We develop an approach to calculate the self-force on a charged particle held in place in a curved spacetime, in which the particle is attached to a massless string and the force is measured by the string's tension. The calculation is based on the Weyl class of static and axially symmetric spacetimes, and the presence of the string is manifested by a conical singularity; the tension is proportional to the angular deficit. A remarkable and appealing aspect of this approach is that the calculation of the self-force requires no renormalization of the particle's field. This is in contract with traditional methods, which incorporate a careful and elaborate subtraction of the singular part of the field. We implement the approach in a number of different situations. First, we examine the case of an electric charge in Schwarzschild spacetime, and recover the classic Smith-Will force in addition to a purely gravitational contribution to the self-force. Second, we turn to the case of electric and magnetic dipoles in Schwarzschild spacetime, and correct expressions for the self-force previously obtained in the literature. Third, we replace the electric charge by a scalar charge, and recover Wiseman's no-force result, which we generalize to a scalar dipole. And fourth, we calculate the force exerted on extended bodies such as Schwarzschild black holes and Janis-Newman-Winicour objects, which describe scalarized naked singularities.
We apply the conical singularity method to the two dimensional version of the Schwarzschild metric to obtain the Kruskal coordinates of the black hole in a very simple and direct way. Then we make use of this metric in an approximated version and calculate the expected value of energy-momentum tensor of a massless quantum field near the horizon, resulting in regular expressions for its components.
Topological solutions in the (2+1)-dimensional Einstein theory of gravity are studied within the ADM canonical formalism. It is found that a conical singularity appears in the closed de Sitter universe solution as a topological defect in the case of the Einstein theory with a cosmological constant. Quantum effects on the conical singularity are studied using the de Broglie-Bohm interpretation. Finite quantum tunneling effects are obtained for the closed de Sitter universe, while no quantum effects are obtained for an open universe.
It has been observed that the area product of horizons for many black hole solutions is mass independent and satisfy the universality relation $A_+A_-=(8π)^2 N$, where $N$ is related to the quantized charges of the solution as angular momentum and electric charge. In this work the same analysis is done for black hole and black ring solutions with conical singularity. We find that the area product is still mass independent and regardless of the horizon topology, the conical characteristic ($κ$) of the solutions, appears in the universality relation as $κA_+A_-=(8π)^2 N$. We also check that the …
Conical singularity in spacetimes with NUT is observer-dependent
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Faculty of Physics, University of Warsaw（华沙大学物理学院）
In the context of Born-Infeld \emph{determinantal} gravity formulated in a n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional \emph{vacuum} circular symmetric solution without cosmological constant consisting in a rotating spacetime with non singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is c…
We find black hole solutions to Euclidean 2+1 gravity coupled to a relativistic particle which have a dynamical conical singularity at the horizon. These solutions mimic the tree level contribution to the partition function of gravity coupled to a quantum field theory. They are found to violate the standard area law for black hole entropy, their entropy being proportional to the total opening angle. Since each solution depends on the number of windings of the particle path around the horizon, the significance of their summation in the path integral is considered.
It is shown that the space-time with a conical singularity, which describes a thin cosmic string, is hyperbolic in the sense that a unique H^1 solution exists to the initial value problem for the wave equation with a certain class of initial data.
Differential properties of a spin 2 boson field $ψ_{μν}$ describing propagation of gravitational perturbations on a straight cosmic string's space-time background are studied by means of methods of the differential spaces theory. It is shown that this field is a smooth one in the interior of cosmic string's space-time and looses this property at the singular boundary except for cosmic string space-times with the following deficits of angle: $Δ=2π(1-1/n) $, $n=1,2,...$. A relationship between smoothness of $ψ_{μν}$ at the singularity and the gravitational conical bremsstrahlung effect is discus…
We consider black holes in an "unsuitable box": a finite cavity coupled to a thermal reservoir at a temperature different than the black hole's Hawking temperature. These black holes are described by metrics that are continuous but not differentiable due to a conical singularity at the horizon. We include them in the Euclidean path integral sum over configurations, and analyze the effect this has on black hole thermodynamics in the canonical ensemble. Black holes with a small deficit (or surplus) angle may have a smaller internal energy or larger density of states than the nearby smooth black …
The replica trick defines Renyi entropies as partition functions on conically singular geometries. We discuss their gravity duals: regular bulk solutions to the Einstein equations inducing conically singular metrics at the boundary. When the conical singularity is supported on a flat or spherical surface, these solutions are rewritings of the hyperbolic black hole. For more general shapes, these solutions are new. We construct them perturbatively in a double expansion in the distance and strength of the conical singularity, and extract the vacuum polarisation due to the cone. Recent results ab…
The temperature of an extremal Reissner - Nordstrom black hole is not restricted by the requirement of absence of a conical singularity. It is demonstrated how Kruskal-like coordinates may be constructed corresponding to any temperature whatsoever. A recently discovered stringy extremal black hole which apparently has an infinite temperature is also shown to have its temperature unrestricted by conical singularity arguments.
