Andrea Giusti, Valerio Faraoni
A recent generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is adapted to general spherically symmetric geometries. It is then applied to several black hole and other spherical solutions of scalar-tensor and $f({\cal R}) $ gravity. The relations of this quasilocal energy with the Abreu-Nielsen-Visser gauge and the Kodama vector are discussed.
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A generalization of the Hawking-Hayward quasilocal mass to scalar-tensor gravity is compared, in vacuo and for asymptotically flat stationary geometries, with a recent multipole expansion of the gravitational field. The quasilocal mass seen at spatial infinity coincides with the monopole term, lending credibility to this construct.
We point out an association between anomalies in the Hawking quasilocal mass (or, in spherical symmetry, in its better known version, the Misner-Sharp-Hernandez mass) and unphysical properties of the spacetime geometry. While anomalous behaviors show up in certain quantum-corrected black holes, they are not unique to this context and signal serious physical pathologies of isolated gravitating systems in general.
Following an existing procedure in general relativity, the turnaround radius of a spherical structure is studied in scalar-tensor gravity using a new prescription for the analog of the Hawking-Hayward quasilocal mass in this class of theories.
The Bel-Robinson tensor $B_{αβμν}$ gives a positive definite gravitational energy in the quasilocal small sphere limit approximation. However, there is an alternative tensor $V_{αβμν}$ that was proposed recently that offers the same positivity as $B_{αβμν}$ does. We have found that $V_{αβμν}$ is the unique alternative tensor with $B_{αβμν}$ which implies that these two tensors are a basis for expressions that have the desirable non-negative gravitational energy in the small sphere limit. In other words, the `energy-momentum' density according to $B_{αβμν}$ and $V_{αβμν}$ are on equal footing a…
The Misner-Sharp-Hernandez mass defined in general relativity and in spherical symmetry has been recognized as having a Newtonian character in previous literature. In order to better understand this aspect we relax spherical symmetry and we study the generalization of the Misner-Sharp-Hernandez mass to general spacetimes, i.e., the Hawking quasilocal mass. The latter is decomposed into a matter and a pure Weyl contribution. The decomposition of the Weyl tensor into an electric part (which has a Newtonian counterpart) and a magnetic one (which does not) further splits the quasilocal mass into "…
A new generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of writing the scalar-tensor field equations as effective Einstein equations and then applying the standard definition of quasilocal mass.
We study the Brown-York quasilocal energy for regular black holes. We also express the identity that relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime for static and spherically symmetric black hole solutions in a convenient way which permits us to understand why this identity is not satisfied when we consider nonlinear electrodynamics. However, we give a relation between quantities evaluated at the horizon and at infinity when nonlinear electrodynamics is considered. Similar relations are obtained for more gener…
The Bel-Robinson tensor $B$ and the tensor $V$ have the same quasilocal energy-momentum in a small sphere. Using a pseudotensor approach to evaluate the energy-momentum in a half-cylinder, we find that $B$ and $V$ have different values, not proportional to the "Bel-Robinson energy-momentum". Furthermore, even if we arrange things so that we do get the same "Bel-Robinson energy-momentum" value, the angular momentum gives different values using $B$ and $V$ in a half cylinder. In addition, we find that $B$ and $V$ have a different number of independent components. The fully trace free property of…
Spherically symmetric spacetimes admit the so-called Kodama vector, which provides a locally conserved current and a preferred time even for dynamical spacetime without any time translation symmetry. A charge associated with this conserved current leads to a quasilocal mass which agrees with the Misner-Sharp mass. In three dimensions, spherically symmetric spacetimes correspond to axisymmetric ones, while axisymmetry allows spacetimes to be rotating with angular momentum. We extend the notion of the Kodama vector to axisymmetric rotating spacetimes in three dimensions. We also define a quasilo…
In several areas of theoretical physics it is useful to know how a quasilocal energy transforms under conformal rescalings or generalized Kerr-Schild mappings. We derive the transformation properties of the Brown-York quasilocal energy in spherical symmetry and we contrast them with those of the Misner-Sharp-Hernandez energy.
