In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole, and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made towards understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semi-classical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in General Relativity and the common effective Hamiltonian proposed in earlier literature.
We study spherically symmetric solutions to the Jordan-Brans-Dicke field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. Assuming a perfect fluid with the equation of state, we show that there are static interior nontrivial solutions in three dimensional Jordan-Brans-Dicke gravity theory.
Using a semi-empirical approach we show that modified gravity affects the internal properties of terrestrial planets, such as their physical characteristics of a core, mantle, and core-mantle boundary. We also apply these findings for modeling a two-layers exoplanet in Palatini $f(R)$ gravity.
In recent work, the Schwarzschild interior of a black hole was investigated, incorporating quantum gravitational modifications due to loop quantum gravity. The central Schwarzschild singularity was shown to be replaced by a Nariai type universe. In this brief report we show that this interior solution is stable with respect to small perturbations, in contrast to the classical Nariai universe.
In a one parameter family of dilaton gravity theories which allow the coupling of the dilaton to gravity and to a U(1) gauge field to differ, we have found the existence of everywhere regular spacetimes describing black holes hiding expanding universes inside their horizon.
We have found some new exact static spherically symmetric interior solutions of metric $f(R)$ gravitational theories describing the equilibrium configuration of a star. Then the solution is matched to the exterior solution and thus gives a complete description of a star in $R^{1-n/2}$ theory.
We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric $f(R)$ theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of $f(R)$. It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in $f(R)$ gravity.
We discuss the interior solutions of fluid Sphere in f(R,T) gravity admitting conformal killing vectors, where R is Ricci scalar and T is trace of energy momentum tensor. The solutions corresponding to isotropic and anisotropic configurations have been investigated explicitly. Further, the anisotropic case has been dealt by the utilization of linear equation of state. The results for both cases have been interpreted graphically. The equation of state parameter, integration constants and other parameters of the theory have been chosen to find the central density equal to standard value of centr…
For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior sol…
We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of freedom when viewed from a semiclassical standpoint. The relation between quantum mechanics and the equivalence principle is subtle, but they are still consistent.
We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Hořava gravity and Einstein-æther theory in presence of anisotropic fluids. We focus for simplicity on the case of a static æther finding a large class of possible viable interior star solutions which present a very rich phenomenology. We study one illustrative example in more detail.
A method for constructing metric gravity's N-body Lagrangian is developed which uses iterative, liner algebraic euqations which enforce invariance properties of gravity --- exterior effacement, interior effacement, and the time dilation and Lorentz contraction of matter under boosts. The method is demonstrated by obtaining the full 1/c^4 order Lagrangian, and a combination of exterior and interior effacement enforcement permits construction of the full Schwarzschild temporal and spatial metric potentials.
The general equations describing hydrostatic equilibrium are developed for Non-singular Gravity. A new type of astrophysical structure, a Super Dense Object (SDO) or "Dark Star", is shown to exist beyond Neutron star field strengths. These structures are intrinsically stable against gravitational collapse and represent the non-singular alternative to General Relativity's Black Holes.
We study the interior spacetimes of stars in the Palatini formalism of f(R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-De Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in General Relativity. These modifications become neglible in models for which $δF(R) \equiv \partial f/\partial R - 1$ is a decreasing function of R however. As a result, both Solar …
The physically realistic model of compact stars undergoing gravitational collapse in $ f(R) $ gravity has been developed. We consider a more general model $ R + f(R) = R + k R^m $ and describe the interior space-time of gravitationally collapsing stars with separable-form of metric admitting homothetic killing vector. We then investigate the junction conditions to match the interior space-time with exterior space-time. Considering all junction conditions, we find analytical solutions describing interior space-time metric, energy density, pressures, and heat flux density of the compact stars un…
We study the effects of a beyond-Horndeski theory of modified gravity in the interior of a population II star. We consider a simple phenomenological model of a $1.1M_{\odot}$ star that has left the main sequence, has a thin Hydrogen burning shell with a partially degenerate isothermal core, surrounded by a radiative envelope having two regions of distinct opacities. Using suitable matching conditions at the two internal boundaries, a numerical analysis of the resulting stellar equations in modified gravity is carried out. While overall, gravity may be weakened, resulting in a decrease of the l…
A quantum-cosmology-suited sliced Milne spacetime, located inside a 'big-bang' forward lightcone, comprises the interiors of a sequence of 4-dimensional slices whose invariant 'age' width is at Planck scale. The age of any lightcone-interior point is its Minkowski distance from the lightcone vertex, but excluded from the spacetime of a 'quantum Milne universe' (QMU) are 3-dimensional slice-separating, ray-carrying hyperboloids. Each (fixed-age) slice boundary houses a Gelfand-Naimark unitarily Lorentz-transformable cosmological-Fock-space ray-a sum of tensor products of complex normed fiber-bu…
In this paper, we explore the interior dynamics of neutral and charged black holes in $f(R)$ gravity. We transform $f(R)$ gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordström geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of $f'$ and a physical scalar field being taken into account. The dynamics in the vicinities of the central singularity of a Schwarzschild black hole and of the inner horizo…
In this paper we calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular we obtain a bounce of the two-sphere for a minimum value of the radius and that it is possible to have another event horizon close to the r=0 point.