We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the worldsheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null-rotation/parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string…
A previously introduced method to renormalize the one-loop stress tensor and the one-loop vacuum fluctuations in a curved background by a direct local $ζ$-function approach is checked in some thermal and nonthermal cases. First the method is checked in the case of a conformally coupled massless field in the static Einstein universe where all hypotheses initially requested by the method hold true. Secondly, dropping the hypothesis of a closed manifold, the method is checked in the open static Einstein universe. Finally, the method is checked for a massless scalar field in the presence of a coni…
In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $ϕ$ with respect to the radius $r$ vanish. If the parameter $α_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2α_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The coni…
We consider the application of the Aichelburg-Sexl boost to plane and line distributions of matter. Our analysis shows that for a domain wall the space-time after the boost is flat except on a null hypersurface which is the history of a null shell. For a cosmic string we study the influence of the boost on the conical singularity and give the new value of the conical deficit.
The conical singularity in flat spacetime is mostly known as a model of the cosmic string or the wedge disclination in solids. Its another, equally important, function is to be a representative of quasiregular singularities. From all these of views it seems interesting to find out whether there exist other similar singularities. To specify what "similar" means I introduce the notion of the string-like singularity, which is, roughly speaking, an absolutely mild singularity concentrated on a curve or on a 2-surface S (depending on whether the space is three- of four-dimensional). A few such sing…
Using Einstein-Maxwell theory I investigate the gravitational field generated by an electric charge and a magnetic dipole, both held in fixed positions, but spinning with prescribed angular momenta. There is a conical singularity between them representing a strut balancing the gravitational attraction of their masses. However, there is in general another singularity, which I call a torsion singularity. I interpret this as a couple needed to maintain the spins at their prescribed values. It vanishes when the parameters obey a certain formula. A conclusion of the work is that the charge and the …
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.
Using techniques of supersymmetric gauge theories, we present the Ricci-flat metrics on non-compact Kahler manifolds whose conical singularity is repaired by the Hermitian symmetric space. These manifolds can be identified as the complex line bundles over the Hermitian symmetric spaces. Each of the metrics contains a resolution parameter which controls the size of these base manifolds, and the conical singularity appears when the parameter vanishes.
A new model for cosmic strings (i.e. conical singularities) attached to black holes is proposed. These string are obtained by a explicit construction via limiting process from the so-called Bonnor rocket. This reveals quite surprising nature of their stress-energy tensor which contains first derivative of Dirac $δ$ distribution. Starting from the Bonnor rocket we explicitly construct the Schwarzschild solution witch conical singularity and the C-metric. In the latter case we show that there is a momentum flux through the cosmic string, causing the acceleration of the black hole and the amount …
This dissertation presents a semiclassical analysis of conical topology change in $1+1$ spacetime dimensions wherein, to lowest order, the ambient spacetime is classical and fixed while the scalar field coupled to it is quantized. The vacuum expectation value of the scalar field stress-energy tensor is calculated via two different approaches. The first of these involves the explicit determination of the so called Sorkin-Johnston state on the cone and an original regularization scheme, while the latter employs the conformal vacuum and the more conventional point-splitting renormalization. It is…
When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes
Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）；The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）
A conical defect in (2+1) anti-de Sitter space is a BTZ solution with a negative mass parameter. This is a naked singularity, but a rather harmless one: it is a point particle. Naturally, the energy density and the spacetime curvature have a delta-like singularity at the apex of the conical defect, but that doesn't give rise to any unphysical situations. Since the conical solution implies the presence of a source, applying reverse enginnering, one can identify the coupling term that is required in the action to account for that source. In that way, a relation is established between the identif…
We analyze a four-parameter class of asymptotically flat magnetized solutions to the Einstein-Maxwell equations constructed by Manko et al., and show that these represent systems of two co-rotating extreme black holes with equal masses and electric charges, and opposite magnetic and NUT charges, connected by a cosmic string. We discuss several three-parameter subclasses, and determine in each case the parameter domain in which the ring singularity is absent. We find a two-parameter subclass and a one-parameter subclass where the conical singularity is also absent in the horizon co-rotating fra…
Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy. The quasilocal energy (QLE) derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the sin…
Motion of a non-relativistic particle on a cone with a magnetic flux running through the cone axis (a ``flux cone'') is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. Probability fluid (``quantum flow'') associated with a particular stationary state is studied close to the singularity, demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that near the singularity quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential d…