The M$ø$ller tetrad gravitational energy-momentum expression was recently evaluated for a small vacuum region using orthonormal frames adapted to Riemann normal coordinates. However the result was not proportional to the Bel-Robinson tensor $B_{αβμν}$. Treating a modified quasilocal expressions in a similar way, we found one unique combination that gives a multiple of $B_{αβμν}$ which provides a non-negative gravitational energy-momentum in the small sphere approximation. Moreover, in addition to $B_{αβμν}$, we found a certain tensor $S_{αβμν}+K_{αβμν}$ which gives the same "energy-momentum" d…
Quasilocal definitions of stress-energy-momentum---that is, in the form of boundary densities (in lieu of local volume densities)---have proven generally very useful in formulating and applying conservation laws in general relativity. In this essay, we take a first basic look into applying these to cosmology, specifically using the Brown-York quasilocal stress-energy-momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source.
Finite-cutoff holography and quasilocal thermodynamics of BTZ black holes in a cavity
本文提出有限截断形式的BTZ黑洞热力学，将圆环腔视为真实反 holographic 屏幕，结合准局部引力系统和AdS_3中的有限半径holography，探讨静态和旋转BTZ几何的热力学。
The quasilocal energy of gravitational and matter fields in a spatially bounded region is obtained by employing a Hamilton-Jacobi analysis of the action functional. First, a surface stress-energy-momentum tensor is defined by the functional derivative of the action with respect to the three-metric on ${}^3B$, the history of the system's boundary. Energy density, momentum density, and spatial stress are defined by projecting the surface stress tensor normally and tangentially to a family of spacelike two-surfaces that foliate ${}^3B$. The integral of the energy density over such a two-surface $…
We revisit the relationship of inequality between the gravitational field energy and the Komar charge, both quantities evaluated at the event horizon, for static and spherically symmetric regular black hole solutions obtained with nonlinear electrodynamics. We found a way to characterize these regular black hole solutions by the energy conditions that they satisfy. In particular, we show the relation between the direction of the inequality and the energy condition that satisfy the regular black hole solutions.
For describing the non-negative gravitational energy-momentum in terms of a pure Bel-Robinson type energy-momentum in a quasilocal 2-surface, both the Bel-Robinson tensor $B$ and tensor $V$ are suitable. We found that this Bel-Robinson type energy-momentum can be modified such that it satisfies the Lorentz covariant, future pointing and non-spacelike properties. We find that these particular energy-momentum properties can be obtained from (i): $B$ or $V$ plus a tensor $S$ in a quasilocal small cube limit, or (ii): directly evaluating the energy-momentum of $B$ or $V$ in a quasilocal small box …
Equilibrium thermodynamic laws are typically applied to horizons in general relativity without stating the conditions that bring them into equilibrium. We fill this gap by applying a new thermodynamic interpretation to a generalized Raychaudhuri equation for a worldsheet orthogonal to a closed spacelike 2-surface, the "screen", which encompasses a system of arbitrary size in nonequilibrium with its surroundings in general. In the case of spherical symmetry this enables us to identify quasilocal thermodynamic potentials directly related to standard quasilocal energy definitions. Quasilocal ther…
We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects. We construct a general quasi}local conservation law based on the Brown and York total (matter plus gravity) stress-energy-momentum tensor (characterized by energy and momentum per unit area), and argue that it does properly account for gravitational effects. As a simple example of the explanatory power of …
Quasilocal definitions of stress-energy-momentum -- that is, in the form of boundary densities (rather than local volume densities) -- have proven generally very useful in formulating and applying conservation laws in general relativity. In this paper, we present a detailed application of such definitions to cosmology, specifically using the Brown-York quasilocal stress-energy-momentum tensor for matter and gravity combined. We compute this tensor, focusing on the energy and its associated conservation law, for FLRW spacetimes with no pertubrations and with scalar cosmological perturbations. F…
We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric. We first extend the Brown-York quasilocal formalism to such theories to obtain the ``unreferenced'' quasilocal mass and prove it to be conformally invariant. The appropriate reference term in this case is defined by generalizing the Hawking-Horowitz prescription, which was originally proposed for general relativity. For such a choice of reference term, the referenced quasilocal m…
General matterless--theories in 1+1 dimensions include dilaton gravity, Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General Relativity. Their recent identification as special cases of 'Poisson--sigma--models' with simple general solution in an arbitrary gauge, allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, resp. notions of quasilocal 'energy--momentum'. In contrast to Noether like quantities, quas…
