The Precise Inner Solutions of Gravity field Equations of Hollow and Solid Spheres and the Theorem of Singularity

Mei Xiaochun

Home/Archive/arXiv

arXiv · 1103.0339

The Precise Inner Solutions of Gravity field Equations of Hollow and Solid Spheres and the Theorem of Singularity

Mei Xiaochun

View original source ↗Read source document ↗Export metadata ↓

Abstract

In the present calculation of the inner solution of gravity field equation with spherical symmetry, in order to avoid the singularity appearing in the center of sphere, we actually let the integral constant to be zero. It is proved in this paper that the constant can not be zero. The metric of inner gravity field of hollow sphere is calculated at first. Then let the inner radius of hollow sphere become zero, we obtain the metric of inner gravity field of solid sphere. Based on the definition of energy momentum tensor of general relativity, the gravity masses of hollow and solid spheres in curved space are calculated strictly. The results indicate that no matter what the masses and densities of hollow sphere and solid sphere are, space-time singularities would appear in the centers of spheres. Meanwhile, no matter what the mass and density are, the intensity of pressure at the center point of solid sphere can not be infinite. That is to say, the material can not collapse towards the center of so-called black hole. In stead, it may be that there exist the spherical surfaces of infinite pressure inside the hollow and solid spheres, and material would collapse toward the surfaces so that the common spheres are unsteady. At the center of solid sphere and on its neighboring region, pressure intensities would become negative values. There may be a region for hollow sphere in which pressure intensities would become negative values too. The results only indicate that the singularity black holes predicated by general relativity are caused by the descriptive method of curved space-time and can not exist in nature actually. If black holes exist really in the universe, they can only be the Newtonian black holes, not the Einstein's black holes.

Explore related subjects

physics.gen-ph

Keep this discovery

BibTeX RIS

Mei Xiaochun. 2011-03-02. The Precise Inner Solutions of Gravity field Equations of Hollow and Solid Spheres and the Theorem of Singularity. https://arxiv.org/abs/1103.0339

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories

We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \& Sawicki and Starobinsky models, with background and large-scale structure (LSS) data. Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($f\sigma_8$, $f$, $\sigma_8$), we place tight constraints on the model parameters governing deviations from General Relativity. For the full dataset combination, we obtain $\log_{10} b_\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \& Sawicki model and $b_\mathrm{S} = (0.8\pm61.0)\times10^{-4}$ for the Starobinsky model. Model comparison based on the Akaike Information Criterion indicates that these $f(R)$ extensions are statistically favored over flat $\Lambda\text{CDM}$ ($|\Delta\text{AIC}| \ge 3.99$) for the combined data. However, when considering the Bayesian Information Criterion, the evidence for support is significantly reduced. Furthermore, we construct two-dimensional phase-space diagrams in the $(\mu, \gamma)$ and $(\mu, \Sigma)$ planes across several redshifts, establishing a novel diagnostic null-test allowing us to probe for deviations from $\Lambda\text{CDM}$, corresponding to the fixed point $(1,1)$ in both planes, using LSS observables. Should future weak-lensing and galaxy surveys provide data points with $\mu-1<0$ and $\gamma-1>1$ or $\Sigma-1 < 0 $, then the aforementioned models could be directly ruled out.

physics.gen-ph↗

arXiv2026

Bound states in the continuum of gravitational waves

Bound states in the continuum (BICs) are ubiquitous wave phenomena, but have not yet been demonstrated for gravitational waves (GWs). Here, in-plane periodic perturbations, exponentially localized at the plane $z = 0$, are shown to lead to distributional surface energy tensors at this plane and to be regular vacuum solutions ($T_{\mu \nu} = 0$) of the linearized Einstein field equations outside of it. These are achieved by explicitly calculating the Ricci tensor components and the Ricci scalar from the metric perturbation tensor. To fulfill each vacuum solution ($R_{{\sigma \nu}_{(+, \times)}} = 0$ and $R_{{}_{(+, \times)}} = 0$), different surface polariton-like dispersions are required. These bound perturbations decay exponentially to a flat metric ($h_{{BIC}_{(+,\times)}} \propto e^{- k_z |z|}$), and each localized metric has a correspondence to a different planar GW polarization ($+,\times$). The Lorenz gauge-fulfilling solutions exist at the $\Gamma$ point in momentum space, dwelling within the continuum of wavevectors of propagating GWs. The strains in the unit cell of the periodic perturbations have opposite parities relative to the corresponding planar GWs under a $C_2$ in-plane rotation, making them incompatible by symmetry with their propagating counterpart, indicating localization via symmetry protection.

physics.gen-ph↗

arXiv2026

Sector-Resolved Bayesian Model Averaging for DESI-Era Cosmology

We present a quotient-space Bayesian formulation for DESI-era anomaly interpretation. Given a pattern-labeled catalog with map $i\mapsto \Act(i)$, the induced posterior $p(\Act\mid D)$, sector inclusion probabilities $P_\alpha$, co-activation probabilities $P_{\alpha\beta}$, and grouped Bayes factors $B_\alpha(D)$ are exact summaries over predeclared physical activation events. Pairwise comparisons such as $\lcdm$ versus $\wacdm$ remain ordinary Bayes-factor tests between specified families; the quotient construction addresses the coarser question of which physical sector carries posterior support when different sectors are represented by unequal numbers of catalog elements. We derive a sector-resolved DESI-CMB-SN likelihood specification for late-time background, early-time ruler, supernova calibration, perturbation, and gravitational-wave propagation sectors. The construction includes an Alcock-Paczynski/isotropic-scale BAO decomposition, a pure-ruler projection, analytic marginalization of low-rank supernova calibration modes, Fisher-normalized sector priors, inactive-sector leakage tests, log-evidence uncertainty propagation, and prior/sector-partition diagnostics. The result is a quantitative procedure for reporting model-comparison support at the level of physically interpretable sectors.

physics.gen-ph↗