Search Results (5)

The methodology is developed here to write Ricci solitons on the newly found structure of the pseudo-spherical cylinder. The methodology is specified for Schwarzschild solitons and for Generalized-Schwarzschild solitons. Accordingly, a new classification is written for the Schwarzschild solitons and for the Generalized-Schwarzschild solitons. The rotational field is spelled out. The potential for a tangent vector field is used. The conditions are recalled to discriminate which submanifold of a Ricci manifold is a soliton or is an almost-Ricci soliton. It is my aim to prove that a concurrent vector field is uniquely determined after the 4-velocity vector of a Schwarzschild soliton. As a result, the analytically specified manifold, which is a spacelike submanifold of the Schwarzschild spacetime that admits Ricci solitons. The rotational killing fields are tangent to the event horizon. The conditions that are needed to match the new aspects are spelled out analytically. As a result, the two manifolds described in the work of Bardeen et al. about the requested mass of a stationary, axisymmetric solution of the Einstein Field Equations of the spacetime, which contains a blackhole surrounded with matter from the new results obtained after correcting the work of Hawking 1972 about would-be point ’beyond the conjugate point’ on the analytic continuation of the would-be geodesics: they are proven here to become the tangent manifold (which is expressed from the tangent bundle in General-Relativistic notation). The prescription here is based on one of the books of Landau et al., that the matter is not put into the metric tensor, not even in the ultra-Relativistic limit. This way, the pseudo-spherical cylinder is one implemented from the Minkowskian description and whose asymptotical limit is proven. The new methodology allows one to describe the outer region of the blackhole as one according to which the (union of the trapped) regions is one with null support. For the purpose of the present investigation, the definition of concurrent vector fields in General-Relativity is newly developed. As a further new result, the paradigm is implemented for the shrinking case, which admits as subcase the Schwarzschild manifolds and the Generalized-Schwarzschild manifolds. The Penrose 1965 Theorem is discussed for the framework outlined here; in particular, the presence of trapped hypersurfaces is discarded. The no-hair theorem can now be discussed. Full article

General relativity (GR) postulates have been verified with high precision, yet our understanding of how gravity interacts with matter fields remains incomplete. Various modifications to GR have been proposed in both classical and quantum realms to address these interactions within the strong gravity regime. One such approach is non-minimal coupling (NMC), where the space-time curvature (scalar and tensor) interacts with matter fields, resulting in matter fields not following the geodesics. To probe the astrophysical implications of NMC, in this work, we investigate non-minimally coupled electromagnetic (EM) fields in the presence of black holes. Specifically, we show that primordial black holes (PBHs) provide a possible tool to constrain the NMC parameter. PBHs represent an intriguing cosmological black hole class that does not conform to the no-hair theorem. We model the PBH as a Sultana–Dyer black hole and compare it with Schwarzschild. We examine observables such as the radius of the photon sphere, critical impact parameter, and total deflection angles for non-minimally coupled photons for Schwarzschild and Sultana–Dyer black holes. Both the black hole space-times lead to similar constraints on the NMC parameter. For a PBH of mass $M={10}^{-5} M_{\odot }$, the photon sphere will not be formed for one mode. Hence, the photons forming the photon sphere will be highly polarized, potentially leading to observable implications. Full article

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy. Full article

We review nonsingular static, spherically symmetric solutions of general relativity with minimally coupled scalar fields. Considered are wormholes and regular black holes (BHs) without a center, including black universes (BHs with expanding cosmology beyond the horizon). Such configurations require a “ghost” field with negative kinetic energy K. Ghosts can be invisible under usual conditions if $K<0$ only in strong-field region (“trapped ghost”), or they rapidly decay at large radii. Before discussing particular examples, some general results are presented, such as the necessity of anisotropic matter for asymptotically flat or AdS wormholes, no-hair and global structure theorems for BHs with scalar fields. The stability properties of scalar wormholes and regular BHs under spherical perturbations are discussed. It is stressed that the effective potential $V_{\mathrm{eff}}$ for perturbations has universal shapes near generic wormhole throats (a positive pole regularizable by a Darboux transformation) and near transition surfaces from canonical to ghost scalar field behavior (a negative pole at which the perturbation finiteness requirement plays a stabilizing role). Positive poles of $V_{\mathrm{eff}}$ emerging at “long throats” (with the radius $r\approx r_0+\mathrm{const}·x^{2n}$ , $n>1$ , $x=0$ is the throat) may be regularized by repeated Darboux transformations for some values of n. Full article