This paper is dedicated to the investigation of the positivity of the Hayward quasilocal energy of tori. Marginally trapped tori have nonnegative Hayward energy. We consider a scenario of a spherically symmetric constant density star matched to an exterior Schwarzschild solution. We show that any generic tori within the star, distorted or not, trapped or not, have strictly positive Hayward energy. Surprisingly we find analytic examples of `thin' tori with negative Hayward energy in the outer neighborhood of the Schwarzschild horizon. These tori are swept out by rotating the standard round circ…
We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $Σ$ contained within a finite topologically spherical boundary $B = \partial Σ$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield…
Spinorial quasilocal mass for spacetimes with negative cosmological constant
本研究针对负宇宙学常数四维时空的紧致二维类空曲面，基于已有零宇宙学常数相关成果提出旋量式新拟局域质量定义，验证了其非负性及多类时空场景下的性质一致性。
The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension $n\geq 4$. After generalising three distinct quasilocal energy definitions to higher dimensions under appropriate assumptions, we evaluate their small sphere limits along lightcone cuts shrinking towards the lightcone vertex. The results in vacuum are conveniently represented in terms of the electromagnetic decompositions of the Weyl tensor. We find that the limits at presence of matter yield the stress tensor as expected, but th…
In general relativity, the local gravitational energy is best characterised by the quasilocal mass. The small sphere limit of quasilocal mass provides us the most local notion of gravitational energy. In four dimensions, the limits were shown be the stress tensor in non-vacuum and the Bel-Robinson tensor in vacuum. We study the local gravitational energy in higher dimensions through the lens of the small sphere limits of various quasilocal mass proposals which can be appropriately generalised beyond four dimensions, and report a new quantity $\Q$ which potentially characterises the local gravi…
From a covariant Hamiltonian formulation, by using symplectic ideas, we obtain certain covariant boundary expressions for the quasilocal quantities of general relativity and other geometric gravity theories. The contribution from each of the independent dynamic geometric variables (the frame, metric or connection) has two possible covariant forms associated with the selected type of boundary condition. The quasilocal expressions also depend on a reference value for each dynamic variable and a displacement vector field. Integrating over a closed two surface with suitable choices for the vector …
We study a recently proposed horizon defining identity for certain black hole spacetimes. It relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime. The Brown-York quasilocal energy is evaluated for some specific choices of spacetime foliations. With a certain condition imposed on the matter distribution, we prove this identity for spherically symmetric static black hole solutions of general relativity. For these cases, we show that the identity can be derived from a Gauss-Codacci condition that any three-dimensional …
Consider the definition E of quasilocal energy stemming from the Hamilton-Jacobi method as applied to the canonical form of the gravitational action. We examine E in the standard "small-sphere limit," first considered by Horowitz and Schmidt in their examination of Hawking's quasilocal mass. By the term "small sphere" we mean a cut S(r), level in an affine radius r, of the lightcone belonging to a generic spacetime point. As a power series in r, we compute the energy E of the gravitational and matter fields on a spacelike hypersurface spanning S(r). Much of our analysis concerns conceptual and…
We define the coarse-grained entropy of a `normal' surface $σ$, i.e., a surface that is neither trapped nor antitrapped. Following Engelhardt and Wall, the entropy is defined in terms of the area of an auxiliary extremal surface. This area is maximized over all auxiliary geometries that can be constructed in the interior of $σ$, while holding fixed the spatial exterior (the outer wedge). We argue that the area is maximized when the stress tensor in the auxiliary geometry vanishes, and we develop a formalism for computing it under this assumption. The coarse-grained entropy can be interpreted a…
Traditional approaches to energy-momentum localization led to reference frame dependent pseudotensors. The more modern idea is quasilocal energy-momentum. We take a Hamiltonian approach. The Hamiltonian boundary term gives not only the quasilocal values but also boundary conditions via the Hamiltonian variation boundary principle. Selecting a Hamiltonian boundary term involves several choices. We found that superpotentials can serve as Hamiltonian boundary terms, consequently pseudotensors are actually quasilocal and legitimate. Various Hamiltonian boundary term quasilocal expressions are cons…
The energy of gravitational waves is a fundamental problem in gravity theory. The existing descriptions for the energy of gravitational waves, such as the well-known Isaacson energy-momentum tensor, suffer from several defects. Due to the equivalence principle, the gravitational energy-momentum can only be defined quasilocally, being associated with a closed spacelike 2-surface bounding a region. We propose a new approach to derive the energy of gravitational waves $directly$ from the quasilocal gravitational energy. Such an approach is natural and consistent with the quasilocality of gravitat…