This paper is devoted to investigate gravitational collapse of dust in metric $f(R)$ gravity. We take FRW metric for the interior region while the Schwarzchild spacetime is considered for the exterior region of a star. The junction conditions have been derived to match interior and exterior spacetimes. The assumption of constant scalar curvature is used to find a solution of field equations. Gravitational mass is found by using the junction conditions. It is concluded that the constant curvature term $f(R_0)$ plays the role of the cosmological constant involved in the field equations of genera…
The perspective is advanced that the time parameter in quantum mechanics corresponds to the time coordinate in a Minkowski flat spacetime local approximation to the actual dynamical curved spacetime of General Relativity, rather than to an external Newtonian reference frame. There is no incompatibility, as generally assumed in the extensively discussed "problem of time" in Quantum Gravity.
This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density whic…
Within $F\left( B^2\right)$ modified Weyl gravity, we consider a model of a spin-$1/2$ electric charge consisting of interior and exterior regions. The interior region is determined by quantum gravitational effects whose approximate description is carried out using Weyl gravity nonminimally coupled to a massless Dirac spinor field. The interior region is embedded in exterior Minkowski spacetime, and the joining surface is a two-dimensional torus. It is shown that mass, electric charge, and spin of the object suggested may be the same as those for a real electron.
We show that loop quantum gravity effects leads to the finiteness of expansion and its rate of change in the effective regime in the interior of the Schwarzschild black hole. As a consequence the singularity is resolved. We find this in line with previous results about curvature scalar and strong curvature singularities in Kantowski-Sachs model which is isometric to Schwarzschild interior.
The field equations of Mannheim's theory of conformal gravity with dynamic mass generation are solved numerically in the interior and exterior regions of a model spherically symmetric sun with matched boundary conditions at the surface. The model consists of a generic fermion field inside the sun, and a scalar Higgs field in both the interior and exterior regions. From the conformal geodesic equations it is shown how an asymptotic gradient in the Higgs field causes an anomalous radial acceleration in qualitative agreement with that observed on the Pioneer 10/11, Galileo, and Ulysses spacecraft…
In the present work, we have discussed the four dimensional spherically symmetric steller system in the framework of modified $f(T)$ gravity theory with electro-magnetic field. The field equations have been written for two cases, either $T'=0$ or $f_{TT}=0$. Next we have discussed the charged gravastar model which has three regions: interior region, shell region and exterior region. In the interior region, we have found the solutions of all physical quantities like density, pressure, electro-magnetic field and also the metric coefficients for both the cases. For $T'=0$, gravastar cannot form b…
We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton's constant is allowed to vary with the radial coordinate throughout the star. Assuming i) a linear equation-of-state in the MIT bag model for quark matter, and ii) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditio…
In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive g…
The idea that quantum gravity manifestations would be associated with a violation of Lorentz invariance is very strongly bounded and faces serious theoretical challenges. Other related ideas seem to be drowning in interpretational quagmires. This leads us to consider alternative lines of thought for such phenomenological search. We discuss the underlying viewpoints and briefly mention their possible connections with other current theoretical ideas.
We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using congruences and their associated expansion scalar and the Raychaudhuri equation. We reaffirm previous results that in loop quantum gravity, in all three major schemes of polymer quantization, the expansion scalar, Raychaudhuri equation and the Kretschmann scalar remain finite everywhere in the interior. In the context of the eneralized uncertainty …
This paper is devoted to investigate the gravitational perfect fluid collapse in the framework of Chern-Simon modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. The Israel junction conditions are used to match the interior and exterior spacetimes. For the sake of simplicity, we take the external field $Θ$ as a function of time parameter $t$ and obtain the solution of the field equations of Chern-Simon modified gravity. Junction conditions have been used to calculate…
The present work includes an analytical investigation of a collapsing spherical star in f (R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration a…
Gravity is one of the most inexplicable forces of nature, controlling everything, from the expansion of the Universe to the ebb and flow of ocean tides. The search for the laws of motion and gravitation began more than two thousand years ago but still we do not have the complete picture of it. In this article, we have outlined how our understanding of gravity is changing drastically with time and how the previous explanations have shaped the most recent developments in the field like superstrings and braneworlds.
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the quantum-reduced model from the perspective of full loop quantum gravity. We show that, in spite of their simplicity, the operators of the quantum-reduced model are simply the operators of the full theory acting on states in the Hilbert space of the quantum-reduced model. The passage from the full theory operators to the "reduced" operators simply consists of noting that …
The improved description of the planets' interior is provided. We examine the modified gravity effects on the Earth-like planets composed of the iron core and silicate mantle. We confirm that the mass-radius relations, as well as density profiles, differ with respect to the commonly adopted Newtonian models.
