Abstract This work studies regular black holes motivated by the scalar sector of density-responsive gravity (DRG). An algebraic prescription with phenomenological local running maps a Gaussian matter profile to a diagnostic density profile. A pressure check shows that this profile does not solve the full static DRG equations. It serves only to select an effective metric family with two horizons. The extremal mass is calibrated to M min = √(1 + A /2) M P ≃ 1.006 M P , where A = 0.024 is the historical scalar response amplitude. A fit to ρ ( r ) = ρ 0 exp[-( r / r c ) n ] selects n = 2. The temperature is nonmonotonic, reaching T H max = 0.02547 M P at M = 1.332 M P before vanishing at M min . The calculation verifies the generic scaling near extremality Z tr α ( M − M min ) -1/2 of a static lapse diagnostic for n = 2, 3, 4, 6 and for the Hayward and Bardeen controls. A regulated integral of coordinate time between the horizons provides a static cavity diagnostic, not a prediction of echoes of gravitational waves. The remaining area entropy equals the area entropy already lost at M cross / M 0 = 0.707107 ≃ 1/√2. This geometric crossing does not establish a Page curve or unitarity. The endpoint area entropy is below 2.6% of the initial Bekenstein-Hawking entropy for M 0 = 5 M P and below 0.03% for M 0 = 50 M P . An inverse source reconstruction confirms an isotropic core of de Sitter type but retains the pressure mismatch. An exploratory collapse calculation with an imposed bounce factor produces bounded configurations with 1 - 2 m / r < 0 without establishing formation of the calibrated geometry. The robust results are the calibrated thermodynamics and generic scaling near extremality.
Abstract Gravito-electromagnetism rewrites linearized gravity in Maxwell form, and gravitational induction extends it to bounded sources whose multipole moments evolve. The contraction A^μ=-h ̅^μν ξ_ν of Clark and Tucker that effects it is a linearized single copy in a restricted sense: it is the contraction with a fixed timelike vector on which Kerr–Schild and contraction-based double copies are built, but it lacks the structure of the double copy proper, and in Lorenz gauge its Maxwell equation is one row of the linearized Einstein equations. We characterize the source map T^μν↦T^μ0 completely. The characterization is kinematical, with no energy condition imposed: a conserved current confined to a fixed ball is the image of a localized symmetric conserved stress tensor if and only if its Poincaré charges are conserved. The mass dipole solves p^i (t)=K^i+tP^i with the boost and momentum charges as coefficients; the magnetic dipole, half the spin, is frozen. The cokernel is the space of iso(3)_ξ^*-valued functions of time, its instantaneous values the six rigid-motion obstructions of linear elasticity that drive our constructive converse; the kernel is the space of elastic self-stresses, and the exterior stress that torques a spinning-down dipole generates the torque obstruction class. Under the dominant energy condition the image second moment obeys |d^2/dt^2 ∫▒〖x^i x^j J^0 〗|≤2M. The two contraction maps in use differ by a term in the trace of the perturbation; for a pulsating source it gives the metric contraction an oscillating Gauss charge, a property of the auxiliary field of the harmonic representative rather than a gauge-invariant observable. Beyond linear order, the relaxed Einstein equations in harmonic coordinates allow the same bookkeeping with a flat-conserved but noncompact pseudotensor source, and the frozen charges become fluxes, fed at the standard gravitational-wave rates through the l=2 channel that the linear theory leaves open.
Abstract We examine a massive scalar field with a nonminimal coupling −βRϕ2/2 in an R + λR2 gravitational theory. The model belongs to the established mixed scalar–scalaron class; λ, β, and the scalar mass are independent parameters. Starting from an action with explicit conventions, we derive the metric and scalar equations, distinguish the separately conserved geometric and matter sources from the jointly conserved scalar and interaction10 contributions, and obtain the spatially flat cosmological equations. Retaining both scalar responses and metric slip gives a scale-dependent quasi-static coupling Geff = Gμ(k, a) for linear matter growth. We provide the limiting response plateaus, their signed difference, and a half-transition scale, stating the conditions under which these limits lie in the approximation’s domain. Illustrative background and growth integrations compare different15 values of β with matched-background force-law controls. The results specify an effective dark-sector application of known gravitational operators; they do not establish observational viability, a complete dark-matter replacement, or the accuracy of the quasi-static approximation for arbitrary initial conditions.
Abstract In this work, the Darmois-Israel junction formalism is extended to the case of discontinuous metrics by employing the framework of Colombeau simplified generalized functions. This formalism provides a mathematically consistent treatment of nonlinear operations involving singular quantities, such as products of distributions, where Colombeau algebra acts as a differential algebra containing distributions as a subspace and $\mathscr{C}^{\infty}$ as a faithful subalgebra. By relaxing the continuity conditions traditionally adopted by Darmois and Israel, the junction conditions naturally incorporate higher-order singular terms in the curvature and the surface energy-momentum tensor, representing nonlinear, singular geometric structures associated with genuine spacetime discontinuities. As a concrete application, we analyze Kerr-Schild spacetimes within this generalized setting, demonstrating how singular metrics and associated curvature tensors are rigorously accommodated. The resulting formalism recovers the traditional Darmois-Israel conditions as a limiting case, while providing a consistent framework applicable to geometric boundaries and abrupt transitions in spacetime.
Abstract Within the FLRW framework, we reconstruct the late-time expansion history in $f(R,L_m,T)$ gravity using a redshift-dependent parametrization of the deceleration parameter. Its free parameters are constrained using Cosmic Chronometers~(CC), DESI DR2 baryon acoustic oscillations and Pantheon+ Type Ia supernovae data. The reconstructed expansion history consistently indicates a transition from deceleration to acceleration at $z_{\rm t}\approx0.6$, with the present-day deceleration parameter constrained to $q_0=-0.52$ for both the CC and CC+DESI DR2 combinations and $q_0=-0.50$ for the combined CC+DESI DR2+Pantheon+ dataset. The Statefinder diagnostic reveals a non-monotonic kinematic evolution, with the reconstructed trajectories successively passing through Chaplygin gas-like, $\Lambda$CDM-like and quintessence-like regimes before returning toward the Chaplygin gas-like region near the present epoch. The reconstructed cosmic age is $t_0\approx13.0$--$13.3~\mathrm{Gyr}$, while the present-day effective equation of state parameter is $\omega_0\approx -0.70$, consistent with accelerated expansion. The NEC and DEC remain satisfied, whereas the SEC is violated at late times. Statistical comparison using the AIC and BIC shows that the proposed model describes the observational data with an accuracy comparable to $\Lambda$CDM, while the BIC generally favors the simpler $\Lambda$CDM model because of its lower complexity.