The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energy-momentum density should be proportional to the Bel-Robinson tensor $B_{αβμν}$. However, we propose a new tensor $V_{αβμν}$ which is the sum of certain tensors $S_{αβμν}$ and $K_{αβμν}$, it has certain properties so that it gives the same gravitational "energy-momentum" content as $B_{αβμν}$ does. …
In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level that these RQF conservation laws are superior to conservation laws based on the local stress-energy-momentum tensor of matter because (1) they do not rely on spacetime symmetries and (2) they properly account for both matter and gravitational effects. Moreover, they provide simple, exact, operational expressions for fluxes of gravitational energy and linear …
Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation-dependent. We expose the problem and discuss possible solutions using the Hawking quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry the apparent horizons are gauge-independent in any spherically symmetric foliation but physical quantities associated with them, such as surface gravity and temperature, are not. The widely used comoving and Kodama …
We construct a general relativistic conservation law for linear and angular momentum for matter and gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic energy conservation law with the same features. Our approach uses the Brown and York quasilocal stress-energy-momentum tensor for matter and gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF approach allows us to construct, in a generic spacetime, frames of reference who…
It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the gauge-invariant quantities. Both degrees of freedom fulfill generalized scalar wave equation. For the axial degree of freedom the radial part of the equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069 (1957)) and for the polar one we get Zerilli result (Phys. Rev. D2, 2141-2160 (1970)), see also Chandrasekhar (The Mathematical Theory of Black…
Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes of mass and energy. The gravity models for which our arguments are valid include theories with dynamical torsion and so-called generalized dilaton theories (GDTs). Our analysis of the canonical action principle (i) provides a rigorous correspondence between the most general first-order two-dimensional Einstein-Cartan model (ECM) and GDT and (ii) allows us to…
An idealized "test" object in general relativity moves along a geodesic. However, if the object has a finite mass, this will create additional curvature in the spacetime, causing it to deviate from geodesic motion. If the mass is nonetheless sufficiently small, such an effect is usually treated perturbatively and is known as the gravitational self-force due to the object. This issue is still an open problem in gravitational physics today, motivated not only by basic foundational interest, but also by the need for its direct application in gravitational-wave astronomy. In particular, the observ…
A complete description of the linearized gravitational field on a flat background is given in terms of gauge-independent quasilocal quantities. This is an extension of the results from gr-qc/9801068. Asymptotic spherical quasilocal parameterization of the Weyl field and its relation with Einstein equations is presented. The field equations are equivalent to the wave equation. A generalization for Schwarzschild background is developed and the axial part of gravitational field is fully analyzed. In the case of axial degree of freedom for linearized gravitational field the corresponding generaliz…
Conformal matter collineations of the energy-momentum tensor for a general spherically symmetric static spacetime are studied. The general form of these collineations is found when the energy-momentum tensor is non-degenerate, and the maximum number of independent conformal matter collineations is \emph{fifteen}. In the degenerate case of the energy-momentum tensor it is found that these collineations have infinite degrees of freedom. In some subcases of degenerate energy-momentum, the Ricci tensor is non-degenerate, that is, there exist non-degenerate Ricci inheritance collineations.
This paper studies a class of $D=n+2(\ge 6)$ dimensional solutions to Lovelock gravity that is described by the warped product of a two-dimensional Lorentzian metric and an $n$-dimensional Einstein space. Assuming that the angular part of the stress-energy tensor is proportional to the Einstein metric, it turns out that the Weyl curvature of an Einstein space must obey two kinds of algebraic conditions. We present some exact solutions satisfying these conditions. We further define the quasilocal mass corresponding to the Misner-Sharp mass in general relativity. It is found that the quasilocal …
We analyze the relationship between quasilocal masses calculated for solutions of conformally related theories. We show that the ADM mass of a static, spherically symmetric solution is conformally invariant (up to a constant factor) only if the background action functional is conformally invariant. Thus, the requirement of conformal invariance places restrictions on the choice of reference spacetimes. We calculate the mass of the black hole solutions obtained by Garfinkle, Horowitz, and Strominger (GHS) for both the string and the Einstein metrics. In addition, the quasilocal thermodynamic qua…
