In order to find a noncommutative analog of Schwarzschild or Schhwarzschild-de Sitter blackhole we investigate spherically symmetric spaces generated by four noncommutative coordinates in the frame formalism. We present two solutions which however do not posess the prescribed commutative limit. Our analysis indicates that the appropriate noncommutative space might be found as a subspace of a higher-dimensional space.
We construct a spherically symmetric noncommutative space in three dimensions by foliating the space with concentric fuzzy spheres. We show how to construct a gauge theory in this space and in particular we derive the noncommutative version of a Yang-Mills-Higgs theory. We find numerical monopole solutions of the equations of motion.
Gravitational collapse of a class of spherically symmetric stars are investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with gravitational collapse.
We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.
Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate space as an infinite set of spheres, is of dimension four and necessarily time-dependent; the second can be time-dependent or static, is of dimension five and uses the truncation to foliate the internal space.
We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter $θ$ and we prove the absence of spherically symmetric solutions for small $θ$.
In this paper we reconsider the formulation for the computation of the Casimir energy in spherically symmetric background potentials. Compared to the previous analysis, the technicalities are much easier to handle and final answers are surprisingly simple.
We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor and does not disturb the geometry. We conjecture the existence of similar solutions for any nonextremal SO(3)-spherically symmetric background.
We classify the spherically symmetric solutions of the Einstein-Maxwell Dilaton field equations in D dimensions and find some exact solutions of the string theory at all orders of the string tension parameter. We also show the uniqueness of the black hole solutions of this theory in static axially symmetric spacetimes.
The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in a simple explicit example.
A model of spherically symmetric SU(2) gauge theory is considered. The self-duality equations are written and it is shown that they are compatible with the Einstein-Yang-Mills equations. It is proven that this property is true for any gauge theory with curved base space-time and having a compact Lie group as structural group.
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order $O(λ)$. Here $λ$ is the deformation parameter, plausibly the Planck scale. We find that $r,t,dr,dt$ are all forced to be central, i.e. undeformed at order $λ$, while for each value of $r,t$ we are forced to have a fuzzy sphere of radius $r$ with a unique differential calculus which is…
We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\cal K}{2π}$ connecting the black hole temperature ($T_h$) with the surface gravity ($\cal K$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed for…
Spherically symmetric static vacuum solutions have been built in $f(T)$ models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting metric coefficients we determine the analytical form of $f(T)$.
We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions.
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the sense that linear time-dependent perturbations cannot exist, and we can conclude that these solutions are stable. Possible reasons for this inconsistency are discussed.
We show that for general spherically symmetric configurations, contributions of general gravitational and mixed gauge-gravitational Chern-Simons terms to the equations of motion vanish identically in $D>3$ dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in $D>3$ static spherically symmetric case Chern-Simons terms do not contribute to the entropy either. Moreover, if one r…
In this paper we investigate wormhole and spherically symmetric solutions in 4D gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending…
We consider the $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new $\mathcal{PT}$-symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order $T$-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies th…
A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered in the same models during the last few years. As the authors point out in their abstract, new progress is supposedly possible if one takes into account crucial features of a certain partial Abelianization of the gauge transformations of spherically symmetric gravity, published by the same authors. In canonical form, these gauge transformations are given by …
In this paper we study massless fermions coupled to spherically symmetric $SU(N)$ monopoles without Yukawa couplings between the Higgs and fermion fields. The corresponding Dirac operator is not Fredholm and the associated eigenfunctions are not $L^2$-normalizable. Here we derive a formula for the dimension of the plane-wave normalizable kernel of such a Dirac operator for fermions of any representation of $SU(N)$ in the presence of any spherically symmetric monopole background. Notably, our results also apply to fermions coupled to monopoles that preserve non-abelian gauge symmetry.
We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of non-spherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time…
We show that a static spherically symmetric black hole, in a generic theory of gravity with generic matter fields, has a two-dimensional Lorentz symmetry.
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential $V(ψ^2)$ is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.
Starting from Clifton's spherical static solution for f(R)-gravity we can derive axial symmetric solutions using a methods that takes the advantage of a complex coordinate transformation. The new solutions are generated by applying the Newman-Janis algorithm previously used to transform any static spherically symmetric into axially metric in General Relativity
We analyse the noncommutative U(1) sigma model, which arises from the vacuum dynamics of the noncommutative charged tachyonic field. The sector of ``spherically symmetric'' excitations of the model is equivalent to a chain of rotators. Classical solutions for this model are found, which are static and ``spherically symmetric'' in noncommutative spatial dimensions. The limit of small noncommutativity reveals the presence of Polyakov vortices in the model. A generalisation of the model to q-deformed space, which may serve as a regularisation of the non-deformed model is also considered.
We study collapse of evaporating spherically-symmetric thin dust shells and dust balls assuming that quantum effects are encapsulated in a spherically-symmetric metric that satisfied mild regularity conditions. The evaporation may accelerate collapse, but for a generic metric the Schwarzschild radius is not crossed. Instead the shell (or the layer in the ball of dust) is always at a certain sub-Planckian distance from it.
We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.
