coordinate prescription, we formulate it as the main reconstruction scheme for the asymptotically $AdS_{d+1}$ backgrounds with $d\geq 2$. On a chosen complex branch, the time-width dependence of TEE supplies the Abel input that determines the TEE-accessible density, while one additional geometric anchor is required to convert that density into a definite radial metric profile. With UV or horizon-scale anchoring and rational continuation from the reconstructed complex-path samples, the method reproduces the benchmark BTZ, four-dimensional Schwarzschild, and Reissner-Nordström (RN) blackening factors. However, the Gubser-Rocha example shows that a single strip observable with a nontrivial spatial warp factor determines only one functional combination of the metric functions.
Regarding the stability of two-fluid star models, we rigorously prove the equivalence between the emergence of a zero-frequency radial oscillation mode and the static critical-curve criterion for mixed stars, after briefly reviewing the hybrid star case. This establishes a sufficient-condition relation between two independently developed stability criteria. Although this connection has often been implicitly assumed in previous studies of mixed stars, it has rarely been demonstrated explicitly. Our derivation can be extended to general multi-fluid systems. As an illustrative example, we consider dark matter-admixed neutron star models and show that their stability boundary differs from that of single-fluid stars. In this case, stable configurations form a surface in the three-dimensional parameter space spanned by central pressure, mass, and radius, giving rise to a class of stable mixed stars. This class includes "twin stars" with identical masses and radii but distinct internal compositions and structures. These results provide a useful framework for interpreting compact star observations and for constraining dark matter properties through astrophysical measurements.
We prove a static criterion for radial zero modes in relativistic multi-fluid stars whose isentropic barotropic components are separately conserved and interact only through gravity. For a regular multi-parameter equilibrium family, the particle-number map is rank deficient if and only if a nontrivial physical radial zero mode exists. The proof establishes a one-to-one correspondence between particle-preserving infinitesimal equilibrium deformations and zero-frequency radial perturbations. We also construct the self-adjoint form realization associated with the coupled pulsation operator, prove that it has compact resolvent, show that its eigenspaces coincide with the physical radial-mode spaces, and establish continuity of every ordered squared mode frequency along the equilibrium family. It follows that every boundary point of strict radial stability within the equilibrium family satisfies the static rank condition. A representative two-fluid example shows that the static criterion and the dynamical zero-mode calculation yield the same critical curve. The rank condition therefore provides an equilibrium-based method for locating radial zero modes and determining their multiplicity.
Dedekind's problem counts monotone Boolean functions, equivalently downsets of a Boolean lattice. We recast this enumeration as a finite layer-ratio reconstruction problem for the Whitney numbers of the ranked ideal lattice. An exact adjacent-layer double count expresses each layer ratio through local averages of the number of addable elements and the number of removable elements. Reversible fixed-layer Markov chains estimate these averages and hence estimate the Dedekind number $M(n)$. Backtests at $M(8)$ and $M(9)$ calibrate seed-level variability under the fixed protocol and measure the observed Monte Carlo budget scaling. The resulting estimate probes the Whitney-number sequence of the ideal lattice. Although these rows have previously been described empirically as unimodal, the high-precision $n=9$ estimate has a shallow two-shoulder feature around the central rank, contrary to that empirical description; $n=11$ and $n=13$ center-window estimates show a larger-contrast analogous pattern. The protocol estimate for $M(10)$ is \[ \widehat M(10)=(8.9360\pm0.0010)\times 10^{78}, \] where the displayed uncertainty is the budget-based forecast scale from the cross-$n$ scaling law under the production budget.
The charge functions for n-dimensional partitions are known for n=2,3,4 in the literature. In a recent work, we gave the expression for arbitrary odd dimension; here we further conjecture a formula for all even-dimensional cases. This conjecture is proved rigorously for 6D, and numerically verified for 8D.
Fast analytic and semi-analytic studies of neutron stars often require an equation of state that is convenient to evaluate while producing relativistic stellar sequences compatible with current multimessenger constraints. We construct such a benchmark by scanning a smooth double polytropic relation for the energy density as a function of pressure, $\hatε(\hat p)=a_1\hat p^{Γ_1}+a_2\hat p^{Γ_2}$. The parameters are selected with filters based on massive pulsars, tidal deformability from the binary-neutron-star event GW170817, and NICER mass-radius measurements. A single polytropic baseline scan finds no model passing all filters, whereas a double-polytrope scan identifies a viable region. A curve-integral score, evaluated against public NICER and GW170817 posterior data sets, is then used to choose benchmark equations of state within this region. The selected representatives support $M_{\max}=2.44$--$2.49\,M_\odot$, with $R_{1.4}\simeq 11.3$ km and $Λ_{1.4}=485$--$512$, and remain causal on the stable branch. This compact analytic family provides reference cases for relativistic stellar-structure tests at current observational scales.
Binary systems may undergo mass transfer while maintaining significant orbital eccentricities. Stellar-mass black holes (sBHs) can strip stars on eccentric orbits and produce micro-tidal disruption events (micro-TDEs). While previous hydrodynamical studies have focused on compact systems on the verge of disruption, the transition between self-regulated eccentric mass transfer and runaway disruption remains poorly understood. We present SPH simulations of a Sun-like star interacting with a $10\,M_\odot$ sBH across a range of initial eccentricities ($e_0=0.30$--$0.70$) and pericenter distances ($b_0=3.33$--$3.57$ in units of the tidal radius), tracking the systems for tens to over 100 orbital periods. Our results reveal that these binaries can evolve along two distinct pathways, dictated by the competition between mass-transfer-driven stellar expansion and orbital widening: (i) Runaway disruption ($b_0\lesssim 3.45$), in which mass loss at pericenter drives adiabatic expansion of the stellar envelope, leading to unstable Roche-lobe overflow and runaway disruption of the star. The stripped debris forms a thick accretion flow with hyper-Eddington accretion rates onto the sBH, potentially powering fast X-ray/UV or blue/optical transients. (ii) Stable mass transfer ($b_0\gtrsim 3.57$), in which the binary settles into a long-lived, stable mass-transfer phase lasting up to 150 orbits (the limit of our simulation), regulated by orbital expansion from pericenter mass loss. These eccentric mass-transfer events could manifest observationally as repeating, quasi-periodic flares.
To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to find the eigenvalues of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.
Applying the holographic 2-flavor Einstein--Maxwell-dilaton model, the parameters of which are fixed by lattice QCD, we extract the equations of state for hot quark--gluon plasma around the critical point at T=182 MeV, and have corresponding quark star cores constructed. By further adding hadron shells, the mass range of the whole stars spans from 2 to 17 solar masses, with the maximum compactness around 0.22. This result allows them to be black hole mimickers and candidates for gap events. The I--Love--Q--C relations are also analyzed, which show consistency with the neutron star cases when the discontinuity at the quark--hadron interface is not large. Furthermore, we illustrate the full parameter maps of the energy density and pressure as functions of the temperature and chemical potential and discuss the constant thermal conductivity case supposing a heat source inside.