Using the Brown-York prescription for the definition of quasilocal gravitational energy-momentum tensor on a boundary and also complete canonical structure on a null boundary which has been found recently \cite{Aghapour:2018icu}, we propose a similar stress tensor on the null boundary. Then we exploit this stress tensor to compute the quasi-local energy and angular momentum for some well-known gravitational solutions. We have found that in addition to reference spacetime method for regularizing total energy, in the case of null boundary we can add a possible counterterm so avoiding embedding d…
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also in the setting of Finsler geometry, or more general geometries on the tangent bundle, where the objects of relevance are d-tensors on the tangent bundle, or tensors in a pullback bundle, instead of ordinary tensors. For this purpose, we construct a set of d-tensor harmonics for spherical symmetry and show how these can be used for calculations in Finsler geo…
We compare the Brown-York (BY) and the standard Misner-Sharp (MS) quasilocal energies for round spheres in spherically symmetric space-times from the point of view of radial geodesics. In particular, we show that the relation between the BY and MS energies is precisely analogous to that between the (relativistic) energy E of a geodesic and the effective (Newtonian) energy E_{eff} appearing in the geodesic equation, thus shedding some light on the relation between the two. Moreover, for Schwarzschild-like metrics we establish a general relationship between the BY energy and the geodesic effecti…
Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass c…
In this work, we extend the analysis of Brown and York to find the quasilocal energy in a spherical box in the Schwarzschild spacetime. Quasilocal energy is the value of the Hamiltonian that generates unit magnitude proper-time translations on the box orthogonal to the spatial hypersurfaces foliating the Schwarzschild spacetime. We call this Hamiltonian the Brown-York Hamiltonian. We find different classes of foliations that correspond to time-evolution by the Brown-York Hamiltonian. We show that although the Brown-York expression for the quasilocal energy is correct, one needs to supplement t…
Approximations of the quasi-local Bartnik mass in general relativity
本研究利用 eth 算子和自旋加权球谐函数表达 ADM 质量，并将其推广至准局部 Bartnik 质量，进而提出一种深度学习方法以数值构造具有指定 Bartnik 质量的静态度量。
A no-hair theorem for spherical black holes in scalar-tensor gravity is presented. Contrary to the existing theorems, which are proved in the Einstein conformal frame, this proof is performed entirely in the Jordan frame. The theorem is limited to spherical symmetry (instead of axisymmetry) but holds for non-constant Brans-Dicke couplings.
We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between locality,gauge,Lorentz and conformal invariance require- ments. "Improved" traceless stress tensors are then constructed;each violates one of the above criteria.However,when d=N+2,there is a duality equivalence between N-form models and massless scalars.Here we show that conformal invariance is not lost,by constructing a quasilocal gauge invariant improved stress tensor.The …
We calculate the quantum stress tensor for a massless scalar field in the 2-d self-similar spherical dust collapse model which admits a naked singularity. We find that the outgoing radiation flux diverges on the Cauchy horizon. This may have two consequences. The resultant back reaction may prevent the naked singularity from forming, thus preserving cosmic censorship through quantum effects. The divergent flux may lead to an observable signature differentiating naked singularities from black holes in astrophysical observations.
We consider a quantum field which is in a Hartle-Hawking state propagating in a general spherically symmetric black hole space-time. We make use of uniform approximations to the radial equation to calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, on the horizons of this space-time. We then specialize these results to the case of the `lukewarm' Reissner-Nordstrom-de Sitter black hole and derive some conditions on the stress tensor for the regularity of the Hartle-Hawking state.
We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum s…
A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[ϕ]$ is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no essential singularity at the origin of coordinates. The weak energy condition $ρ_ϕ> 0$ fails to be satisfied for $r\lesssim 1.3r_S$ (where $r_S$ is the Schwarzschild radius) but the strong energy condition $ρ_ϕ+3p_ϕ> 0$ is satisfied. The classical Einstein-scalar-tensor solution is regular everywhere in spacetime without a black hole event horizon. However, the viol…
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a pont-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the dou…
Stability of spherical thin-shell wormholes in scalar-tensor theories
本文研究了标量-张量理论中球形薄壳虫洞的稳定性，通过分析径向扰动和特定引力耦合模型，证明了在合适参数下可实现稳定配置。
Matter collineations of spherically Symmetric Lorentzian Manifolds are considered. These are investigated when the energy-momentum tensor is non-degenerate and also when it is degenerate. We have classified spacetimes admitting higher symmetries and spacetimes admitting SO(3) as the maximal isometry group. For the non-degenerate case, we obtain either {\it four}, {\it six}, {\it seven} or {\it ten} independent matter collineations in which {\it four} are isometries and the rest are proper. The results of the previous paper [1] are recovered as a special case. It is worth noting that we have al…
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