In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric $f(R)$ gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude …
Black Hole Interior and Quantum Error Correction with Dynamical Gravity
Center for Gravitational Physics and Quantum Information (CGPQI), Yukawa Institute for Theoretical Physics (YITP), Kyoto University（京都大学引力物理与量子信息中心（CGPQI），理论物理汤川研究所（YITP））；Department of Physics, Rikkyo University（立教大学物理系）
We propose a unique stellar model under the $f(R,\mathcal{T})$ gravity by using the conjecture of Mazur-Mottola [P. Mazur and E. Mottola, Report number: LA-UR-01-5067., P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004)] which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides…
Sakharov's 1967 notion of ``induced gravity'' is currently enjoying a significant resurgence. The basic idea, originally presented in a very brief 3-page paper with a total of 4 formulas, is that gravity is not ``fundamental'' in the sense of particle physics. Instead it was argued that gravity (general relativity) emerges from quantum field theory in roughly the same sense that hydrodynamics or continuum elasticity theory emerges from molecular physics. In this article I will translate the key ideas into modern language, and explain the various versions of Sakharov's idea currently on the mar…
We provide a set of exact spherically symmetric solutions describing the interior of a relativistic star under f(T) modified gravity. To tackle the problem with lucidity we also assume the existence of a conformal Killing vector field within this f(T) gravity. We study several cases of interest to explore physically valid features of the solutions.
We study Faddeev formulation of gravity, in which the metric is composed of vector fields. We consider these fields constant in the interior of the 4-simplices of a simplicial complex. The action depends not only on the values of the fields in the interior of the 4-simplices but on the details of (regularized) jump of the fields between the 4-simplices. Though, when the fields vary arbitrarily slowly from the 4-simplex to 4-simplex, the latter dependence is negligible (of the next-to-leading order of magnitude). We put the earlier proposed in our work first order (connection) representation of…
We explore an interior solution of a physically symmetric vierbein with two unknown functions in conformal teleparallel gravity. The field equations can be described in a closed system for a particular form of the metric potentials and an appropriate anisotropic function. As a result, we find a new set of configurations consistent with observed pulsars. In particular, the boundary conditions for the interior spacetime are used for the Schwarzschild spacetime to constrain the conformal field that with a unit value through the surface of a compact object. Furthermore, we apply the present model …
Physical arguments related with the existence of black hole solutions having a non trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field approaching a constant value at the horizon are given. It is argued that the coupled Einstein-Klein-Gordon equations can be satisfied in the sense of the generalized functions after removing a particular regularization designed for matching the interior solution with an external Scwartzschild spacetime. The scalar field appears as just avoiding the appearance of clo…
In a previous work we derived an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We now use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian, though still bearing the well known ambiguities of the quantum Hamiltonian operator, preserves all relevant information abo…
Source-free equations of nonlinear electrodynamics minimally coupled to gravity admit regular axially symmetric asymptotically Kerr-Newman solutions which describe charged rotating black holes and electromagnetic spinning solitons (lumps). Asymptotic analysis of solutions shows, for both black holes and solitons, the existence of de Sitter vacuum interior which has the properties of a perfect conductor and ideal diamagnetic and displays superconducting behaviour which can be responsible for practically unlimited life time of an object. Superconducting current flows on the equatorial ring repla…
In the context of Born-Infeld gravity theories we report the existence of a regular black hole interior representing a spherically symmetric vacuum solution of the theory. It reduces to the Schwarzschild interior metric in the weak field region. In particular, there is a new length scale which is related to the Born-Infeld parameter. This endows the spacetime with an inner (i.e. well inside the event horizon) asymptotic region which is unattainable for observers. The central curvature singularity is replaced by an infinitely long cosmic string with constant curvature invariants related to the …
We study the spontaneously induced general relativity (GR) from the scalar-tensor gravity. We demonstrate by numerical methods that a novel inner core can be connected to the Schwarzschild exterior with cosmological constants and any sectional curvature. Deriving an analytic core metric for a general exterior, we show that all the nontrivial features of the core, including the locally holographic entropy packing, are universal for the general exterior in static spacetimes. We also investigate whether the f(R) gravity can accommodate the nontrivial core.
We study the interior structure of five dimensional neutral helical black holes in Einstein gravity and charged helical black holes in Einstein-Maxwell gravity. Inside the neutral helical black holes, the systems evolve to a stable spacelike Kasner singularity. The metric field related to the helical deformation strength exhibits oscillation behavior close to the horizon at low temperature and small helical deformation strength. Inside the charged helical black holes, we show that the inner Cauchy horizon can not exist. The systems also evolve from the horizon to a stable Kasner singularity. W…
