For a twist-free null hypersurface, the cut-local Hollands–Wald–Zhang (HWZ) representative S_loc=(4 G)^-1∫ (1-Vθ )dA obeys an exact off-shell Raychaudhuri identity containing no term linear in the instantaneous expansion, so no final equilibrium cut is required. Given an entropy density 1/(4 G) , the Unruh temperature κ /2π for an approximate local boost, local equilibrium cuts, and stress-tensor conservation, equating the leading equilibrium change of S_loc to matter boost heat yields R_kk=8π GT_kk for every null direction, and hence the Einstein equation with an undetermined cosmological constant. This is an equation of state in Jacobson’s conditional sense: a consistency condition on these inputs, not a derivation of them. On a fixed caustic-free generator bundle with dA=J dA_ref , the functional S_L=(4 G)^-1∫ (1+ln J-Vθ )dA_ref satisfies an exact balance, normalized per reference cell, whose curvature, shear, and expansion terms all enter with positive sign; the null convergence condition then makes S_L nondecreasing for V≥ 0 , until the first caustic. Requiring that balance throughout an interval of positive affine parameter, on every small bundle and in every null direction, is conversely equivalent to the Einstein equation under stress-tensor conservation and the stated normalization. Cut-locality, positivity, and first-order HWZ normalization select the density 1+ln J-Vθ uniquely within a natural two-function class. Both functionals depend on the affine origin. We give their transformation laws under an affine shift, identify the anchoring-invariant content, and show that the origin is physical data fixed by the equilibrium cut. The entropy interpretation is restricted accordingly. Near an equilibrium cut, S_L agrees with the HWZ dynamical entropy at first order, and the temperature-weighted change of its Hessian across a horizon segment equals the HWZ modified canonical-energy flux under the stated stationary-vacuum perturbation hypotheses. At finite amplitude, S_L is established only as a monotone geometric functional; reading it as an entropy requires an additional coarse-graining postulate that is stated but not derived.
We develop an algebraic equation to describe the collapse and possible bounce of dust in quantum-inspired gravity models with spherical symmetry from knowledge of the vacuum solution. Starting from a wide class of spherically symmetric spacetimes, we write down the covariant Hamiltonian constraints that under dynamical flow give rise to metrics of many spherically symmetric gravity models. The constraint equations are solved for the Hamiltonian evolution and simple equations for the location of the outer boundary of the dust versus time and the apparent horizons in terms of metric shape functions are obtained. The dust density is not assumed to be homogeneous inside the collapsing ball. Using the developed algebraic equations, we examine several quantum-inspired gravity metrics to obtain bounce results either previously obtained by different methods or new results.
Recent developments in Gravitational-Wave (GW) astronomy offer a powerful and independent probe of gravity beyond General Relativity (GR). In this work, we study the Gravitational-Wave and cosmological implications of f(Q, T) gravity, a modified theory in which the gravitational action depends on the non-metricity scalar Q and the trace of the energy-momentum tensor T. We derive the gravitational wave propagation equation within the considered separable f(Q, T) framework and obtain the corresponding modified GW luminosity distance induced by the altered cosmological background evolution. We consider two representative functional forms of f(Q, T) and constrain their parameters using mock GW standard-siren datasets corresponding to current (LIGO-Virgo), space-based (LISA), and next-generation (Einstein Telescope) detectors. We use simulated Gravitational-Wave standard-siren catalogs corresponding to LISA, LIGO-Virgo, and the Einstein Telescope to investigate the prospective sensitivity of these observations to the model parameters. The analysis is formulated as a forecast study based on a fiducial Λ CDM mock cosmology. We emphasize that the resulting parameter estimates are sensitivity indicators for the adopted mock realization rather than definitive observational prospective constraints. Our results show that the increasing number of standard sirens, particularly for an ET-like catalog, substantially improves the sensitivity to the background cosmological parameters, while significant degeneracies remain among the parameters describing the non-metricity sector and the matter–geometry coupling. This highlights the strong potential of next-generation GW cosmology to test the fundamental nature of gravity and assess the viability of f(Q, T) gravity.
We investigate the stability of an axion dark energy model characterized by a periodic scalar-field potential motivated by pseudo Nambu Goldstone bosons. While such models are well suited to drive late-time cosmic acceleration and can exhibit rich dynamical features, including oscillatory behavior of the dark-energy equation-of-state parameter, their viability crucially depends on the existence of stable cosmological solutions. By reformulating the background evolution equations as an autonomous dynamical system, we identify the fixed points corresponding to radiation-dominated, matter-dominated, and dark energy dominated epochs. Using both analytical and numerical techniques, we analyze the stability properties of these fixed points within the observationally allowed region of parameter space. Our results show that the radiation- and matter-dominated phases emerge naturally as saddle points, ensuring a standard cosmological evolution, while the late-time dark energy dominated solution acts as a stable attractor. This guarantees the robustness of cosmic acceleration against variations in initial conditions. Overall, our study establishes the axion dark energy model as a dynamically consistent and observationally viable candidate for explaining the late-time accelerated expansion of the Universe.
The recent detection of gravitational waves has revolutionized astronomy and may be revealing new potential sources such as cosmic strings. These hypothetical structures, formed during symmetry-breaking phase transitions in the early universe, could offer crucial insights into fundamental physics and the formation of large-scale cosmic structures. This study explores the Goldstone boson model within a cosmic string background, where spontaneous U(1) symmetry breaking leads to two coupled nonlinear equations. By employing the tanh ( sech) method, these equations yield two soliton solutions, one corresponding to a massive boson field and the other to a massless one. The static solutions, in the (r, z) plane, show that these fields appear as solitons along the string axis, remaining localized near its center. It is noteworthy that the amplitude of these waves increases with distance from the axis, giving rise to more energetic soliton waves. Finally, the energy-dense regions could act as seeds for matter accumulation, potentially shaping the early development of the cosmic web.
